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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/* $NoKeywords: $ */</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">/*</span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">//</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// Copyright (c) 1993-2012 Robert McNeel & Associates. All rights reserved.</span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// OpenNURBS, Rhinoceros, and Rhino3D are registered trademarks of Robert</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// McNeel & Associates.</span></div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// THIS SOFTWARE IS PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY.</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// ALL IMPLIED WARRANTIES OF FITNESS FOR ANY PARTICULAR PURPOSE AND OF</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// MERCHANTABILITY ARE HEREBY DISCLAIMED.</span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// </span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// For complete openNURBS copyright information see <http://www.opennurbs.org>.</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment">//</span><span class="comment"></span></div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">////////////////////////////////////////////////////////////////</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"></span>*/</div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> </div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#if !defined(ON_MATH_INC_)</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="preprocessor">#define ON_MATH_INC_</span></div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> </div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="keyword">class </span><a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>;</div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="keyword">class </span><a class="code" href="class_o_n___interval.html">ON_Interval</a>;</div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="keyword">class </span><a class="code" href="class_o_n___line.html">ON_Line</a>;</div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="keyword">class </span><a class="code" href="class_o_n___arc.html">ON_Arc</a>;</div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="keyword">class </span><a class="code" href="class_o_n___plane.html">ON_Plane</a>;</div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span> </div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment">/*</span></div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">Description:</span></div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment"> Class for carefully adding long list of numbers.</span></div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">*/</span></div><div class="line"><a name="l00030"></a><span class="lineno"><a class="line" href="class_o_n___sum.html"> 30</a></span> <span class="keyword">class </span>ON_CLASS <a class="code" href="class_o_n___sum.html">ON_Sum</a></div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span> {</div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="keyword">public</span>:</div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span> </div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="comment">/*</span></div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment"> Description:</span></div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment"> Calls ON_Sum::Begin(x)</span></div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment"> */</span></div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="keywordtype">void</span> operator=(<span class="keywordtype">double</span> x);</div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span> </div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="comment">/*</span></div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment"> Description:</span></div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment"> Calls ON_Sum::Plus(x);</span></div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment"> */</span></div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keywordtype">void</span> operator+=(<span class="keywordtype">double</span> x);</div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span> </div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="comment">/*</span></div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment"> Description:</span></div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment"> Calls ON_Sum::Plus(-x);</span></div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment"> */</span></div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keywordtype">void</span> operator-=(<span class="keywordtype">double</span> x);</div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span> </div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="comment">/*</span></div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment"> Description:</span></div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment"> Creates a sum that is ready to be used.</span></div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment"> */</span></div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <a class="code" href="class_o_n___sum.html">ON_Sum</a>();</div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span> </div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="comment">/*</span></div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment"> Description:</span></div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment"> If a sum is being used more than once, call Begin()</span></div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment"> before starting each sum.</span></div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="comment"> Parameters:</span></div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment"> starting_value - [in] Initial value of sum.</span></div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment"> */</span></div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keywordtype">void</span> Begin( <span class="keywordtype">double</span> starting_value = 0.0 );</div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span> </div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="comment">/*</span></div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment"> Description:</span></div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment"> Add x to the current sum.</span></div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment"> Parameters:</span></div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment"> x - [in] value to add to the current sum.</span></div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment"> */</span></div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="keywordtype">void</span> Plus( <span class="keywordtype">double</span> x );</div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span> </div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="comment">/*</span></div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment"> Description:</span></div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment"> Add x to the current sum.</span></div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment"> Parameters:</span></div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment"> x - [in] value to add to the current sum.</span></div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment"> dx - [in] symmetric uncertainty in x.</span></div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment"> (true value is in the range x-dx to x+dx</span></div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment"> */</span></div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keywordtype">void</span> Plus( <span class="keywordtype">double</span> x, <span class="keywordtype">double</span> dx );</div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span> </div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="comment">/*</span></div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment"> Description:</span></div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment"> Calculates the total sum. </span></div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment"> Parameters:</span></div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="comment"> error_estimate - [out] if not nullptr, the returned value of</span></div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="comment"> *error_estimate is an estimate of the error in the sum.</span></div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="comment"> Returns:</span></div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="comment"> Total of the sum.</span></div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="comment"> Remarks:</span></div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="comment"> You can get subtotals by mixing calls to Plus() and Total().</span></div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="comment"> In delicate sums, some precision may be lost in the final</span></div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="comment"> total if you call Total() to calculate subtotals.</span></div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="comment"> */</span></div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordtype">double</span> Total( <span class="keywordtype">double</span>* error_estimate = <span class="keyword">nullptr</span> );</div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span> </div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="comment">/*</span></div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment"> Returns:</span></div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="comment"> Number of summands.</span></div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="comment"> */</span></div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keywordtype">int</span> SummandCount() <span class="keyword">const</span>;</div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span> </div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="keyword">private</span>:</div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="keyword">enum</span> {</div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  sum1_max_count=256,</div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  sum2_max_count=512,</div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  sum3_max_count=1024</div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  };</div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordtype">double</span> m_sum_err;</div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keywordtype">double</span> m_pos_sum; </div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="keywordtype">double</span> m_neg_sum; </div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  </div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keywordtype">int</span> m_zero_count; <span class="comment">// number of zeros added</span></div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keywordtype">int</span> m_pos_count; <span class="comment">// number of positive numbers added</span></div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="keywordtype">int</span> m_neg_count; <span class="comment">// number of negative numbers added</span></div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  </div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keywordtype">int</span> m_pos_sum1_count;</div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="keywordtype">int</span> m_pos_sum2_count;</div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="keywordtype">int</span> m_pos_sum3_count;</div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="keywordtype">double</span> m_pos_sum1[sum1_max_count];</div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="keywordtype">double</span> m_pos_sum2[sum2_max_count];</div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keywordtype">double</span> m_pos_sum3[sum3_max_count];</div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  </div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keywordtype">int</span> m_neg_sum1_count;</div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordtype">int</span> m_neg_sum2_count;</div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="keywordtype">int</span> m_neg_sum3_count;</div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keywordtype">double</span> m_neg_sum1[sum1_max_count];</div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keywordtype">double</span> m_neg_sum2[sum2_max_count];</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keywordtype">double</span> m_neg_sum3[sum3_max_count];</div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span> </div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordtype">double</span> SortAndSum( <span class="keywordtype">int</span>, <span class="keywordtype">double</span>* );</div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span> };</div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span> </div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="comment">/*</span></div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="comment">Description:</span></div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="comment"> Abstract function with an arbitrary number of parameters</span></div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="comment"> and values. ON_Evaluator is used to pass functions to</span></div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="comment"> local solvers.</span></div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="comment">*/</span></div><div class="line"><a name="l00143"></a><span class="lineno"><a class="line" href="class_o_n___evaluator.html"> 143</a></span> <span class="keyword">class </span>ON_CLASS <a class="code" href="class_o_n___evaluator.html">ON_Evaluator</a></div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span> {</div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="keyword">public</span>:</div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span> </div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="comment">/*</span></div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span> <span class="comment"> Description:</span></div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="comment"> Construction of the class for a function that takes</span></div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span> <span class="comment"> parameter_count input functions and returns</span></div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="comment"> value_count values. If the domain is infinite, pass</span></div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="comment"> a nullptr for the domain[] and periodic[] arrays. If</span></div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="comment"> the domain is finite, pass a domain[] array with</span></div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="comment"> parameter_count increasing intervals. If one or more of</span></div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="comment"> the parameters is periodic, pass the fundamental domain</span></div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="comment"> in the domain[] array and a true in the periodic[] array.</span></div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="comment"> Parameters:</span></div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="comment"> parameter_count - [in] >= 1. Number of input parameters</span></div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="comment"> value_count - [in] >= 1. Number of output values.</span></div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="comment"> domain - [in] If not nullptr, then this is an array</span></div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span> <span class="comment"> of parameter_count increasing intervals</span></div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="comment"> that defines the domain of the function.</span></div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="comment"> periodic - [in] if not nullptr, then this is an array of </span></div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="comment"> parameter_count bools where b[i] is true if</span></div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span> <span class="comment"> the i-th parameter is periodic. Valid </span></div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span> <span class="comment"> increasing finite domains must be specificed</span></div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="comment"> when this parameter is not nullptr.</span></div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="comment"> */</span></div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <a class="code" href="class_o_n___evaluator.html">ON_Evaluator</a>( </div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="keywordtype">int</span> parameter_count,</div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <span class="keywordtype">int</span> value_count,</div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___interval.html">ON_Interval</a>* domain,</div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="keyword">const</span> <span class="keywordtype">bool</span>* periodic</div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  );</div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span> </div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <span class="keyword">virtual</span> ~<a class="code" href="class_o_n___evaluator.html">ON_Evaluator</a>();</div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  </div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="comment">/*</span></div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="comment"> Description:</span></div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="comment"> Evaluate the function that takes m_parameter_count parameters</span></div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="comment"> and returns a m_value_count dimensional point.</span></div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="comment"> Parameters:</span></div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="comment"> parameters - [in] array of m_parameter_count evaluation parameters</span></div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="comment"> values - [out] array of m_value_count function values</span></div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span> <span class="comment"> jacobian - [out] If nullptr, simply evaluate the value of the function.</span></div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span> <span class="comment"> If not nullptr, this is the jacobian of the function.</span></div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="comment"> jacobian[i][j] = j-th partial of the i-th value</span></div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span> <span class="comment"> 0 <= i < m_value_count,</span></div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span> <span class="comment"> 0 <= j < m_parameter_count</span></div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span> <span class="comment"> If not nullptr, then all the memory for the</span></div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="comment"> jacobian is allocated, you just need to fill</span></div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span> <span class="comment"> in the answers.</span></div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="comment"> Example:</span></div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span> <span class="comment"> If f(u,v) = square of the distance from a fixed point P to a </span></div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span> <span class="comment"> surface evaluated at (u,v), then</span></div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span> <span class="comment"></span></div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span> <span class="comment"> values[0] = (S-P)o(S-P)</span></div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span> <span class="comment"> jacobian[0] = ( 2*(Du o (S-P)), 2*(Dv o (S-P)) )</span></div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span> <span class="comment"></span></div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="comment"> where S, Du, Dv = surface point and first partials evaluated</span></div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span> <span class="comment"> at u=parameters[0], v = parameters[1].</span></div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span> <span class="comment"></span></div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span> <span class="comment"> If the function takes 3 parameters, say (x,y,z), and returns</span></div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span> <span class="comment"> two values, say f(x,y,z) and g(z,y,z), then</span></div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span> <span class="comment"></span></div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="comment"> values[0] = f(x,y,z)</span></div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span> <span class="comment"> values[1] = g(x,y,z)</span></div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span> <span class="comment"></span></div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="comment"> jacobian[0] = (DfDx, DfDy, DfDz)</span></div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span> <span class="comment"> jacobian[1] = (DgDx, DgDy, DgDz)</span></div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span> <span class="comment"></span></div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span> <span class="comment"> where dfx denotes the first partial of f with respect to x.</span></div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span> <span class="comment"></span></div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span> <span class="comment"> Returns:</span></div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="comment"> 0 = unable to evaluate</span></div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="comment"> 1 = successful evaluation</span></div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="comment"> 2 = found answer, terminate search</span></div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="comment"> */</span></div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keyword">virtual</span> <span class="keywordtype">int</span> Evaluate(</div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* parameters,</div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="keywordtype">double</span>* values,</div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="keywordtype">double</span>** jacobian</div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  ) = 0;</div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span> </div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <span class="comment">/*</span></div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span> <span class="comment"> Description:</span></div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span> <span class="comment"> OPTIONAL ability to evaluate the hessian in the case when </span></div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span> <span class="comment"> m_value_count is one. If your function has more that</span></div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span> <span class="comment"> one value or it is not feasable to evaluate the hessian,</span></div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span> <span class="comment"> then do not override this function. The default implementation</span></div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span> <span class="comment"> returns -1.</span></div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span> <span class="comment"> Parameters:</span></div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span> <span class="comment"> parameters - [in] array of m_parameter_count evaluation parameters</span></div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span> <span class="comment"> value - [out] value of the function (one double)</span></div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span> <span class="comment"> gradient - [out] The gradient of the function. This is a vector</span></div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span> <span class="comment"> of length m_parameter_count; gradient[i] is</span></div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span> <span class="comment"> the first partial of the function with respect to</span></div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span> <span class="comment"> the i-th parameter.</span></div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span> <span class="comment"> hessian - [out] The hessian of the function. This is an</span></div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="comment"> m_parameter_count x m_parameter_count </span></div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span> <span class="comment"> symmetric matrix: hessian[i][j] is the</span></div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span> <span class="comment"> second partial of the function with respect</span></div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span> <span class="comment"> to the i-th and j-th parameters. The evaluator</span></div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span> <span class="comment"> is responsible for filling in both the upper</span></div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span> <span class="comment"> and lower triangles. Since the matrix is</span></div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span> <span class="comment"> symmetrix, you should do something like evaluate</span></div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span> <span class="comment"> the upper triangle and copy the values to the</span></div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span> <span class="comment"> lower tiangle.</span></div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span> <span class="comment"> Returns:</span></div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span> <span class="comment"> -1 = Hessian evaluation not available.</span></div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span> <span class="comment"> 0 = unable to evaluate</span></div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span> <span class="comment"> 1 = successful evaluation</span></div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span> <span class="comment"> 2 = found answer, terminate search</span></div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span> <span class="comment"> */</span></div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  <span class="keyword">virtual</span> <span class="keywordtype">int</span> EvaluateHessian(</div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* parameters,</div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="keywordtype">double</span>* value,</div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="keywordtype">double</span>* gradient,</div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="keywordtype">double</span>** hessian</div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  );</div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  </div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <span class="comment">// Number of the function's input parameters. This number</span></div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="comment">// is >= 1 and is specified in the constructor.</span></div><div class="line"><a name="l00264"></a><span class="lineno"><a class="line" href="class_o_n___evaluator.html#a9d8118ded2762c9e5f38be107e2a5d2d"> 264</a></span>  <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code" href="class_o_n___evaluator.html#a9d8118ded2762c9e5f38be107e2a5d2d">m_parameter_count</a>;</div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span> </div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="comment">// Number of the function's output values. This number</span></div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="comment">// is >= 1 and is specified in the constructor.</span></div><div class="line"><a name="l00268"></a><span class="lineno"><a class="line" href="class_o_n___evaluator.html#a61abf86c2c652d0ab38548f6eba4d482"> 268</a></span>  <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code" href="class_o_n___evaluator.html#a61abf86c2c652d0ab38548f6eba4d482">m_value_count</a>;</div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span> </div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  <span class="comment">/*</span></div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span> <span class="comment"> Description:</span></div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span> <span class="comment"> Functions can have finite or infinite domains. Finite domains</span></div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span> <span class="comment"> are specified by passing the domain[] array to the constructor</span></div><div class="line"><a name="l00274"></a><span class="lineno"> 274</span> <span class="comment"> or filling in the m_domain[] member variable. If</span></div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span> <span class="comment"> m_domain.Count() == m_parameter_count > 0, then the function</span></div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span> <span class="comment"> has finite domains.</span></div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span> <span class="comment"> Returns:</span></div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span> <span class="comment"> True if the domain of the function is finite.</span></div><div class="line"><a name="l00279"></a><span class="lineno"> 279</span> <span class="comment"> */</span></div><div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <span class="keywordtype">bool</span> FiniteDomain() <span class="keyword">const</span>;</div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span> </div><div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="comment">/*</span></div><div class="line"><a name="l00283"></a><span class="lineno"> 283</span> <span class="comment"> Description:</span></div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span> <span class="comment"> If a function has a periodic parameter, then the m_domain</span></div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span> <span class="comment"> interval for that parameter is the fundamental domain and</span></div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span> <span class="comment"> the m_bPeriodicParameter bool for that parameter is true.</span></div><div class="line"><a name="l00287"></a><span class="lineno"> 287</span> <span class="comment"> A parameter is periodic if, and only if, </span></div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span> <span class="comment"> m_domain.Count() == m_parameter_count, and </span></div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span> <span class="comment"> m_bPeriodicParameter.Count() == m_parameter_count, and</span></div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span> <span class="comment"> m_bPeriodicParameter[parameter_index] is true.</span></div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span> <span class="comment"> Returns:</span></div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span> <span class="comment"> True if the function parameter is periodic.</span></div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span> <span class="comment"> */</span></div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <span class="keywordtype">bool</span> Periodic(</div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <span class="keywordtype">int</span> parameter_index</div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  ) <span class="keyword">const</span>;</div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span> </div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <span class="comment">/*</span></div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span> <span class="comment"> Description:</span></div><div class="line"><a name="l00300"></a><span class="lineno"> 300</span> <span class="comment"> If a function has a periodic parameter, then the m_domain</span></div><div class="line"><a name="l00301"></a><span class="lineno"> 301</span> <span class="comment"> interval for that parameter is the fundamental domain and</span></div><div class="line"><a name="l00302"></a><span class="lineno"> 302</span> <span class="comment"> the m_bPeriodicParameter bool for that parameter is true.</span></div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span> <span class="comment"> A parameter is periodic if, and only if, </span></div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span> <span class="comment"> m_domain.Count() == m_parameter_count, and </span></div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span> <span class="comment"> m_bPeriodicParameter.Count() == m_parameter_count, and</span></div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span> <span class="comment"> m_bPeriodicParameter[parameter_index] is true.</span></div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span> <span class="comment"> Returns:</span></div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span> <span class="comment"> The domain of the parameter. If the domain is infinite,</span></div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span> <span class="comment"> the (-1.0e300, +1.0e300) is returned.</span></div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span> <span class="comment"> */</span></div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  <a class="code" href="class_o_n___interval.html">ON_Interval</a> Domain(</div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="keywordtype">int</span> parameter_index</div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  ) <span class="keyword">const</span>;</div><div class="line"><a name="l00314"></a><span class="lineno"> 314</span> </div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span> </div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  <span class="comment">// If the function has a finite domain or periodic</span></div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <span class="comment">// parameters, then m_domain[] is an array of </span></div><div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  <span class="comment">// m_parameter_count finite increasing intervals.</span></div><div class="line"><a name="l00319"></a><span class="lineno"><a class="line" href="class_o_n___evaluator.html#a8e7e3d681c06c498b26529affd1d22f7"> 319</a></span>  <a class="code" href="class_o_n___simple_array.html">ON_SimpleArray<ON_Interval></a> <a class="code" href="class_o_n___evaluator.html#a8e7e3d681c06c498b26529affd1d22f7">m_domain</a>;</div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span> </div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <span class="comment">// If the function has periodic parameters, then </span></div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <span class="comment">// m_bPeriodicParameter[] is an array of m_parameter_count</span></div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  <span class="comment">// bools. If m_bPeriodicParameter[i] is true, then</span></div><div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  <span class="comment">// the i-th parameter is periodic and m_domain[i] is </span></div><div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  <span class="comment">// the fundamental domain for that parameter.</span></div><div class="line"><a name="l00326"></a><span class="lineno"><a class="line" href="class_o_n___evaluator.html#a39ab8c1ebc601902f5a2ff8a0d21c6e4"> 326</a></span>  <a class="code" href="class_o_n___simple_array.html">ON_SimpleArray<bool></a> <a class="code" href="class_o_n___evaluator.html#a39ab8c1ebc601902f5a2ff8a0d21c6e4">m_bPeriodicParameter</a>;</div><div class="line"><a name="l00327"></a><span class="lineno"> 327</span> </div><div class="line"><a name="l00328"></a><span class="lineno"> 328</span> <span class="keyword">private</span>:</div><div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <a class="code" href="class_o_n___evaluator.html">ON_Evaluator</a>(); <span class="comment">// prohibit default constructor</span></div><div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  <a class="code" href="class_o_n___evaluator.html">ON_Evaluator</a>& operator=(<span class="keyword">const</span> <a class="code" href="class_o_n___evaluator.html">ON_Evaluator</a>&); <span class="comment">// prohibit operator= (can't copy const members)</span></div><div class="line"><a name="l00331"></a><span class="lineno"> 331</span> };</div><div class="line"><a name="l00332"></a><span class="lineno"> 332</span> </div><div class="line"><a name="l00333"></a><span class="lineno"> 333</span> <span class="comment">/*</span></div><div class="line"><a name="l00334"></a><span class="lineno"> 334</span> <span class="comment">Description:</span></div><div class="line"><a name="l00335"></a><span class="lineno"> 335</span> <span class="comment"> Test a double to make sure it is a valid number.</span></div><div class="line"><a name="l00336"></a><span class="lineno"> 336</span> <span class="comment">Returns:</span></div><div class="line"><a name="l00337"></a><span class="lineno"> 337</span> <span class="comment"> True if x != ON_UNSET_VALUE and _finite(x) is true.</span></div><div class="line"><a name="l00338"></a><span class="lineno"> 338</span> <span class="comment">*/</span></div><div class="line"><a name="l00339"></a><span class="lineno"> 339</span> ON_DECL</div><div class="line"><a name="l00340"></a><span class="lineno"> 340</span> <span class="keywordtype">bool</span> ON_IsValid( <span class="keywordtype">double</span> x );</div><div class="line"><a name="l00341"></a><span class="lineno"> 341</span> </div><div class="line"><a name="l00342"></a><span class="lineno"> 342</span> <span class="comment">/*</span></div><div class="line"><a name="l00343"></a><span class="lineno"> 343</span> <span class="comment">Returns:</span></div><div class="line"><a name="l00344"></a><span class="lineno"> 344</span> <span class="comment"> -1: a < b or a is not a nan and b is a nan</span></div><div class="line"><a name="l00345"></a><span class="lineno"> 345</span> <span class="comment"> +1: a > b or a is a nan and b is a not nan</span></div><div class="line"><a name="l00346"></a><span class="lineno"> 346</span> <span class="comment"> 0: a == b or both a and b are nans</span></div><div class="line"><a name="l00347"></a><span class="lineno"> 347</span> <span class="comment">*/</span></div><div class="line"><a name="l00348"></a><span class="lineno"> 348</span> ON_DECL</div><div class="line"><a name="l00349"></a><span class="lineno"> 349</span> <span class="keywordtype">int</span> ON_CompareDouble( </div><div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  <span class="keywordtype">double</span> a, </div><div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  <span class="keywordtype">double</span> b </div><div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  );</div><div class="line"><a name="l00353"></a><span class="lineno"> 353</span> </div><div class="line"><a name="l00354"></a><span class="lineno"> 354</span> ON_DECL</div><div class="line"><a name="l00355"></a><span class="lineno"> 355</span> <span class="keywordtype">int</span> ON_CompareDoubleArray( </div><div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  <span class="keywordtype">size_t</span> count,</div><div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* a, </div><div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* b</div><div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  );</div><div class="line"><a name="l00360"></a><span class="lineno"> 360</span> </div><div class="line"><a name="l00361"></a><span class="lineno"> 361</span> <span class="comment">/*</span></div><div class="line"><a name="l00362"></a><span class="lineno"> 362</span> <span class="comment">Returns:</span></div><div class="line"><a name="l00363"></a><span class="lineno"> 363</span> <span class="comment"> -1: a < b or a is not a nan and b is a nan</span></div><div class="line"><a name="l00364"></a><span class="lineno"> 364</span> <span class="comment"> +1: a > b or a is a nan and b is a not nan</span></div><div class="line"><a name="l00365"></a><span class="lineno"> 365</span> <span class="comment"> 0: a == b or both a and b are nans</span></div><div class="line"><a name="l00366"></a><span class="lineno"> 366</span> <span class="comment">*/</span></div><div class="line"><a name="l00367"></a><span class="lineno"> 367</span> ON_DECL</div><div class="line"><a name="l00368"></a><span class="lineno"> 368</span> <span class="keywordtype">int</span> ON_CompareFloat(</div><div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  <span class="keywordtype">float</span> a,</div><div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  <span class="keywordtype">float</span> b</div><div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  );</div><div class="line"><a name="l00372"></a><span class="lineno"> 372</span> </div><div class="line"><a name="l00373"></a><span class="lineno"> 373</span> ON_DECL</div><div class="line"><a name="l00374"></a><span class="lineno"> 374</span> <span class="keywordtype">bool</span> ON_IsValidFloat( <span class="keywordtype">float</span> x );</div><div class="line"><a name="l00375"></a><span class="lineno"> 375</span> </div><div class="line"><a name="l00376"></a><span class="lineno"> 376</span> ON_DECL</div><div class="line"><a name="l00377"></a><span class="lineno"> 377</span> <span class="keywordtype">bool</span> ON_IsNaNd(<span class="keywordtype">double</span> x);</div><div class="line"><a name="l00378"></a><span class="lineno"> 378</span> </div><div class="line"><a name="l00379"></a><span class="lineno"> 379</span> ON_DECL</div><div class="line"><a name="l00380"></a><span class="lineno"> 380</span> <span class="keywordtype">bool</span> ON_IsQNaNd(<span class="keywordtype">double</span> x);</div><div class="line"><a name="l00381"></a><span class="lineno"> 381</span> </div><div class="line"><a name="l00382"></a><span class="lineno"> 382</span> ON_DECL</div><div class="line"><a name="l00383"></a><span class="lineno"> 383</span> <span class="keywordtype">bool</span> ON_IsSNaNd(<span class="keywordtype">double</span> x);</div><div class="line"><a name="l00384"></a><span class="lineno"> 384</span> </div><div class="line"><a name="l00385"></a><span class="lineno"> 385</span> ON_DECL</div><div class="line"><a name="l00386"></a><span class="lineno"> 386</span> <span class="keywordtype">bool</span> ON_IsNaNf(<span class="keywordtype">float</span> x);</div><div class="line"><a name="l00387"></a><span class="lineno"> 387</span> </div><div class="line"><a name="l00388"></a><span class="lineno"> 388</span> ON_DECL</div><div class="line"><a name="l00389"></a><span class="lineno"> 389</span> <span class="keywordtype">bool</span> ON_IsQNaNf(<span class="keywordtype">float</span> x);</div><div class="line"><a name="l00390"></a><span class="lineno"> 390</span> </div><div class="line"><a name="l00391"></a><span class="lineno"> 391</span> ON_DECL</div><div class="line"><a name="l00392"></a><span class="lineno"> 392</span> <span class="keywordtype">bool</span> ON_IsSNaNf(<span class="keywordtype">float</span> x);</div><div class="line"><a name="l00393"></a><span class="lineno"> 393</span> </div><div class="line"><a name="l00394"></a><span class="lineno"> 394</span> <span class="comment">/*</span></div><div class="line"><a name="l00395"></a><span class="lineno"> 395</span> <span class="comment">class ON_CLASS ON_TimeLimit</span></div><div class="line"><a name="l00396"></a><span class="lineno"> 396</span> <span class="comment">{</span></div><div class="line"><a name="l00397"></a><span class="lineno"> 397</span> <span class="comment"> ON_TimeLimit();</span></div><div class="line"><a name="l00398"></a><span class="lineno"> 398</span> <span class="comment"> ON_TimeLimit(ON__UINT64 time_limit_seconds);</span></div><div class="line"><a name="l00399"></a><span class="lineno"> 399</span> <span class="comment"> void SetTimeLimit(ON__UINT64 time_limit_seconds);</span></div><div class="line"><a name="l00400"></a><span class="lineno"> 400</span> <span class="comment"> bool Continue() const;</span></div><div class="line"><a name="l00401"></a><span class="lineno"> 401</span> <span class="comment"> bool IsSet() const;</span></div><div class="line"><a name="l00402"></a><span class="lineno"> 402</span> <span class="comment">private:</span></div><div class="line"><a name="l00403"></a><span class="lineno"> 403</span> <span class="comment"> ON__UINT64 m_time_limit[2];</span></div><div class="line"><a name="l00404"></a><span class="lineno"> 404</span> <span class="comment">};</span></div><div class="line"><a name="l00405"></a><span class="lineno"> 405</span> <span class="comment">*/</span></div><div class="line"><a name="l00406"></a><span class="lineno"> 406</span> </div><div class="line"><a name="l00407"></a><span class="lineno"> 407</span> <span class="comment">// The ON_IS_FINITE and ON_IS_VALID defines are much faster</span></div><div class="line"><a name="l00408"></a><span class="lineno"> 408</span> <span class="comment">// than calling ON_IsValid(), but need to be used when</span></div><div class="line"><a name="l00409"></a><span class="lineno"> 409</span> <span class="comment">// the macro expansion works.</span></div><div class="line"><a name="l00410"></a><span class="lineno"> 410</span> </div><div class="line"><a name="l00411"></a><span class="lineno"> 411</span> <span class="preprocessor">#if defined(ON_LITTLE_ENDIAN)</span></div><div class="line"><a name="l00412"></a><span class="lineno"> 412</span> </div><div class="line"><a name="l00413"></a><span class="lineno"> 413</span> <span class="comment">// works on little endian CPUs with IEEE doubles</span></div><div class="line"><a name="l00414"></a><span class="lineno"> 414</span> <span class="preprocessor">#define ON_IS_FINITE(x) (0x7FF0 != (*((unsigned short*)(&x) + 3) & 0x7FF0))</span></div><div class="line"><a name="l00415"></a><span class="lineno"> 415</span> <span class="preprocessor">#define ON_IS_INFINITE(x) (0x7FF0 == (*((unsigned short*)(&x) + 3) & 0x7FF0))</span></div><div class="line"><a name="l00416"></a><span class="lineno"> 416</span> </div><div class="line"><a name="l00417"></a><span class="lineno"> 417</span> <span class="preprocessor">#elif defined(ON_BIG_ENDIAN)</span></div><div class="line"><a name="l00418"></a><span class="lineno"> 418</span> </div><div class="line"><a name="l00419"></a><span class="lineno"> 419</span> <span class="comment">// works on big endian CPUs with IEEE doubles</span></div><div class="line"><a name="l00420"></a><span class="lineno"> 420</span> <span class="preprocessor">#define ON_IS_FINITE(x) (0x7FF0 != (*((unsigned short*)(&x)) & 0x7FF0))</span></div><div class="line"><a name="l00421"></a><span class="lineno"> 421</span> <span class="preprocessor">#define ON_IS_INFINITE(x) (0x7FF0 == (*((unsigned short*)(&x)) & 0x7FF0))</span></div><div class="line"><a name="l00422"></a><span class="lineno"> 422</span> </div><div class="line"><a name="l00423"></a><span class="lineno"> 423</span> <span class="preprocessor">#else</span></div><div class="line"><a name="l00424"></a><span class="lineno"> 424</span> </div><div class="line"><a name="l00425"></a><span class="lineno"> 425</span> <span class="comment">// Returns true if x is a finite double. Specifically,</span></div><div class="line"><a name="l00426"></a><span class="lineno"> 426</span> <span class="comment">// _finite returns a nonzero value (true) if its argument x</span></div><div class="line"><a name="l00427"></a><span class="lineno"> 427</span> <span class="comment">// is not infinite, that is, if -INF < x < +INF. </span></div><div class="line"><a name="l00428"></a><span class="lineno"> 428</span> <span class="comment">// It returns 0 (false) if the argument is infinite or a NaN.</span></div><div class="line"><a name="l00429"></a><span class="lineno"> 429</span> <span class="comment">//</span></div><div class="line"><a name="l00430"></a><span class="lineno"> 430</span> <span class="comment">// If you are trying to compile opennurbs on a platform</span></div><div class="line"><a name="l00431"></a><span class="lineno"> 431</span> <span class="comment">// that does not support finite(), then see if you can</span></div><div class="line"><a name="l00432"></a><span class="lineno"> 432</span> <span class="comment">// use _fpclass(), fpclass(), _isnan(), or isnan(). If</span></div><div class="line"><a name="l00433"></a><span class="lineno"> 433</span> <span class="comment">// you can't find anything, then just set this</span></div><div class="line"><a name="l00434"></a><span class="lineno"> 434</span> <span class="comment">// function to return true.</span></div><div class="line"><a name="l00435"></a><span class="lineno"> 435</span> </div><div class="line"><a name="l00436"></a><span class="lineno"> 436</span> <span class="preprocessor">#if defined(_GNU_SOURCE)</span></div><div class="line"><a name="l00437"></a><span class="lineno"> 437</span> <span class="comment">// if you are using an older version of gcc, use finite()</span></div><div class="line"><a name="l00438"></a><span class="lineno"> 438</span> <span class="comment">//#define ON_IS_FINITE(x) (finite(x)?true:false)</span></div><div class="line"><a name="l00439"></a><span class="lineno"> 439</span> <span class="preprocessor">#define ON_IS_FINITE(x) (isfinite(x)?true:false)</span></div><div class="line"><a name="l00440"></a><span class="lineno"> 440</span> <span class="preprocessor">#else</span></div><div class="line"><a name="l00441"></a><span class="lineno"> 441</span> <span class="preprocessor">#define ON_IS_FINITE(x) (_finite(x)?true:false)</span></div><div class="line"><a name="l00442"></a><span class="lineno"> 442</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00443"></a><span class="lineno"> 443</span> </div><div class="line"><a name="l00444"></a><span class="lineno"> 444</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00445"></a><span class="lineno"> 445</span> </div><div class="line"><a name="l00446"></a><span class="lineno"> 446</span> <span class="preprocessor">#define ON_IS_FINITE_FLOAT(x) ((x) <= 3.402823466e+38F && (x) >= -3.402823466e+38F)</span></div><div class="line"><a name="l00447"></a><span class="lineno"> 447</span> <span class="preprocessor">#define ON_IS_INFINITE_FLOAT(x) ((x) > 3.402823466e+38F || (x) < -3.402823466e+38F)</span></div><div class="line"><a name="l00448"></a><span class="lineno"> 448</span> </div><div class="line"><a name="l00449"></a><span class="lineno"> 449</span> <span class="preprocessor">#define ON_IS_VALID(x) ((x) != ON_UNSET_VALUE && (x) != ON_UNSET_POSITIVE_VALUE && ON_IS_FINITE(x))</span></div><div class="line"><a name="l00450"></a><span class="lineno"> 450</span> <span class="preprocessor">#define ON_IS_VALID_FLOAT(x) ((x) != ON_UNSET_FLOAT && (x) != ON_UNSET_POSITIVE_FLOAT && ON_IS_FINITE_FLOAT(x))</span></div><div class="line"><a name="l00451"></a><span class="lineno"> 451</span> <span class="preprocessor">#define ON_IS_UNSET_DOUBLE(x) (ON_UNSET_VALUE == (x) || ON_UNSET_POSITIVE_VALUE == (x))</span></div><div class="line"><a name="l00452"></a><span class="lineno"> 452</span> <span class="preprocessor">#define ON_IS_UNSET_FLOAT(x) (ON_UNSET_FLOAT == (x) || ON_UNSET_POSITIVE_FLOAT == (x))</span></div><div class="line"><a name="l00453"></a><span class="lineno"> 453</span> <span class="preprocessor">#define ON_IS_NAN(x) (!((x)==(x))</span></div><div class="line"><a name="l00454"></a><span class="lineno"> 454</span> </div><div class="line"><a name="l00455"></a><span class="lineno"> 455</span> ON_DECL</div><div class="line"><a name="l00456"></a><span class="lineno"> 456</span> <span class="keywordtype">float</span> ON_ArrayDotProduct( <span class="comment">// returns AoB</span></div><div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  <span class="keywordtype">int</span>, <span class="comment">// size of arrays (can be zero)</span></div><div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  <span class="keyword">const</span> <span class="keywordtype">float</span>*, <span class="comment">// A[]</span></div><div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  <span class="keyword">const</span> <span class="keywordtype">float</span>* <span class="comment">// B[]</span></div><div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  );</div><div class="line"><a name="l00461"></a><span class="lineno"> 461</span> </div><div class="line"><a name="l00462"></a><span class="lineno"> 462</span> ON_DECL</div><div class="line"><a name="l00463"></a><span class="lineno"> 463</span> <span class="keywordtype">void</span> ON_ArrayScale( </div><div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  <span class="keywordtype">int</span>, <span class="comment">// size of arrays (can be zero)</span></div><div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  <span class="keywordtype">float</span>, <span class="comment">// a</span></div><div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  <span class="keyword">const</span> <span class="keywordtype">float</span>*, <span class="comment">// A[]</span></div><div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  <span class="keywordtype">float</span>* <span class="comment">// returns a*A[]</span></div><div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  );</div><div class="line"><a name="l00469"></a><span class="lineno"> 469</span> </div><div class="line"><a name="l00470"></a><span class="lineno"> 470</span> ON_DECL</div><div class="line"><a name="l00471"></a><span class="lineno"> 471</span> <span class="keywordtype">void</span> ON_Array_aA_plus_B( </div><div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  <span class="keywordtype">int</span>, <span class="comment">// size of arrays (can be zero)</span></div><div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  <span class="keywordtype">float</span>, <span class="comment">// a</span></div><div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  <span class="keyword">const</span> <span class="keywordtype">float</span>*, <span class="comment">// A[]</span></div><div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  <span class="keyword">const</span> <span class="keywordtype">float</span>*, <span class="comment">// B[]</span></div><div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  <span class="keywordtype">float</span>* <span class="comment">// returns a*A[] + B[]</span></div><div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  );</div><div class="line"><a name="l00478"></a><span class="lineno"> 478</span> </div><div class="line"><a name="l00479"></a><span class="lineno"> 479</span> ON_DECL</div><div class="line"><a name="l00480"></a><span class="lineno"> 480</span> <span class="keywordtype">double</span> ON_ArrayDotProduct( <span class="comment">// returns AoB</span></div><div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  <span class="keywordtype">int</span>, <span class="comment">// size of arrays (can be zero)</span></div><div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// A[]</span></div><div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* <span class="comment">// B[]</span></div><div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  );</div><div class="line"><a name="l00485"></a><span class="lineno"> 485</span> </div><div class="line"><a name="l00486"></a><span class="lineno"> 486</span> ON_DECL</div><div class="line"><a name="l00487"></a><span class="lineno"> 487</span> <span class="keywordtype">double</span> ON_ArrayDotDifference( <span class="comment">// returns A o ( B - C )</span></div><div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  <span class="keywordtype">int</span>, <span class="comment">// size of arrays (can be zero)</span></div><div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// A[]</span></div><div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// B[]</span></div><div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* <span class="comment">// C[]</span></div><div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  );</div><div class="line"><a name="l00493"></a><span class="lineno"> 493</span> </div><div class="line"><a name="l00494"></a><span class="lineno"> 494</span> ON_DECL</div><div class="line"><a name="l00495"></a><span class="lineno"> 495</span> <span class="keywordtype">double</span> ON_ArrayMagnitude( <span class="comment">// returns sqrt(AoA)</span></div><div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  <span class="keywordtype">int</span>, <span class="comment">// size of arrays (can be zero)</span></div><div class="line"><a name="l00497"></a><span class="lineno"> 497</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* <span class="comment">// A[]</span></div><div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  );</div><div class="line"><a name="l00499"></a><span class="lineno"> 499</span> </div><div class="line"><a name="l00500"></a><span class="lineno"> 500</span> ON_DECL</div><div class="line"><a name="l00501"></a><span class="lineno"> 501</span> <span class="keywordtype">double</span> ON_ArrayMagnitudeSquared( <span class="comment">// returns AoA</span></div><div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  <span class="keywordtype">int</span>, <span class="comment">// size of arrays (can be zero)</span></div><div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* <span class="comment">// A[]</span></div><div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  );</div><div class="line"><a name="l00505"></a><span class="lineno"> 505</span> </div><div class="line"><a name="l00506"></a><span class="lineno"> 506</span> ON_DECL</div><div class="line"><a name="l00507"></a><span class="lineno"> 507</span> <span class="keywordtype">double</span> ON_ArrayDistance( <span class="comment">// returns sqrt((A-B)o(A-B))</span></div><div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  <span class="keywordtype">int</span>, <span class="comment">// size of arrays (can be zero)</span></div><div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// A[]</span></div><div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* <span class="comment">// B[]</span></div><div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  );</div><div class="line"><a name="l00512"></a><span class="lineno"> 512</span> </div><div class="line"><a name="l00513"></a><span class="lineno"> 513</span> ON_DECL</div><div class="line"><a name="l00514"></a><span class="lineno"> 514</span> <span class="keywordtype">double</span> ON_ArrayDistanceSquared( <span class="comment">// returns (A-B)o(A-B)</span></div><div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  <span class="keywordtype">int</span>, <span class="comment">// size of arrays (can be zero)</span></div><div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// A[]</span></div><div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* <span class="comment">// B[]</span></div><div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  );</div><div class="line"><a name="l00519"></a><span class="lineno"> 519</span> </div><div class="line"><a name="l00520"></a><span class="lineno"> 520</span> ON_DECL</div><div class="line"><a name="l00521"></a><span class="lineno"> 521</span> <span class="keywordtype">void</span> ON_ArrayScale( </div><div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  <span class="keywordtype">int</span>, <span class="comment">// size of arrays (can be zero)</span></div><div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  <span class="keywordtype">double</span>, <span class="comment">// a</span></div><div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// A[]</span></div><div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  <span class="keywordtype">double</span>* <span class="comment">// returns a*A[]</span></div><div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  );</div><div class="line"><a name="l00527"></a><span class="lineno"> 527</span> </div><div class="line"><a name="l00528"></a><span class="lineno"> 528</span> ON_DECL</div><div class="line"><a name="l00529"></a><span class="lineno"> 529</span> <span class="keywordtype">void</span> ON_Array_aA_plus_B( </div><div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  <span class="keywordtype">int</span>, <span class="comment">// size of arrays (can be zero)</span></div><div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  <span class="keywordtype">double</span>, <span class="comment">// a</span></div><div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// A[]</span></div><div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// B[]</span></div><div class="line"><a name="l00534"></a><span class="lineno"> 534</span>  <span class="keywordtype">double</span>* <span class="comment">// returns a*A[] + B[]</span></div><div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  );</div><div class="line"><a name="l00536"></a><span class="lineno"> 536</span> </div><div class="line"><a name="l00537"></a><span class="lineno"> 537</span> ON_DECL</div><div class="line"><a name="l00538"></a><span class="lineno"> 538</span> <span class="keywordtype">int</span> ON_SearchMonotoneArray( <span class="comment">// find a value in an increasing array</span></div><div class="line"><a name="l00539"></a><span class="lineno"> 539</span>  <span class="comment">// returns -1: t < array[0]</span></div><div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  <span class="comment">// i: array[i] <= t < array[i+1] ( 0 <= i < length-1 )</span></div><div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  <span class="comment">// length-1: t == array[length-1]</span></div><div class="line"><a name="l00542"></a><span class="lineno"> 542</span>  <span class="comment">// length: t >= array[length-1]</span></div><div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// array[]</span></div><div class="line"><a name="l00544"></a><span class="lineno"> 544</span>  <span class="keywordtype">int</span>, <span class="comment">// length of array</span></div><div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  <span class="keywordtype">double</span> <span class="comment">// t = value to search for</span></div><div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  );</div><div class="line"><a name="l00547"></a><span class="lineno"> 547</span> </div><div class="line"><a name="l00548"></a><span class="lineno"> 548</span> </div><div class="line"><a name="l00549"></a><span class="lineno"> 549</span> <span class="comment">/* </span></div><div class="line"><a name="l00550"></a><span class="lineno"> 550</span> <span class="comment">Description:</span></div><div class="line"><a name="l00551"></a><span class="lineno"> 551</span> <span class="comment"> Compute a binomial coefficient.</span></div><div class="line"><a name="l00552"></a><span class="lineno"> 552</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l00553"></a><span class="lineno"> 553</span> <span class="comment"> i - [in]</span></div><div class="line"><a name="l00554"></a><span class="lineno"> 554</span> <span class="comment"> j - [in]</span></div><div class="line"><a name="l00555"></a><span class="lineno"> 555</span> <span class="comment">Returns:</span></div><div class="line"><a name="l00556"></a><span class="lineno"> 556</span> <span class="comment"> (i+j)!/(i!j!), if 0 <= i and 0 <= j, and 0 otherwise.</span></div><div class="line"><a name="l00557"></a><span class="lineno"> 557</span> <span class="comment">See Also:</span></div><div class="line"><a name="l00558"></a><span class="lineno"> 558</span> <span class="comment"> ON_TrinomialCoefficient()</span></div><div class="line"><a name="l00559"></a><span class="lineno"> 559</span> <span class="comment">Remarks:</span></div><div class="line"><a name="l00560"></a><span class="lineno"> 560</span> <span class="comment"> If (i+j) <= 52, this function is fast and returns the exact</span></div><div class="line"><a name="l00561"></a><span class="lineno"> 561</span> <span class="comment"> value of the binomial coefficient. </span></div><div class="line"><a name="l00562"></a><span class="lineno"> 562</span> <span class="comment"></span></div><div class="line"><a name="l00563"></a><span class="lineno"> 563</span> <span class="comment"> For (i+j) > 52, the coefficient is computed recursively using</span></div><div class="line"><a name="l00564"></a><span class="lineno"> 564</span> <span class="comment"> the formula bc(i,j) = bc(i-1,j) + bc(i,j-1).</span></div><div class="line"><a name="l00565"></a><span class="lineno"> 565</span> <span class="comment"> For (i+j) much larger than 60, this is inefficient.</span></div><div class="line"><a name="l00566"></a><span class="lineno"> 566</span> <span class="comment"> If you need binomial coefficients for large i and j, then you</span></div><div class="line"><a name="l00567"></a><span class="lineno"> 567</span> <span class="comment"> should probably be using something like Stirling's Formula. </span></div><div class="line"><a name="l00568"></a><span class="lineno"> 568</span> <span class="comment"> (Look up "Stirling" or "Gamma function" in a calculus book.)</span></div><div class="line"><a name="l00569"></a><span class="lineno"> 569</span> <span class="comment">*/</span></div><div class="line"><a name="l00570"></a><span class="lineno"> 570</span> ON_DECL</div><div class="line"><a name="l00571"></a><span class="lineno"> 571</span> <span class="keywordtype">double</span> ON_BinomialCoefficient( </div><div class="line"><a name="l00572"></a><span class="lineno"> 572</span>  <span class="keywordtype">int</span> i,</div><div class="line"><a name="l00573"></a><span class="lineno"> 573</span>  <span class="keywordtype">int</span> j</div><div class="line"><a name="l00574"></a><span class="lineno"> 574</span>  );</div><div class="line"><a name="l00575"></a><span class="lineno"> 575</span> </div><div class="line"><a name="l00576"></a><span class="lineno"> 576</span> </div><div class="line"><a name="l00577"></a><span class="lineno"> 577</span> <span class="comment">/* </span></div><div class="line"><a name="l00578"></a><span class="lineno"> 578</span> <span class="comment">Description:</span></div><div class="line"><a name="l00579"></a><span class="lineno"> 579</span> <span class="comment"> Compute a trinomial coefficient.</span></div><div class="line"><a name="l00580"></a><span class="lineno"> 580</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l00581"></a><span class="lineno"> 581</span> <span class="comment"> i - [in]</span></div><div class="line"><a name="l00582"></a><span class="lineno"> 582</span> <span class="comment"> j - [in]</span></div><div class="line"><a name="l00583"></a><span class="lineno"> 583</span> <span class="comment"> k - [in]</span></div><div class="line"><a name="l00584"></a><span class="lineno"> 584</span> <span class="comment">Returns:</span></div><div class="line"><a name="l00585"></a><span class="lineno"> 585</span> <span class="comment"> (i+j+k)!/(i!j!k!), if 0 <= i, 0 <= j and 0<= k, and 0 otherwise.</span></div><div class="line"><a name="l00586"></a><span class="lineno"> 586</span> <span class="comment">See Also:</span></div><div class="line"><a name="l00587"></a><span class="lineno"> 587</span> <span class="comment"> ON_BinomialCoefficient()</span></div><div class="line"><a name="l00588"></a><span class="lineno"> 588</span> <span class="comment">Remarks:</span></div><div class="line"><a name="l00589"></a><span class="lineno"> 589</span> <span class="comment"> The trinomial coefficient is computed using the formula</span></div><div class="line"><a name="l00590"></a><span class="lineno"> 590</span> <span class="comment"></span></div><div class="line"><a name="l00591"></a><span class="lineno"> 591</span> <span class="comment"> (i+j+k)! (i+j+k)! (j+k)!</span></div><div class="line"><a name="l00592"></a><span class="lineno"> 592</span> <span class="comment"> -------- = -------- * -------</span></div><div class="line"><a name="l00593"></a><span class="lineno"> 593</span> <span class="comment"> i! j! k! i! (j+k)! j! k!</span></div><div class="line"><a name="l00594"></a><span class="lineno"> 594</span> <span class="comment"></span></div><div class="line"><a name="l00595"></a><span class="lineno"> 595</span> <span class="comment"> = ON_BinomialCoefficient(i,j+k)*ON_BinomialCoefficient(j,k)</span></div><div class="line"><a name="l00596"></a><span class="lineno"> 596</span> <span class="comment"> </span></div><div class="line"><a name="l00597"></a><span class="lineno"> 597</span> <span class="comment">*/</span></div><div class="line"><a name="l00598"></a><span class="lineno"> 598</span> ON_DECL</div><div class="line"><a name="l00599"></a><span class="lineno"> 599</span> <span class="keywordtype">double</span> ON_TrinomialCoefficient( </div><div class="line"><a name="l00600"></a><span class="lineno"> 600</span>  <span class="keywordtype">int</span> i,</div><div class="line"><a name="l00601"></a><span class="lineno"> 601</span>  <span class="keywordtype">int</span> j,</div><div class="line"><a name="l00602"></a><span class="lineno"> 602</span>  <span class="keywordtype">int</span> k</div><div class="line"><a name="l00603"></a><span class="lineno"> 603</span>  );</div><div class="line"><a name="l00604"></a><span class="lineno"> 604</span> </div><div class="line"><a name="l00605"></a><span class="lineno"> 605</span> </div><div class="line"><a name="l00606"></a><span class="lineno"> 606</span> ON_DECL</div><div class="line"><a name="l00607"></a><span class="lineno"> 607</span> <span class="keywordtype">bool</span> ON_GetParameterTolerance(</div><div class="line"><a name="l00608"></a><span class="lineno"> 608</span>  <span class="keywordtype">double</span>, <span class="keywordtype">double</span>, <span class="comment">// domain</span></div><div class="line"><a name="l00609"></a><span class="lineno"> 609</span>  <span class="keywordtype">double</span>, <span class="comment">// parameter in domain</span></div><div class="line"><a name="l00610"></a><span class="lineno"> 610</span>  <span class="keywordtype">double</span>*, <span class="keywordtype">double</span>* <span class="comment">// parameter tolerance (tminus, tplus) returned here</span></div><div class="line"><a name="l00611"></a><span class="lineno"> 611</span>  );</div><div class="line"><a name="l00612"></a><span class="lineno"> 612</span> </div><div class="line"><a name="l00613"></a><span class="lineno"> 613</span> </div><div class="line"><a name="l00614"></a><span class="lineno"> 614</span> ON_DECL</div><div class="line"><a name="l00615"></a><span class="lineno"> 615</span> <span class="keywordtype">bool</span> ON_IsValidPointList(</div><div class="line"><a name="l00616"></a><span class="lineno"> 616</span>  <span class="keywordtype">int</span>, <span class="comment">// dim</span></div><div class="line"><a name="l00617"></a><span class="lineno"> 617</span>  <span class="keywordtype">bool</span>, <span class="comment">// true for homogeneous rational points</span></div><div class="line"><a name="l00618"></a><span class="lineno"> 618</span>  <span class="keywordtype">int</span>, <span class="comment">// count</span></div><div class="line"><a name="l00619"></a><span class="lineno"> 619</span>  <span class="keywordtype">int</span>, <span class="comment">// stride</span></div><div class="line"><a name="l00620"></a><span class="lineno"> 620</span>  <span class="keyword">const</span> <span class="keywordtype">float</span>*</div><div class="line"><a name="l00621"></a><span class="lineno"> 621</span>  );</div><div class="line"><a name="l00622"></a><span class="lineno"> 622</span> </div><div class="line"><a name="l00623"></a><span class="lineno"> 623</span> ON_DECL</div><div class="line"><a name="l00624"></a><span class="lineno"> 624</span> <span class="keywordtype">bool</span> ON_IsValidPointList(</div><div class="line"><a name="l00625"></a><span class="lineno"> 625</span>  <span class="keywordtype">int</span>, <span class="comment">// dim</span></div><div class="line"><a name="l00626"></a><span class="lineno"> 626</span>  <span class="keywordtype">bool</span>, <span class="comment">// true for homogeneous rational points</span></div><div class="line"><a name="l00627"></a><span class="lineno"> 627</span>  <span class="keywordtype">int</span>, <span class="comment">// count</span></div><div class="line"><a name="l00628"></a><span class="lineno"> 628</span>  <span class="keywordtype">int</span>, <span class="comment">// stride</span></div><div class="line"><a name="l00629"></a><span class="lineno"> 629</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>*</div><div class="line"><a name="l00630"></a><span class="lineno"> 630</span>  );</div><div class="line"><a name="l00631"></a><span class="lineno"> 631</span> </div><div class="line"><a name="l00632"></a><span class="lineno"> 632</span> <span class="comment">/*</span></div><div class="line"><a name="l00633"></a><span class="lineno"> 633</span> <span class="comment">Description:</span></div><div class="line"><a name="l00634"></a><span class="lineno"> 634</span> <span class="comment"> Determine if a list of points is planar.</span></div><div class="line"><a name="l00635"></a><span class="lineno"> 635</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l00636"></a><span class="lineno"> 636</span> <span class="comment"> bRational - [in]</span></div><div class="line"><a name="l00637"></a><span class="lineno"> 637</span> <span class="comment"> false if the points are euclidean (x,y,z)</span></div><div class="line"><a name="l00638"></a><span class="lineno"> 638</span> <span class="comment"> true if the points are homogeneous rational (x,y,z,w)</span></div><div class="line"><a name="l00639"></a><span class="lineno"> 639</span> <span class="comment"> point_count - [in]</span></div><div class="line"><a name="l00640"></a><span class="lineno"> 640</span> <span class="comment"> number of points</span></div><div class="line"><a name="l00641"></a><span class="lineno"> 641</span> <span class="comment"> point_stride - [in]</span></div><div class="line"><a name="l00642"></a><span class="lineno"> 642</span> <span class="comment"> number of doubles between point x coordinates</span></div><div class="line"><a name="l00643"></a><span class="lineno"> 643</span> <span class="comment"> first point's x coordinate = points[0],</span></div><div class="line"><a name="l00644"></a><span class="lineno"> 644</span> <span class="comment"> second point's x coordinate = points[point_stride],...</span></div><div class="line"><a name="l00645"></a><span class="lineno"> 645</span> <span class="comment"> points - [in]</span></div><div class="line"><a name="l00646"></a><span class="lineno"> 646</span> <span class="comment"> point coordinates (3d or 4d homogeneous rational)</span></div><div class="line"><a name="l00647"></a><span class="lineno"> 647</span> <span class="comment"> boxMin - [in]</span></div><div class="line"><a name="l00648"></a><span class="lineno"> 648</span> <span class="comment"> boxMax - [in]</span></div><div class="line"><a name="l00649"></a><span class="lineno"> 649</span> <span class="comment"> optional 3d bounding box - pass nulls if not readily available</span></div><div class="line"><a name="l00650"></a><span class="lineno"> 650</span> <span class="comment"> tolerance - [in] >= 0.0</span></div><div class="line"><a name="l00651"></a><span class="lineno"> 651</span> <span class="comment"> plane_equation0 - [in]</span></div><div class="line"><a name="l00652"></a><span class="lineno"> 652</span> <span class="comment"> If you want to test for planarity in a specific plane,</span></div><div class="line"><a name="l00653"></a><span class="lineno"> 653</span> <span class="comment"> pass the plane equation in here. If you want to find</span></div><div class="line"><a name="l00654"></a><span class="lineno"> 654</span> <span class="comment"> a plane containing the points, pass null here.</span></div><div class="line"><a name="l00655"></a><span class="lineno"> 655</span> <span class="comment"> plane_equation - [out]</span></div><div class="line"><a name="l00656"></a><span class="lineno"> 656</span> <span class="comment"> If this point is not null, then the equation of the plane</span></div><div class="line"><a name="l00657"></a><span class="lineno"> 657</span> <span class="comment"> containing the points is retuened here.</span></div><div class="line"><a name="l00658"></a><span class="lineno"> 658</span> <span class="comment">Returns:</span></div><div class="line"><a name="l00659"></a><span class="lineno"> 659</span> <span class="comment"> 0 - points are not coplanar to the specified tolerance</span></div><div class="line"><a name="l00660"></a><span class="lineno"> 660</span> <span class="comment"> 1 - points are coplanar to the specified tolerance</span></div><div class="line"><a name="l00661"></a><span class="lineno"> 661</span> <span class="comment"> 2 - points are collinear to the specified tolerance</span></div><div class="line"><a name="l00662"></a><span class="lineno"> 662</span> <span class="comment"> (in this case, plane_equation is not a unique answer)</span></div><div class="line"><a name="l00663"></a><span class="lineno"> 663</span> <span class="comment"> 3 - points are coincident to the specified tolerance</span></div><div class="line"><a name="l00664"></a><span class="lineno"> 664</span> <span class="comment"> (in this case, plane_equation is not a unique answer)</span></div><div class="line"><a name="l00665"></a><span class="lineno"> 665</span> <span class="comment">*/</span></div><div class="line"><a name="l00666"></a><span class="lineno"> 666</span> ON_DECL</div><div class="line"><a name="l00667"></a><span class="lineno"> 667</span> <span class="keywordtype">int</span> ON_IsPointListPlanar(</div><div class="line"><a name="l00668"></a><span class="lineno"> 668</span>  <span class="keywordtype">bool</span> bRational,</div><div class="line"><a name="l00669"></a><span class="lineno"> 669</span>  <span class="keywordtype">int</span> count,</div><div class="line"><a name="l00670"></a><span class="lineno"> 670</span>  <span class="keywordtype">int</span> stride,</div><div class="line"><a name="l00671"></a><span class="lineno"> 671</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* points,</div><div class="line"><a name="l00672"></a><span class="lineno"> 672</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* boxMin,</div><div class="line"><a name="l00673"></a><span class="lineno"> 673</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* boxMax,</div><div class="line"><a name="l00674"></a><span class="lineno"> 674</span>  <span class="keywordtype">double</span> tolerance,</div><div class="line"><a name="l00675"></a><span class="lineno"> 675</span>  <a class="code" href="class_o_n___plane_equation.html">ON_PlaneEquation</a>* plane_equation</div><div class="line"><a name="l00676"></a><span class="lineno"> 676</span>  );</div><div class="line"><a name="l00677"></a><span class="lineno"> 677</span> </div><div class="line"><a name="l00678"></a><span class="lineno"> 678</span> ON_DECL</div><div class="line"><a name="l00679"></a><span class="lineno"> 679</span> <span class="keywordtype">bool</span> ON_IsValidPointGrid(</div><div class="line"><a name="l00680"></a><span class="lineno"> 680</span>  <span class="keywordtype">int</span>, <span class="comment">// dim</span></div><div class="line"><a name="l00681"></a><span class="lineno"> 681</span>  <span class="keywordtype">bool</span>, <span class="comment">// true for homogeneous rational points</span></div><div class="line"><a name="l00682"></a><span class="lineno"> 682</span>  <span class="keywordtype">int</span>, <span class="keywordtype">int</span>, <span class="comment">// point_count0, point_count1,</span></div><div class="line"><a name="l00683"></a><span class="lineno"> 683</span>  <span class="keywordtype">int</span>, <span class="keywordtype">int</span>, <span class="comment">// point_stride0, point_stride1,</span></div><div class="line"><a name="l00684"></a><span class="lineno"> 684</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>*</div><div class="line"><a name="l00685"></a><span class="lineno"> 685</span>  );</div><div class="line"><a name="l00686"></a><span class="lineno"> 686</span> </div><div class="line"><a name="l00687"></a><span class="lineno"> 687</span> ON_DECL</div><div class="line"><a name="l00688"></a><span class="lineno"> 688</span> <span class="keywordtype">bool</span> ON_ReversePointList(</div><div class="line"><a name="l00689"></a><span class="lineno"> 689</span>  <span class="keywordtype">int</span>, <span class="comment">// dim</span></div><div class="line"><a name="l00690"></a><span class="lineno"> 690</span>  <span class="keywordtype">bool</span>, <span class="comment">// true for homogeneous rational points</span></div><div class="line"><a name="l00691"></a><span class="lineno"> 691</span>  <span class="keywordtype">int</span>, <span class="comment">// count</span></div><div class="line"><a name="l00692"></a><span class="lineno"> 692</span>  <span class="keywordtype">int</span>, <span class="comment">// stride</span></div><div class="line"><a name="l00693"></a><span class="lineno"> 693</span>  <span class="keywordtype">double</span>*</div><div class="line"><a name="l00694"></a><span class="lineno"> 694</span>  );</div><div class="line"><a name="l00695"></a><span class="lineno"> 695</span> </div><div class="line"><a name="l00696"></a><span class="lineno"> 696</span> ON_DECL</div><div class="line"><a name="l00697"></a><span class="lineno"> 697</span> <span class="keywordtype">bool</span> ON_ReversePointGrid(</div><div class="line"><a name="l00698"></a><span class="lineno"> 698</span>  <span class="keywordtype">int</span>, <span class="comment">// dim</span></div><div class="line"><a name="l00699"></a><span class="lineno"> 699</span>  <span class="keywordtype">bool</span>, <span class="comment">// true for homogeneous rational points</span></div><div class="line"><a name="l00700"></a><span class="lineno"> 700</span>  <span class="keywordtype">int</span>, <span class="keywordtype">int</span>, <span class="comment">// point_count0, point_count1,</span></div><div class="line"><a name="l00701"></a><span class="lineno"> 701</span>  <span class="keywordtype">int</span>, <span class="keywordtype">int</span>, <span class="comment">// point_stride0, point_stride1,</span></div><div class="line"><a name="l00702"></a><span class="lineno"> 702</span>  <span class="keywordtype">double</span>*,</div><div class="line"><a name="l00703"></a><span class="lineno"> 703</span>  <span class="keywordtype">int</span> <span class="comment">// dir = 0 or 1</span></div><div class="line"><a name="l00704"></a><span class="lineno"> 704</span>  );</div><div class="line"><a name="l00705"></a><span class="lineno"> 705</span> </div><div class="line"><a name="l00706"></a><span class="lineno"> 706</span> ON_DECL</div><div class="line"><a name="l00707"></a><span class="lineno"> 707</span> <span class="keywordtype">bool</span> ON_SwapPointListCoordinates( </div><div class="line"><a name="l00708"></a><span class="lineno"> 708</span>  <span class="keywordtype">int</span>, <span class="comment">// count</span></div><div class="line"><a name="l00709"></a><span class="lineno"> 709</span>  <span class="keywordtype">int</span>, <span class="comment">// stride</span></div><div class="line"><a name="l00710"></a><span class="lineno"> 710</span>  <span class="keywordtype">float</span>*,</div><div class="line"><a name="l00711"></a><span class="lineno"> 711</span>  <span class="keywordtype">int</span>, <span class="keywordtype">int</span> <span class="comment">// coordinates to swap</span></div><div class="line"><a name="l00712"></a><span class="lineno"> 712</span>  );</div><div class="line"><a name="l00713"></a><span class="lineno"> 713</span> </div><div class="line"><a name="l00714"></a><span class="lineno"> 714</span> ON_DECL</div><div class="line"><a name="l00715"></a><span class="lineno"> 715</span> <span class="keywordtype">bool</span> ON_SwapPointListCoordinates( </div><div class="line"><a name="l00716"></a><span class="lineno"> 716</span>  <span class="keywordtype">int</span>, <span class="comment">// count</span></div><div class="line"><a name="l00717"></a><span class="lineno"> 717</span>  <span class="keywordtype">int</span>, <span class="comment">// stride</span></div><div class="line"><a name="l00718"></a><span class="lineno"> 718</span>  <span class="keywordtype">double</span>*,</div><div class="line"><a name="l00719"></a><span class="lineno"> 719</span>  <span class="keywordtype">int</span>, <span class="keywordtype">int</span> <span class="comment">// coordinates to swap</span></div><div class="line"><a name="l00720"></a><span class="lineno"> 720</span>  );</div><div class="line"><a name="l00721"></a><span class="lineno"> 721</span> </div><div class="line"><a name="l00722"></a><span class="lineno"> 722</span> ON_DECL</div><div class="line"><a name="l00723"></a><span class="lineno"> 723</span> <span class="keywordtype">bool</span> ON_SwapPointGridCoordinates(</div><div class="line"><a name="l00724"></a><span class="lineno"> 724</span>  <span class="keywordtype">int</span>, <span class="keywordtype">int</span>, <span class="comment">// point_count0, point_count1,</span></div><div class="line"><a name="l00725"></a><span class="lineno"> 725</span>  <span class="keywordtype">int</span>, <span class="keywordtype">int</span>, <span class="comment">// point_stride0, point_stride1,</span></div><div class="line"><a name="l00726"></a><span class="lineno"> 726</span>  <span class="keywordtype">double</span>*,</div><div class="line"><a name="l00727"></a><span class="lineno"> 727</span>  <span class="keywordtype">int</span>, <span class="keywordtype">int</span> <span class="comment">// coordinates to swap</span></div><div class="line"><a name="l00728"></a><span class="lineno"> 728</span>  );</div><div class="line"><a name="l00729"></a><span class="lineno"> 729</span> </div><div class="line"><a name="l00730"></a><span class="lineno"> 730</span> ON_DECL</div><div class="line"><a name="l00731"></a><span class="lineno"> 731</span> <span class="keywordtype">bool</span> ON_TransformPointList(</div><div class="line"><a name="l00732"></a><span class="lineno"> 732</span>  <span class="keywordtype">int</span>, <span class="comment">// dim</span></div><div class="line"><a name="l00733"></a><span class="lineno"> 733</span>  <span class="keywordtype">bool</span>, <span class="comment">// true for homogeneous rational points</span></div><div class="line"><a name="l00734"></a><span class="lineno"> 734</span>  <span class="keywordtype">int</span>, <span class="comment">// count</span></div><div class="line"><a name="l00735"></a><span class="lineno"> 735</span>  <span class="keywordtype">int</span>, <span class="comment">// stride</span></div><div class="line"><a name="l00736"></a><span class="lineno"> 736</span>  <span class="keywordtype">float</span>*,</div><div class="line"><a name="l00737"></a><span class="lineno"> 737</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___xform.html">ON_Xform</a>&</div><div class="line"><a name="l00738"></a><span class="lineno"> 738</span>  );</div><div class="line"><a name="l00739"></a><span class="lineno"> 739</span> </div><div class="line"><a name="l00740"></a><span class="lineno"> 740</span> ON_DECL</div><div class="line"><a name="l00741"></a><span class="lineno"> 741</span> <span class="keywordtype">bool</span> ON_TransformPointList(</div><div class="line"><a name="l00742"></a><span class="lineno"> 742</span>  <span class="keywordtype">int</span>, <span class="comment">// dim</span></div><div class="line"><a name="l00743"></a><span class="lineno"> 743</span>  <span class="keywordtype">bool</span>, <span class="comment">// true for homogeneous rational points</span></div><div class="line"><a name="l00744"></a><span class="lineno"> 744</span>  <span class="keywordtype">int</span>, <span class="comment">// count</span></div><div class="line"><a name="l00745"></a><span class="lineno"> 745</span>  <span class="keywordtype">int</span>, <span class="comment">// stride</span></div><div class="line"><a name="l00746"></a><span class="lineno"> 746</span>  <span class="keywordtype">double</span>*,</div><div class="line"><a name="l00747"></a><span class="lineno"> 747</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___xform.html">ON_Xform</a>&</div><div class="line"><a name="l00748"></a><span class="lineno"> 748</span>  );</div><div class="line"><a name="l00749"></a><span class="lineno"> 749</span> </div><div class="line"><a name="l00750"></a><span class="lineno"> 750</span> ON_DECL</div><div class="line"><a name="l00751"></a><span class="lineno"> 751</span> <span class="keywordtype">bool</span> ON_TransformPointGrid(</div><div class="line"><a name="l00752"></a><span class="lineno"> 752</span>  <span class="keywordtype">int</span>, <span class="comment">// dim</span></div><div class="line"><a name="l00753"></a><span class="lineno"> 753</span>  <span class="keywordtype">bool</span>, <span class="comment">// true for homogeneous rational points</span></div><div class="line"><a name="l00754"></a><span class="lineno"> 754</span>  <span class="keywordtype">int</span>, <span class="keywordtype">int</span>, <span class="comment">// point_count0, point_count1,</span></div><div class="line"><a name="l00755"></a><span class="lineno"> 755</span>  <span class="keywordtype">int</span>, <span class="keywordtype">int</span>, <span class="comment">// point_stride0, point_stride1,</span></div><div class="line"><a name="l00756"></a><span class="lineno"> 756</span>  <span class="keywordtype">double</span>*,</div><div class="line"><a name="l00757"></a><span class="lineno"> 757</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___xform.html">ON_Xform</a>&</div><div class="line"><a name="l00758"></a><span class="lineno"> 758</span>  );</div><div class="line"><a name="l00759"></a><span class="lineno"> 759</span> </div><div class="line"><a name="l00760"></a><span class="lineno"> 760</span> ON_DECL</div><div class="line"><a name="l00761"></a><span class="lineno"> 761</span> <span class="keywordtype">bool</span> ON_TransformVectorList(</div><div class="line"><a name="l00762"></a><span class="lineno"> 762</span>  <span class="keywordtype">int</span>, <span class="comment">// dim</span></div><div class="line"><a name="l00763"></a><span class="lineno"> 763</span>  <span class="keywordtype">int</span>, <span class="comment">// count</span></div><div class="line"><a name="l00764"></a><span class="lineno"> 764</span>  <span class="keywordtype">int</span>, <span class="comment">// stride</span></div><div class="line"><a name="l00765"></a><span class="lineno"> 765</span>  <span class="keywordtype">float</span>*,</div><div class="line"><a name="l00766"></a><span class="lineno"> 766</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___xform.html">ON_Xform</a>&</div><div class="line"><a name="l00767"></a><span class="lineno"> 767</span>  );</div><div class="line"><a name="l00768"></a><span class="lineno"> 768</span> </div><div class="line"><a name="l00769"></a><span class="lineno"> 769</span> ON_DECL</div><div class="line"><a name="l00770"></a><span class="lineno"> 770</span> <span class="keywordtype">bool</span> ON_TransformVectorList(</div><div class="line"><a name="l00771"></a><span class="lineno"> 771</span>  <span class="keywordtype">int</span>, <span class="comment">// dim</span></div><div class="line"><a name="l00772"></a><span class="lineno"> 772</span>  <span class="keywordtype">int</span>, <span class="comment">// count</span></div><div class="line"><a name="l00773"></a><span class="lineno"> 773</span>  <span class="keywordtype">int</span>, <span class="comment">// stride</span></div><div class="line"><a name="l00774"></a><span class="lineno"> 774</span>  <span class="keywordtype">double</span>*,</div><div class="line"><a name="l00775"></a><span class="lineno"> 775</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___xform.html">ON_Xform</a>&</div><div class="line"><a name="l00776"></a><span class="lineno"> 776</span>  );</div><div class="line"><a name="l00777"></a><span class="lineno"> 777</span> </div><div class="line"><a name="l00778"></a><span class="lineno"> 778</span> <span class="comment">/*</span></div><div class="line"><a name="l00779"></a><span class="lineno"> 779</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l00780"></a><span class="lineno"> 780</span> <span class="comment"> dim - [in]</span></div><div class="line"><a name="l00781"></a><span class="lineno"> 781</span> <span class="comment"> >= 1</span></div><div class="line"><a name="l00782"></a><span class="lineno"> 782</span> <span class="comment"> is_rat - [in]</span></div><div class="line"><a name="l00783"></a><span class="lineno"> 783</span> <span class="comment"> true if the points are rational and points[dim] is the "weight"</span></div><div class="line"><a name="l00784"></a><span class="lineno"> 784</span> <span class="comment"> pointA - [in]</span></div><div class="line"><a name="l00785"></a><span class="lineno"> 785</span> <span class="comment"> pointB - [in]</span></div><div class="line"><a name="l00786"></a><span class="lineno"> 786</span> <span class="comment"> point coordinates</span></div><div class="line"><a name="l00787"></a><span class="lineno"> 787</span> <span class="comment">Returns:</span></div><div class="line"><a name="l00788"></a><span class="lineno"> 788</span> <span class="comment"> True if the input is valid and for each coordinate pair,</span></div><div class="line"><a name="l00789"></a><span class="lineno"> 789</span> <span class="comment"> |a-b| <= ON_ZERO_TOLERANCE </span></div><div class="line"><a name="l00790"></a><span class="lineno"> 790</span> <span class="comment"> or |a-b| <= (fabs(a)+fabs(b))*ON_RELATIVE_TOLERANCE.</span></div><div class="line"><a name="l00791"></a><span class="lineno"> 791</span> <span class="comment"> False otherwise.</span></div><div class="line"><a name="l00792"></a><span class="lineno"> 792</span> <span class="comment">*/</span></div><div class="line"><a name="l00793"></a><span class="lineno"> 793</span> ON_DECL</div><div class="line"><a name="l00794"></a><span class="lineno"> 794</span> <span class="keywordtype">bool</span> ON_PointsAreCoincident(</div><div class="line"><a name="l00795"></a><span class="lineno"> 795</span>  <span class="keywordtype">int</span> dim,</div><div class="line"><a name="l00796"></a><span class="lineno"> 796</span>  <span class="keywordtype">bool</span> is_rat,</div><div class="line"><a name="l00797"></a><span class="lineno"> 797</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* pointA,</div><div class="line"><a name="l00798"></a><span class="lineno"> 798</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* pointB</div><div class="line"><a name="l00799"></a><span class="lineno"> 799</span>  );</div><div class="line"><a name="l00800"></a><span class="lineno"> 800</span> </div><div class="line"><a name="l00801"></a><span class="lineno"> 801</span> <span class="comment">/*</span></div><div class="line"><a name="l00802"></a><span class="lineno"> 802</span> <span class="comment">Description</span></div><div class="line"><a name="l00803"></a><span class="lineno"> 803</span> <span class="comment"> See ON_PointsAreCoincident() for a description of when opennurbs</span></div><div class="line"><a name="l00804"></a><span class="lineno"> 804</span> <span class="comment"> considers two points to be conincident.</span></div><div class="line"><a name="l00805"></a><span class="lineno"> 805</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l00806"></a><span class="lineno"> 806</span> <span class="comment"> dim - [in]</span></div><div class="line"><a name="l00807"></a><span class="lineno"> 807</span> <span class="comment"> >= 1</span></div><div class="line"><a name="l00808"></a><span class="lineno"> 808</span> <span class="comment"> is_rat - [in]</span></div><div class="line"><a name="l00809"></a><span class="lineno"> 809</span> <span class="comment"> true if the points are rational and points[dim] is the "weight"</span></div><div class="line"><a name="l00810"></a><span class="lineno"> 810</span> <span class="comment"> point_count - [in]</span></div><div class="line"><a name="l00811"></a><span class="lineno"> 811</span> <span class="comment"> number of points >= 2</span></div><div class="line"><a name="l00812"></a><span class="lineno"> 812</span> <span class="comment"> point_stride - [in]</span></div><div class="line"><a name="l00813"></a><span class="lineno"> 813</span> <span class="comment"> >= (0 != is_rat) ? (dim+1) : dim</span></div><div class="line"><a name="l00814"></a><span class="lineno"> 814</span> <span class="comment"> points - [in]</span></div><div class="line"><a name="l00815"></a><span class="lineno"> 815</span> <span class="comment"> point coordinates</span></div><div class="line"><a name="l00816"></a><span class="lineno"> 816</span> <span class="comment">Returns:</span></div><div class="line"><a name="l00817"></a><span class="lineno"> 817</span> <span class="comment"> True if the first and last points are coincident and all other</span></div><div class="line"><a name="l00818"></a><span class="lineno"> 818</span> <span class="comment"> points in the list are coincident with the previous point.</span></div><div class="line"><a name="l00819"></a><span class="lineno"> 819</span> <span class="comment"> False if there are points that are not coincident or</span></div><div class="line"><a name="l00820"></a><span class="lineno"> 820</span> <span class="comment"> point_count < 2 or other input parameters are invalid.</span></div><div class="line"><a name="l00821"></a><span class="lineno"> 821</span> <span class="comment">*/</span></div><div class="line"><a name="l00822"></a><span class="lineno"> 822</span> ON_DECL</div><div class="line"><a name="l00823"></a><span class="lineno"> 823</span> <span class="keywordtype">bool</span> ON_PointsAreCoincident(</div><div class="line"><a name="l00824"></a><span class="lineno"> 824</span>  <span class="keywordtype">int</span> dim,</div><div class="line"><a name="l00825"></a><span class="lineno"> 825</span>  <span class="keywordtype">bool</span> is_rat,</div><div class="line"><a name="l00826"></a><span class="lineno"> 826</span>  <span class="keywordtype">int</span> point_count,</div><div class="line"><a name="l00827"></a><span class="lineno"> 827</span>  <span class="keywordtype">int</span> point_stride,</div><div class="line"><a name="l00828"></a><span class="lineno"> 828</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* points</div><div class="line"><a name="l00829"></a><span class="lineno"> 829</span>  );</div><div class="line"><a name="l00830"></a><span class="lineno"> 830</span> </div><div class="line"><a name="l00831"></a><span class="lineno"> 831</span> ON_DECL</div><div class="line"><a name="l00832"></a><span class="lineno"> 832</span> <span class="keywordtype">int</span> ON_ComparePoint( <span class="comment">// returns </span></div><div class="line"><a name="l00833"></a><span class="lineno"> 833</span>  <span class="comment">// -1: first < second</span></div><div class="line"><a name="l00834"></a><span class="lineno"> 834</span>  <span class="comment">// 0: first == second</span></div><div class="line"><a name="l00835"></a><span class="lineno"> 835</span>  <span class="comment">// +1: first > second</span></div><div class="line"><a name="l00836"></a><span class="lineno"> 836</span>  <span class="keywordtype">int</span> dim, <span class="comment">// dim (>=0)</span></div><div class="line"><a name="l00837"></a><span class="lineno"> 837</span>  <span class="keywordtype">bool</span> israt, <span class="comment">// true for rational CVs</span></div><div class="line"><a name="l00838"></a><span class="lineno"> 838</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* cv0, <span class="comment">// first CV</span></div><div class="line"><a name="l00839"></a><span class="lineno"> 839</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* cv1 <span class="comment">// secont CV</span></div><div class="line"><a name="l00840"></a><span class="lineno"> 840</span>  );</div><div class="line"><a name="l00841"></a><span class="lineno"> 841</span> </div><div class="line"><a name="l00842"></a><span class="lineno"> 842</span> ON_DECL</div><div class="line"><a name="l00843"></a><span class="lineno"> 843</span> <span class="keywordtype">int</span> ON_ComparePointList( <span class="comment">// returns </span></div><div class="line"><a name="l00844"></a><span class="lineno"> 844</span>  <span class="comment">// -1: first < second</span></div><div class="line"><a name="l00845"></a><span class="lineno"> 845</span>  <span class="comment">// 0: first == second</span></div><div class="line"><a name="l00846"></a><span class="lineno"> 846</span>  <span class="comment">// +1: first > second</span></div><div class="line"><a name="l00847"></a><span class="lineno"> 847</span>  <span class="keywordtype">int</span>, <span class="comment">// dim (>=0)</span></div><div class="line"><a name="l00848"></a><span class="lineno"> 848</span>  <span class="keywordtype">bool</span>, <span class="comment">// true for rational CVs</span></div><div class="line"><a name="l00849"></a><span class="lineno"> 849</span>  <span class="keywordtype">int</span>, <span class="comment">// count</span></div><div class="line"><a name="l00850"></a><span class="lineno"> 850</span>  <span class="comment">// first point list</span></div><div class="line"><a name="l00851"></a><span class="lineno"> 851</span>  <span class="keywordtype">int</span>, <span class="comment">// stride</span></div><div class="line"><a name="l00852"></a><span class="lineno"> 852</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// point</span></div><div class="line"><a name="l00853"></a><span class="lineno"> 853</span>  <span class="comment">// second point list</span></div><div class="line"><a name="l00854"></a><span class="lineno"> 854</span>  <span class="keywordtype">int</span>, <span class="comment">// stride</span></div><div class="line"><a name="l00855"></a><span class="lineno"> 855</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* <span class="comment">// point</span></div><div class="line"><a name="l00856"></a><span class="lineno"> 856</span>  );</div><div class="line"><a name="l00857"></a><span class="lineno"> 857</span> </div><div class="line"><a name="l00858"></a><span class="lineno"> 858</span> ON_DECL</div><div class="line"><a name="l00859"></a><span class="lineno"> 859</span> <span class="keywordtype">bool</span> ON_IsPointListClosed(</div><div class="line"><a name="l00860"></a><span class="lineno"> 860</span>  <span class="keywordtype">int</span>, <span class="comment">// dim</span></div><div class="line"><a name="l00861"></a><span class="lineno"> 861</span>  <span class="keywordtype">bool</span>, <span class="comment">// true for homogeneos rational points</span></div><div class="line"><a name="l00862"></a><span class="lineno"> 862</span>  <span class="keywordtype">int</span>, <span class="comment">// count</span></div><div class="line"><a name="l00863"></a><span class="lineno"> 863</span>  <span class="keywordtype">int</span>, <span class="comment">// stride</span></div><div class="line"><a name="l00864"></a><span class="lineno"> 864</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>*</div><div class="line"><a name="l00865"></a><span class="lineno"> 865</span>  );</div><div class="line"><a name="l00866"></a><span class="lineno"> 866</span> </div><div class="line"><a name="l00867"></a><span class="lineno"> 867</span> ON_DECL</div><div class="line"><a name="l00868"></a><span class="lineno"> 868</span> <span class="keywordtype">bool</span> ON_IsPointGridClosed(</div><div class="line"><a name="l00869"></a><span class="lineno"> 869</span>  <span class="keywordtype">int</span>, <span class="comment">// dim</span></div><div class="line"><a name="l00870"></a><span class="lineno"> 870</span>  <span class="keywordtype">bool</span>, <span class="comment">// true for homogeneous rational points</span></div><div class="line"><a name="l00871"></a><span class="lineno"> 871</span>  <span class="keywordtype">int</span>, <span class="keywordtype">int</span>, <span class="comment">// point_count0, point_count1,</span></div><div class="line"><a name="l00872"></a><span class="lineno"> 872</span>  <span class="keywordtype">int</span>, <span class="keywordtype">int</span>, <span class="comment">// point_stride0, point_stride1,</span></div><div class="line"><a name="l00873"></a><span class="lineno"> 873</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>*,</div><div class="line"><a name="l00874"></a><span class="lineno"> 874</span>  <span class="keywordtype">int</span> <span class="comment">// dir = 0 or 1</span></div><div class="line"><a name="l00875"></a><span class="lineno"> 875</span>  );</div><div class="line"><a name="l00876"></a><span class="lineno"> 876</span> </div><div class="line"><a name="l00877"></a><span class="lineno"> 877</span> </div><div class="line"><a name="l00878"></a><span class="lineno"> 878</span> <span class="comment">/*</span></div><div class="line"><a name="l00879"></a><span class="lineno"> 879</span> <span class="comment">Description:</span></div><div class="line"><a name="l00880"></a><span class="lineno"> 880</span> <span class="comment"> Assign a unique id to each point location. Coincident points</span></div><div class="line"><a name="l00881"></a><span class="lineno"> 881</span> <span class="comment"> get the same id.</span></div><div class="line"><a name="l00882"></a><span class="lineno"> 882</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l00883"></a><span class="lineno"> 883</span> <span class="comment"> point_dim - [in]</span></div><div class="line"><a name="l00884"></a><span class="lineno"> 884</span> <span class="comment"> 2 or 3</span></div><div class="line"><a name="l00885"></a><span class="lineno"> 885</span> <span class="comment"> point_count - [in]</span></div><div class="line"><a name="l00886"></a><span class="lineno"> 886</span> <span class="comment"> >= 1</span></div><div class="line"><a name="l00887"></a><span class="lineno"> 887</span> <span class="comment"> point_stride - [in]</span></div><div class="line"><a name="l00888"></a><span class="lineno"> 888</span> <span class="comment"> number of coordinates to skip between points</span></div><div class="line"><a name="l00889"></a><span class="lineno"> 889</span> <span class="comment"> >= point_dim</span></div><div class="line"><a name="l00890"></a><span class="lineno"> 890</span> <span class="comment"> points - [in]</span></div><div class="line"><a name="l00891"></a><span class="lineno"> 891</span> <span class="comment"> The first coordinate of the i-th point is points[i*point_stride]</span></div><div class="line"><a name="l00892"></a><span class="lineno"> 892</span> <span class="comment"> first_point_id - [in]</span></div><div class="line"><a name="l00893"></a><span class="lineno"> 893</span> <span class="comment"> Initial point id. Typically 1 or 0.</span></div><div class="line"><a name="l00894"></a><span class="lineno"> 894</span> <span class="comment"> point_ids - [out]</span></div><div class="line"><a name="l00895"></a><span class="lineno"> 895</span> <span class="comment"> If not null, then point_ids[] must be an array of length point_count</span></div><div class="line"><a name="l00896"></a><span class="lineno"> 896</span> <span class="comment"> and the ids are retuened in this array. point_ids[0] = first_point_id.</span></div><div class="line"><a name="l00897"></a><span class="lineno"> 897</span> <span class="comment"> point_id_map - [out]</span></div><div class="line"><a name="l00898"></a><span class="lineno"> 898</span> <span class="comment"> If point_id_index is not null, then it must have length point_count.</span></div><div class="line"><a name="l00899"></a><span class="lineno"> 899</span> <span class="comment"> The returned values are a permutation of (0,1,...,point_count-1) such that</span></div><div class="line"><a name="l00900"></a><span class="lineno"> 900</span> <span class="comment"> (point_ids[point_id_map[0]], ..., point_ids[point_id_map[point_count-1]])</span></div><div class="line"><a name="l00901"></a><span class="lineno"> 901</span> <span class="comment"> is an increasing list of values and point_id_map[0] = 0.</span></div><div class="line"><a name="l00902"></a><span class="lineno"> 902</span> <span class="comment">Returns:</span></div><div class="line"><a name="l00903"></a><span class="lineno"> 903</span> <span class="comment"> If input is valid, then an array of point_count point location</span></div><div class="line"><a name="l00904"></a><span class="lineno"> 904</span> <span class="comment"> ids is returned. The i-th and j-th values in the returned array are</span></div><div class="line"><a name="l00905"></a><span class="lineno"> 905</span> <span class="comment"> equal if and only if the i-th and j-th points have the same location.</span></div><div class="line"><a name="l00906"></a><span class="lineno"> 906</span> <span class="comment"> If the input point_ids pointer was null, then the array memory is</span></div><div class="line"><a name="l00907"></a><span class="lineno"> 907</span> <span class="comment"> allocated on the heap by calling onmalloc(). If input is not valid,</span></div><div class="line"><a name="l00908"></a><span class="lineno"> 908</span> <span class="comment"> nullptr is returned.</span></div><div class="line"><a name="l00909"></a><span class="lineno"> 909</span> <span class="comment">Remarks:</span></div><div class="line"><a name="l00910"></a><span class="lineno"> 910</span> <span class="comment"> The ids are invarient under invertable transformations. </span></div><div class="line"><a name="l00911"></a><span class="lineno"> 911</span> <span class="comment"> Specifically, if one point point set is a rotation of another, then</span></div><div class="line"><a name="l00912"></a><span class="lineno"> 912</span> <span class="comment"> the assiged ids will be the same.</span></div><div class="line"><a name="l00913"></a><span class="lineno"> 913</span> <span class="comment">*/</span></div><div class="line"><a name="l00914"></a><span class="lineno"> 914</span> ON_DECL</div><div class="line"><a name="l00915"></a><span class="lineno"> 915</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>* ON_GetPointLocationIds(</div><div class="line"><a name="l00916"></a><span class="lineno"> 916</span>  <span class="keywordtype">size_t</span> point_dim,</div><div class="line"><a name="l00917"></a><span class="lineno"> 917</span>  <span class="keywordtype">size_t</span> point_count,</div><div class="line"><a name="l00918"></a><span class="lineno"> 918</span>  <span class="keywordtype">size_t</span> point_stride,</div><div class="line"><a name="l00919"></a><span class="lineno"> 919</span>  <span class="keyword">const</span> <span class="keywordtype">float</span>* points,</div><div class="line"><a name="l00920"></a><span class="lineno"> 920</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> first_point_id,</div><div class="line"><a name="l00921"></a><span class="lineno"> 921</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>* point_ids,</div><div class="line"><a name="l00922"></a><span class="lineno"> 922</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>* point_id_map</div><div class="line"><a name="l00923"></a><span class="lineno"> 923</span>  );</div><div class="line"><a name="l00924"></a><span class="lineno"> 924</span> </div><div class="line"><a name="l00925"></a><span class="lineno"> 925</span> ON_DECL</div><div class="line"><a name="l00926"></a><span class="lineno"> 926</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>* ON_GetPointLocationIds(</div><div class="line"><a name="l00927"></a><span class="lineno"> 927</span>  <span class="keywordtype">size_t</span> point_dim,</div><div class="line"><a name="l00928"></a><span class="lineno"> 928</span>  <span class="keywordtype">size_t</span> point_count,</div><div class="line"><a name="l00929"></a><span class="lineno"> 929</span>  <span class="keywordtype">size_t</span> point_stride,</div><div class="line"><a name="l00930"></a><span class="lineno"> 930</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* points,</div><div class="line"><a name="l00931"></a><span class="lineno"> 931</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> first_point_id,</div><div class="line"><a name="l00932"></a><span class="lineno"> 932</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>* point_ids,</div><div class="line"><a name="l00933"></a><span class="lineno"> 933</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>* point_id_map</div><div class="line"><a name="l00934"></a><span class="lineno"> 934</span>  );</div><div class="line"><a name="l00935"></a><span class="lineno"> 935</span> </div><div class="line"><a name="l00936"></a><span class="lineno"> 936</span> ON_DECL</div><div class="line"><a name="l00937"></a><span class="lineno"> 937</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>* ON_GetPointLocationIds(</div><div class="line"><a name="l00938"></a><span class="lineno"> 938</span>  <span class="keywordtype">size_t</span> point_count,</div><div class="line"><a name="l00939"></a><span class="lineno"> 939</span>  <span class="keyword">const</span> <span class="keyword">class</span> <a class="code" href="class_o_n__2f_point.html">ON_2fPoint</a>* points,</div><div class="line"><a name="l00940"></a><span class="lineno"> 940</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> first_point_id,</div><div class="line"><a name="l00941"></a><span class="lineno"> 941</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>* point_ids,</div><div class="line"><a name="l00942"></a><span class="lineno"> 942</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>* point_id_map</div><div class="line"><a name="l00943"></a><span class="lineno"> 943</span>  );</div><div class="line"><a name="l00944"></a><span class="lineno"> 944</span> </div><div class="line"><a name="l00945"></a><span class="lineno"> 945</span> ON_DECL</div><div class="line"><a name="l00946"></a><span class="lineno"> 946</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>* ON_GetPointLocationIds(</div><div class="line"><a name="l00947"></a><span class="lineno"> 947</span>  <span class="keywordtype">size_t</span> point_count,</div><div class="line"><a name="l00948"></a><span class="lineno"> 948</span>  <span class="keyword">const</span> <span class="keyword">class</span> <a class="code" href="class_o_n__3f_point.html">ON_3fPoint</a>* points,</div><div class="line"><a name="l00949"></a><span class="lineno"> 949</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> first_point_id,</div><div class="line"><a name="l00950"></a><span class="lineno"> 950</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>* point_ids,</div><div class="line"><a name="l00951"></a><span class="lineno"> 951</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>* point_id_map</div><div class="line"><a name="l00952"></a><span class="lineno"> 952</span>  );</div><div class="line"><a name="l00953"></a><span class="lineno"> 953</span> </div><div class="line"><a name="l00954"></a><span class="lineno"> 954</span> ON_DECL</div><div class="line"><a name="l00955"></a><span class="lineno"> 955</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>* ON_GetPointLocationIds(</div><div class="line"><a name="l00956"></a><span class="lineno"> 956</span>  <span class="keywordtype">size_t</span> point_count,</div><div class="line"><a name="l00957"></a><span class="lineno"> 957</span>  <span class="keyword">const</span> <span class="keyword">class</span> <a class="code" href="class_o_n__2d_point.html">ON_2dPoint</a>* points,</div><div class="line"><a name="l00958"></a><span class="lineno"> 958</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> first_point_id,</div><div class="line"><a name="l00959"></a><span class="lineno"> 959</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>* point_ids,</div><div class="line"><a name="l00960"></a><span class="lineno"> 960</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>* point_id_map</div><div class="line"><a name="l00961"></a><span class="lineno"> 961</span>  );</div><div class="line"><a name="l00962"></a><span class="lineno"> 962</span> </div><div class="line"><a name="l00963"></a><span class="lineno"> 963</span> ON_DECL</div><div class="line"><a name="l00964"></a><span class="lineno"> 964</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>* ON_GetPointLocationIds(</div><div class="line"><a name="l00965"></a><span class="lineno"> 965</span>  <span class="keywordtype">size_t</span> point_count,</div><div class="line"><a name="l00966"></a><span class="lineno"> 966</span>  <span class="keyword">const</span> <span class="keyword">class</span> <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a>* points,</div><div class="line"><a name="l00967"></a><span class="lineno"> 967</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> first_point_id,</div><div class="line"><a name="l00968"></a><span class="lineno"> 968</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>* point_ids,</div><div class="line"><a name="l00969"></a><span class="lineno"> 969</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>* point_id_map</div><div class="line"><a name="l00970"></a><span class="lineno"> 970</span>  );</div><div class="line"><a name="l00971"></a><span class="lineno"> 971</span> </div><div class="line"><a name="l00972"></a><span class="lineno"> 972</span> </div><div class="line"><a name="l00973"></a><span class="lineno"> 973</span> ON_DECL</div><div class="line"><a name="l00974"></a><span class="lineno"> 974</span> <span class="keywordtype">int</span> ON_SolveQuadraticEquation( <span class="comment">// solve a*X^2 + b*X + c = 0</span></div><div class="line"><a name="l00975"></a><span class="lineno"> 975</span>  <span class="comment">// returns 0: two distinct real roots (r0 < r1)</span></div><div class="line"><a name="l00976"></a><span class="lineno"> 976</span>  <span class="comment">// 1: one real root (r0 = r1)</span></div><div class="line"><a name="l00977"></a><span class="lineno"> 977</span>  <span class="comment">// 2: two complex conjugate roots (r0 +/- (r1)*sqrt(-1))</span></div><div class="line"><a name="l00978"></a><span class="lineno"> 978</span>  <span class="comment">// -1: failure - a = 0, b != 0 (r0 = r1 = -c/b)</span></div><div class="line"><a name="l00979"></a><span class="lineno"> 979</span>  <span class="comment">// -2: failure - a = 0, b = 0 c != 0 (r0 = r1 = 0.0)</span></div><div class="line"><a name="l00980"></a><span class="lineno"> 980</span>  <span class="comment">// -3: failure - a = 0, b = 0 c = 0 (r0 = r1 = 0.0)</span></div><div class="line"><a name="l00981"></a><span class="lineno"> 981</span>  <span class="keywordtype">double</span>, <span class="keywordtype">double</span>, <span class="keywordtype">double</span>, <span class="comment">// a, b, c</span></div><div class="line"><a name="l00982"></a><span class="lineno"> 982</span>  <span class="keywordtype">double</span>*, <span class="keywordtype">double</span>* <span class="comment">// roots r0 and r1 returned here</span></div><div class="line"><a name="l00983"></a><span class="lineno"> 983</span>  );</div><div class="line"><a name="l00984"></a><span class="lineno"> 984</span> </div><div class="line"><a name="l00985"></a><span class="lineno"> 985</span> <span class="comment">/*</span></div><div class="line"><a name="l00986"></a><span class="lineno"> 986</span> <span class="comment">Returns:</span></div><div class="line"><a name="l00987"></a><span class="lineno"> 987</span> <span class="comment"> 0: success</span></div><div class="line"><a name="l00988"></a><span class="lineno"> 988</span> <span class="comment"> <0: failure</span></div><div class="line"><a name="l00989"></a><span class="lineno"> 989</span> <span class="comment">*/</span></div><div class="line"><a name="l00990"></a><span class="lineno"> 990</span> ON_DECL</div><div class="line"><a name="l00991"></a><span class="lineno"> 991</span> <span class="keywordtype">int</span> ON_SolveTriDiagonal( <span class="comment">// solve TriDiagMatrix( a,b,c )*X = d</span></div><div class="line"><a name="l00992"></a><span class="lineno"> 992</span>  <span class="keywordtype">int</span>, <span class="comment">// dimension of d and X (>=1)</span></div><div class="line"><a name="l00993"></a><span class="lineno"> 993</span>  <span class="keywordtype">int</span>, <span class="comment">// number of equations (>=2)</span></div><div class="line"><a name="l00994"></a><span class="lineno"> 994</span>  <span class="keywordtype">double</span>*, <span class="comment">// a[n-1] = sub-diagonal (a is modified)</span></div><div class="line"><a name="l00995"></a><span class="lineno"> 995</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// b[n] = diagonal</span></div><div class="line"><a name="l00996"></a><span class="lineno"> 996</span>  <span class="keywordtype">double</span>*, <span class="comment">// c[n-1] = supra-diagonal</span></div><div class="line"><a name="l00997"></a><span class="lineno"> 997</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// d[n*dim]</span></div><div class="line"><a name="l00998"></a><span class="lineno"> 998</span>  <span class="keywordtype">double</span>* <span class="comment">// X[n*dim] = unknowns</span></div><div class="line"><a name="l00999"></a><span class="lineno"> 999</span>  );</div><div class="line"><a name="l01000"></a><span class="lineno"> 1000</span> </div><div class="line"><a name="l01001"></a><span class="lineno"> 1001</span> <span class="comment">// returns rank - if rank != 2, system is under determined</span></div><div class="line"><a name="l01002"></a><span class="lineno"> 1002</span> <span class="comment">// If rank = 2, then solution to </span></div><div class="line"><a name="l01003"></a><span class="lineno"> 1003</span> <span class="comment">//</span></div><div class="line"><a name="l01004"></a><span class="lineno"> 1004</span> <span class="comment">// a00*x0 + a01*x1 = b0, </span></div><div class="line"><a name="l01005"></a><span class="lineno"> 1005</span> <span class="comment">// a10*x0 + a11*x1 = b1 </span></div><div class="line"><a name="l01006"></a><span class="lineno"> 1006</span> <span class="comment">//</span></div><div class="line"><a name="l01007"></a><span class="lineno"> 1007</span> <span class="comment">// is returned</span></div><div class="line"><a name="l01008"></a><span class="lineno"> 1008</span> ON_DECL</div><div class="line"><a name="l01009"></a><span class="lineno"> 1009</span> <span class="keywordtype">int</span> ON_Solve2x2( </div><div class="line"><a name="l01010"></a><span class="lineno"> 1010</span>  <span class="keywordtype">double</span>, <span class="keywordtype">double</span>, <span class="comment">// a00 a01 = first row of 2x2 matrix</span></div><div class="line"><a name="l01011"></a><span class="lineno"> 1011</span>  <span class="keywordtype">double</span>, <span class="keywordtype">double</span>, <span class="comment">// a10 a11 = second row of 2x2 matrix</span></div><div class="line"><a name="l01012"></a><span class="lineno"> 1012</span>  <span class="keywordtype">double</span>, <span class="keywordtype">double</span>, <span class="comment">// b0 b1</span></div><div class="line"><a name="l01013"></a><span class="lineno"> 1013</span>  <span class="keywordtype">double</span>*, <span class="keywordtype">double</span>*, <span class="comment">// x0, x1 if not nullptr, then solution is returned here</span></div><div class="line"><a name="l01014"></a><span class="lineno"> 1014</span>  <span class="keywordtype">double</span>* <span class="comment">// if not nullptr, then pivot_ratio returned here</span></div><div class="line"><a name="l01015"></a><span class="lineno"> 1015</span>  );</div><div class="line"><a name="l01016"></a><span class="lineno"> 1016</span> </div><div class="line"><a name="l01017"></a><span class="lineno"> 1017</span> <span class="comment">// Description:</span></div><div class="line"><a name="l01018"></a><span class="lineno"> 1018</span> <span class="comment">// Solves a system of 3 linear equations and 2 unknowns.</span></div><div class="line"><a name="l01019"></a><span class="lineno"> 1019</span> <span class="comment">//</span></div><div class="line"><a name="l01020"></a><span class="lineno"> 1020</span> <span class="comment">// x*col0[0] + y*col1[0] = d0</span></div><div class="line"><a name="l01021"></a><span class="lineno"> 1021</span> <span class="comment">// x*col0[1] + y*col1[1] = d0</span></div><div class="line"><a name="l01022"></a><span class="lineno"> 1022</span> <span class="comment">// x*col0[2] + y*col1[2] = d0</span></div><div class="line"><a name="l01023"></a><span class="lineno"> 1023</span> <span class="comment">//</span></div><div class="line"><a name="l01024"></a><span class="lineno"> 1024</span> <span class="comment">// Parameters:</span></div><div class="line"><a name="l01025"></a><span class="lineno"> 1025</span> <span class="comment">// col0 - [in] coefficents for "x" unknown</span></div><div class="line"><a name="l01026"></a><span class="lineno"> 1026</span> <span class="comment">// col1 - [in] coefficents for "y" unknown</span></div><div class="line"><a name="l01027"></a><span class="lineno"> 1027</span> <span class="comment">// d0 - [in] constants</span></div><div class="line"><a name="l01028"></a><span class="lineno"> 1028</span> <span class="comment">// d1 - [in]</span></div><div class="line"><a name="l01029"></a><span class="lineno"> 1029</span> <span class="comment">// d2 - [in]</span></div><div class="line"><a name="l01030"></a><span class="lineno"> 1030</span> <span class="comment">// x - [out]</span></div><div class="line"><a name="l01031"></a><span class="lineno"> 1031</span> <span class="comment">// y - [out]</span></div><div class="line"><a name="l01032"></a><span class="lineno"> 1032</span> <span class="comment">// error - [out]</span></div><div class="line"><a name="l01033"></a><span class="lineno"> 1033</span> <span class="comment">// pivot_ratio - [out]</span></div><div class="line"><a name="l01034"></a><span class="lineno"> 1034</span> <span class="comment">//</span></div><div class="line"><a name="l01035"></a><span class="lineno"> 1035</span> <span class="comment">// Returns:</span></div><div class="line"><a name="l01036"></a><span class="lineno"> 1036</span> <span class="comment">// rank of the system. </span></div><div class="line"><a name="l01037"></a><span class="lineno"> 1037</span> <span class="comment">// If rank != 2, system is under determined</span></div><div class="line"><a name="l01038"></a><span class="lineno"> 1038</span> <span class="comment">// If rank = 2, then the solution is</span></div><div class="line"><a name="l01039"></a><span class="lineno"> 1039</span> <span class="comment">//</span></div><div class="line"><a name="l01040"></a><span class="lineno"> 1040</span> <span class="comment">// (*x)*[col0] + (*y)*[col1]</span></div><div class="line"><a name="l01041"></a><span class="lineno"> 1041</span> <span class="comment">// + (*error)*((col0 X col1)/|col0 X col1|)</span></div><div class="line"><a name="l01042"></a><span class="lineno"> 1042</span> <span class="comment">// = (d0,d1,d2).</span></div><div class="line"><a name="l01043"></a><span class="lineno"> 1043</span> ON_DECL</div><div class="line"><a name="l01044"></a><span class="lineno"> 1044</span> <span class="keywordtype">int</span> ON_Solve3x2( </div><div class="line"><a name="l01045"></a><span class="lineno"> 1045</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>[3], <span class="comment">// col0</span></div><div class="line"><a name="l01046"></a><span class="lineno"> 1046</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>[3], <span class="comment">// col1</span></div><div class="line"><a name="l01047"></a><span class="lineno"> 1047</span>  <span class="keywordtype">double</span>, <span class="comment">// d0</span></div><div class="line"><a name="l01048"></a><span class="lineno"> 1048</span>  <span class="keywordtype">double</span>, <span class="comment">// d1</span></div><div class="line"><a name="l01049"></a><span class="lineno"> 1049</span>  <span class="keywordtype">double</span>, <span class="comment">// d2</span></div><div class="line"><a name="l01050"></a><span class="lineno"> 1050</span>  <span class="keywordtype">double</span>*, <span class="comment">// x</span></div><div class="line"><a name="l01051"></a><span class="lineno"> 1051</span>  <span class="keywordtype">double</span>*, <span class="comment">// y</span></div><div class="line"><a name="l01052"></a><span class="lineno"> 1052</span>  <span class="keywordtype">double</span>*, <span class="comment">// error</span></div><div class="line"><a name="l01053"></a><span class="lineno"> 1053</span>  <span class="keywordtype">double</span>* <span class="comment">// pivot_ratio</span></div><div class="line"><a name="l01054"></a><span class="lineno"> 1054</span>  );</div><div class="line"><a name="l01055"></a><span class="lineno"> 1055</span> </div><div class="line"><a name="l01056"></a><span class="lineno"> 1056</span> <span class="comment">/* </span></div><div class="line"><a name="l01057"></a><span class="lineno"> 1057</span> <span class="comment">Description:</span></div><div class="line"><a name="l01058"></a><span class="lineno"> 1058</span> <span class="comment"> Use Gauss-Jordan elimination with full pivoting to solve </span></div><div class="line"><a name="l01059"></a><span class="lineno"> 1059</span> <span class="comment"> a system of 3 linear equations and 3 unknowns(x,y,z)</span></div><div class="line"><a name="l01060"></a><span class="lineno"> 1060</span> <span class="comment"></span></div><div class="line"><a name="l01061"></a><span class="lineno"> 1061</span> <span class="comment"> x*row0[0] + y*row0[1] + z*row0[2] = d0</span></div><div class="line"><a name="l01062"></a><span class="lineno"> 1062</span> <span class="comment"> x*row1[0] + y*row1[1] + z*row1[2] = d1</span></div><div class="line"><a name="l01063"></a><span class="lineno"> 1063</span> <span class="comment"> x*row2[0] + y*row2[1] + z*row2[2] = d2</span></div><div class="line"><a name="l01064"></a><span class="lineno"> 1064</span> <span class="comment"></span></div><div class="line"><a name="l01065"></a><span class="lineno"> 1065</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l01066"></a><span class="lineno"> 1066</span> <span class="comment"> row0 - [in] first row of 3x3 matrix</span></div><div class="line"><a name="l01067"></a><span class="lineno"> 1067</span> <span class="comment"> row1 - [in] second row of 3x3 matrix</span></div><div class="line"><a name="l01068"></a><span class="lineno"> 1068</span> <span class="comment"> row2 - [in] third row of 3x3 matrix</span></div><div class="line"><a name="l01069"></a><span class="lineno"> 1069</span> <span class="comment"> d0 - [in] </span></div><div class="line"><a name="l01070"></a><span class="lineno"> 1070</span> <span class="comment"> d1 - [in] </span></div><div class="line"><a name="l01071"></a><span class="lineno"> 1071</span> <span class="comment"> d2 - [in] (d0,d1,d2) right hand column of system</span></div><div class="line"><a name="l01072"></a><span class="lineno"> 1072</span> <span class="comment"> x_addr - [in] first unknown</span></div><div class="line"><a name="l01073"></a><span class="lineno"> 1073</span> <span class="comment"> y_addr - [in] second unknown</span></div><div class="line"><a name="l01074"></a><span class="lineno"> 1074</span> <span class="comment"> z_addr - [in] third unknown</span></div><div class="line"><a name="l01075"></a><span class="lineno"> 1075</span> <span class="comment"> pivot_ratio - [out] if not nullptr, the pivot ration is </span></div><div class="line"><a name="l01076"></a><span class="lineno"> 1076</span> <span class="comment"> returned here. If the pivot ratio is "small",</span></div><div class="line"><a name="l01077"></a><span class="lineno"> 1077</span> <span class="comment"> then the matrix may be singular or ill </span></div><div class="line"><a name="l01078"></a><span class="lineno"> 1078</span> <span class="comment"> conditioned. You should test the results </span></div><div class="line"><a name="l01079"></a><span class="lineno"> 1079</span> <span class="comment"> before you use them. "Small" depends on the</span></div><div class="line"><a name="l01080"></a><span class="lineno"> 1080</span> <span class="comment"> precision of the input coefficients and the</span></div><div class="line"><a name="l01081"></a><span class="lineno"> 1081</span> <span class="comment"> use of the solution. If you can't figure out</span></div><div class="line"><a name="l01082"></a><span class="lineno"> 1082</span> <span class="comment"> what "small" means in your case, then you</span></div><div class="line"><a name="l01083"></a><span class="lineno"> 1083</span> <span class="comment"> must check the solution before you use it.</span></div><div class="line"><a name="l01084"></a><span class="lineno"> 1084</span> <span class="comment"></span></div><div class="line"><a name="l01085"></a><span class="lineno"> 1085</span> <span class="comment">Returns:</span></div><div class="line"><a name="l01086"></a><span class="lineno"> 1086</span> <span class="comment"> The rank of the 3x3 matrix (0,1,2, or 3)</span></div><div class="line"><a name="l01087"></a><span class="lineno"> 1087</span> <span class="comment"> If ON_Solve3x3() is successful (returns 3), then</span></div><div class="line"><a name="l01088"></a><span class="lineno"> 1088</span> <span class="comment"> the solution is returned in </span></div><div class="line"><a name="l01089"></a><span class="lineno"> 1089</span> <span class="comment"> (*x_addr, *y_addr, *z_addr)</span></div><div class="line"><a name="l01090"></a><span class="lineno"> 1090</span> <span class="comment"> and *pivot_ratio = min(|pivots|)/max(|pivots|).</span></div><div class="line"><a name="l01091"></a><span class="lineno"> 1091</span> <span class="comment"> If the return code is < 3, then (0,0,0) is returned</span></div><div class="line"><a name="l01092"></a><span class="lineno"> 1092</span> <span class="comment"> as the "solution".</span></div><div class="line"><a name="l01093"></a><span class="lineno"> 1093</span> <span class="comment"></span></div><div class="line"><a name="l01094"></a><span class="lineno"> 1094</span> <span class="comment">See Also:</span></div><div class="line"><a name="l01095"></a><span class="lineno"> 1095</span> <span class="comment"> ON_Solve2x2</span></div><div class="line"><a name="l01096"></a><span class="lineno"> 1096</span> <span class="comment"> ON_Solve3x2</span></div><div class="line"><a name="l01097"></a><span class="lineno"> 1097</span> <span class="comment"> ON_Solve4x4</span></div><div class="line"><a name="l01098"></a><span class="lineno"> 1098</span> <span class="comment">*/</span></div><div class="line"><a name="l01099"></a><span class="lineno"> 1099</span> ON_DECL</div><div class="line"><a name="l01100"></a><span class="lineno"> 1100</span> <span class="keywordtype">int</span> ON_Solve3x3( </div><div class="line"><a name="l01101"></a><span class="lineno"> 1101</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> row0[3], </div><div class="line"><a name="l01102"></a><span class="lineno"> 1102</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> row1[3], </div><div class="line"><a name="l01103"></a><span class="lineno"> 1103</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> row2[3],</div><div class="line"><a name="l01104"></a><span class="lineno"> 1104</span>  <span class="keywordtype">double</span> d0, </div><div class="line"><a name="l01105"></a><span class="lineno"> 1105</span>  <span class="keywordtype">double</span> d1, </div><div class="line"><a name="l01106"></a><span class="lineno"> 1106</span>  <span class="keywordtype">double</span> d2,</div><div class="line"><a name="l01107"></a><span class="lineno"> 1107</span>  <span class="keywordtype">double</span>* x_addr, </div><div class="line"><a name="l01108"></a><span class="lineno"> 1108</span>  <span class="keywordtype">double</span>* y_addr, </div><div class="line"><a name="l01109"></a><span class="lineno"> 1109</span>  <span class="keywordtype">double</span>* z_addr,</div><div class="line"><a name="l01110"></a><span class="lineno"> 1110</span>  <span class="keywordtype">double</span>* pivot_ratio</div><div class="line"><a name="l01111"></a><span class="lineno"> 1111</span>  );</div><div class="line"><a name="l01112"></a><span class="lineno"> 1112</span> </div><div class="line"><a name="l01113"></a><span class="lineno"> 1113</span> <span class="comment">/* </span></div><div class="line"><a name="l01114"></a><span class="lineno"> 1114</span> <span class="comment">Description:</span></div><div class="line"><a name="l01115"></a><span class="lineno"> 1115</span> <span class="comment"> Use Gauss-Jordan elimination with full pivoting to solve </span></div><div class="line"><a name="l01116"></a><span class="lineno"> 1116</span> <span class="comment"> a system of 4 linear equations and 4 unknowns(x,y,z,w)</span></div><div class="line"><a name="l01117"></a><span class="lineno"> 1117</span> <span class="comment"></span></div><div class="line"><a name="l01118"></a><span class="lineno"> 1118</span> <span class="comment"> x*row0[0] + y*row0[1] + z*row0[2] + w*row0[3] = d0</span></div><div class="line"><a name="l01119"></a><span class="lineno"> 1119</span> <span class="comment"> x*row1[0] + y*row1[1] + z*row1[2] + w*row1[3] = d1</span></div><div class="line"><a name="l01120"></a><span class="lineno"> 1120</span> <span class="comment"> x*row2[0] + y*row2[1] + z*row2[2] + w*row2[3] = d2</span></div><div class="line"><a name="l01121"></a><span class="lineno"> 1121</span> <span class="comment"> x*row3[0] + y*row3[1] + z*row3[2] + w*row3[2] = d3</span></div><div class="line"><a name="l01122"></a><span class="lineno"> 1122</span> <span class="comment"></span></div><div class="line"><a name="l01123"></a><span class="lineno"> 1123</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l01124"></a><span class="lineno"> 1124</span> <span class="comment"> row0 - [in] first row of 4x4 matrix</span></div><div class="line"><a name="l01125"></a><span class="lineno"> 1125</span> <span class="comment"> row1 - [in] second row of 4x4 matrix</span></div><div class="line"><a name="l01126"></a><span class="lineno"> 1126</span> <span class="comment"> row2 - [in] third row of 4x4 matrix</span></div><div class="line"><a name="l01127"></a><span class="lineno"> 1127</span> <span class="comment"> row3 - [in] forth row of 4x4 matrix</span></div><div class="line"><a name="l01128"></a><span class="lineno"> 1128</span> <span class="comment"> d0 - [in] </span></div><div class="line"><a name="l01129"></a><span class="lineno"> 1129</span> <span class="comment"> d1 - [in] </span></div><div class="line"><a name="l01130"></a><span class="lineno"> 1130</span> <span class="comment"> d2 - [in] </span></div><div class="line"><a name="l01131"></a><span class="lineno"> 1131</span> <span class="comment"> d3 - [in] (d0,d1,d2,d3) right hand column of system</span></div><div class="line"><a name="l01132"></a><span class="lineno"> 1132</span> <span class="comment"> x_addr - [in] first unknown</span></div><div class="line"><a name="l01133"></a><span class="lineno"> 1133</span> <span class="comment"> y_addr - [in] second unknown</span></div><div class="line"><a name="l01134"></a><span class="lineno"> 1134</span> <span class="comment"> z_addr - [in] third unknown</span></div><div class="line"><a name="l01135"></a><span class="lineno"> 1135</span> <span class="comment"> w_addr - [in] forth unknown</span></div><div class="line"><a name="l01136"></a><span class="lineno"> 1136</span> <span class="comment"> pivot_ratio - [out] if not nullptr, the pivot ration is </span></div><div class="line"><a name="l01137"></a><span class="lineno"> 1137</span> <span class="comment"> returned here. If the pivot ratio is "small",</span></div><div class="line"><a name="l01138"></a><span class="lineno"> 1138</span> <span class="comment"> then the matrix may be singular or ill </span></div><div class="line"><a name="l01139"></a><span class="lineno"> 1139</span> <span class="comment"> conditioned. You should test the results </span></div><div class="line"><a name="l01140"></a><span class="lineno"> 1140</span> <span class="comment"> before you use them. "Small" depends on the</span></div><div class="line"><a name="l01141"></a><span class="lineno"> 1141</span> <span class="comment"> precision of the input coefficients and the</span></div><div class="line"><a name="l01142"></a><span class="lineno"> 1142</span> <span class="comment"> use of the solution. If you can't figure out</span></div><div class="line"><a name="l01143"></a><span class="lineno"> 1143</span> <span class="comment"> what "small" means in your case, then you</span></div><div class="line"><a name="l01144"></a><span class="lineno"> 1144</span> <span class="comment"> must check the solution before you use it.</span></div><div class="line"><a name="l01145"></a><span class="lineno"> 1145</span> <span class="comment"></span></div><div class="line"><a name="l01146"></a><span class="lineno"> 1146</span> <span class="comment">Returns:</span></div><div class="line"><a name="l01147"></a><span class="lineno"> 1147</span> <span class="comment"> The rank of the 4x4 matrix (0,1,2,3, or 4)</span></div><div class="line"><a name="l01148"></a><span class="lineno"> 1148</span> <span class="comment"> If ON_Solve4x4() is successful (returns 4), then</span></div><div class="line"><a name="l01149"></a><span class="lineno"> 1149</span> <span class="comment"> the solution is returned in </span></div><div class="line"><a name="l01150"></a><span class="lineno"> 1150</span> <span class="comment"> (*x_addr, *y_addr, *z_addr, *w_addr)</span></div><div class="line"><a name="l01151"></a><span class="lineno"> 1151</span> <span class="comment"> and *pivot_ratio = min(|pivots|)/max(|pivots|).</span></div><div class="line"><a name="l01152"></a><span class="lineno"> 1152</span> <span class="comment"> If the return code is < 4, then, it a solution exists,</span></div><div class="line"><a name="l01153"></a><span class="lineno"> 1153</span> <span class="comment"> on is returned. However YOU MUST CHECK THE SOLUTION</span></div><div class="line"><a name="l01154"></a><span class="lineno"> 1154</span> <span class="comment"> IF THE RETURN CODE IS < 4.</span></div><div class="line"><a name="l01155"></a><span class="lineno"> 1155</span> <span class="comment"></span></div><div class="line"><a name="l01156"></a><span class="lineno"> 1156</span> <span class="comment">See Also:</span></div><div class="line"><a name="l01157"></a><span class="lineno"> 1157</span> <span class="comment"> ON_Solve2x2</span></div><div class="line"><a name="l01158"></a><span class="lineno"> 1158</span> <span class="comment"> ON_Solve3x2</span></div><div class="line"><a name="l01159"></a><span class="lineno"> 1159</span> <span class="comment"> ON_Solve3x3</span></div><div class="line"><a name="l01160"></a><span class="lineno"> 1160</span> <span class="comment">*/</span></div><div class="line"><a name="l01161"></a><span class="lineno"> 1161</span> ON_DECL</div><div class="line"><a name="l01162"></a><span class="lineno"> 1162</span> <span class="keywordtype">int</span></div><div class="line"><a name="l01163"></a><span class="lineno"> 1163</span> ON_Solve4x4(</div><div class="line"><a name="l01164"></a><span class="lineno"> 1164</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> row0[4], </div><div class="line"><a name="l01165"></a><span class="lineno"> 1165</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> row1[4], </div><div class="line"><a name="l01166"></a><span class="lineno"> 1166</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> row2[4], </div><div class="line"><a name="l01167"></a><span class="lineno"> 1167</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> row3[4],</div><div class="line"><a name="l01168"></a><span class="lineno"> 1168</span>  <span class="keywordtype">double</span> d0, </div><div class="line"><a name="l01169"></a><span class="lineno"> 1169</span>  <span class="keywordtype">double</span> d1, </div><div class="line"><a name="l01170"></a><span class="lineno"> 1170</span>  <span class="keywordtype">double</span> d2, </div><div class="line"><a name="l01171"></a><span class="lineno"> 1171</span>  <span class="keywordtype">double</span> d3,</div><div class="line"><a name="l01172"></a><span class="lineno"> 1172</span>  <span class="keywordtype">double</span>* x_addr, </div><div class="line"><a name="l01173"></a><span class="lineno"> 1173</span>  <span class="keywordtype">double</span>* y_addr, </div><div class="line"><a name="l01174"></a><span class="lineno"> 1174</span>  <span class="keywordtype">double</span>* z_addr, </div><div class="line"><a name="l01175"></a><span class="lineno"> 1175</span>  <span class="keywordtype">double</span>* w_addr,</div><div class="line"><a name="l01176"></a><span class="lineno"> 1176</span>  <span class="keywordtype">double</span>* pivot_ratio</div><div class="line"><a name="l01177"></a><span class="lineno"> 1177</span>  );</div><div class="line"><a name="l01178"></a><span class="lineno"> 1178</span> </div><div class="line"><a name="l01179"></a><span class="lineno"> 1179</span> <span class="comment">/*</span></div><div class="line"><a name="l01180"></a><span class="lineno"> 1180</span> <span class="comment">Description:</span></div><div class="line"><a name="l01181"></a><span class="lineno"> 1181</span> <span class="comment"> Use Gauss-Jordan elimination to find a numerical </span></div><div class="line"><a name="l01182"></a><span class="lineno"> 1182</span> <span class="comment"> solution to M*X = B where M is a n x n matrix,</span></div><div class="line"><a name="l01183"></a><span class="lineno"> 1183</span> <span class="comment"> B is a known n-dimensional vector and X is</span></div><div class="line"><a name="l01184"></a><span class="lineno"> 1184</span> <span class="comment"> an unknown.</span></div><div class="line"><a name="l01185"></a><span class="lineno"> 1185</span> <span class="comment">Paramters:</span></div><div class="line"><a name="l01186"></a><span class="lineno"> 1186</span> <span class="comment"> bFullPivot - [in] if true, full pivoting is used,</span></div><div class="line"><a name="l01187"></a><span class="lineno"> 1187</span> <span class="comment"> otherwise partial pivoting is used. In rare</span></div><div class="line"><a name="l01188"></a><span class="lineno"> 1188</span> <span class="comment"> cases full pivoting can produce a more accurate</span></div><div class="line"><a name="l01189"></a><span class="lineno"> 1189</span> <span class="comment"> answer and never produces a less accurate answer.</span></div><div class="line"><a name="l01190"></a><span class="lineno"> 1190</span> <span class="comment"> However full pivoting is slower. If speed is an</span></div><div class="line"><a name="l01191"></a><span class="lineno"> 1191</span> <span class="comment"> issue, then experiement with bFullPivot=false</span></div><div class="line"><a name="l01192"></a><span class="lineno"> 1192</span> <span class="comment"> and see if it makes a difference. Otherwise,</span></div><div class="line"><a name="l01193"></a><span class="lineno"> 1193</span> <span class="comment"> set it to true.</span></div><div class="line"><a name="l01194"></a><span class="lineno"> 1194</span> <span class="comment"> bNormalize - [in]</span></div><div class="line"><a name="l01195"></a><span class="lineno"> 1195</span> <span class="comment"> If bNormalize is true, then the rows of the</span></div><div class="line"><a name="l01196"></a><span class="lineno"> 1196</span> <span class="comment"> matrix are scaled so the sum of their squares</span></div><div class="line"><a name="l01197"></a><span class="lineno"> 1197</span> <span class="comment"> is one. This doesn't make the solution more</span></div><div class="line"><a name="l01198"></a><span class="lineno"> 1198</span> <span class="comment"> accurate but in some cases it makes the pivot</span></div><div class="line"><a name="l01199"></a><span class="lineno"> 1199</span> <span class="comment"> ratio more meaningful. Set bNormalize to</span></div><div class="line"><a name="l01200"></a><span class="lineno"> 1200</span> <span class="comment"> false unless you have a reason for setting it</span></div><div class="line"><a name="l01201"></a><span class="lineno"> 1201</span> <span class="comment"> to true.</span></div><div class="line"><a name="l01202"></a><span class="lineno"> 1202</span> <span class="comment"> n - [in] size of the matrix and vectors.</span></div><div class="line"><a name="l01203"></a><span class="lineno"> 1203</span> <span class="comment"> M - [in] n x n matrix. The values in M are</span></div><div class="line"><a name="l01204"></a><span class="lineno"> 1204</span> <span class="comment"> changed as the solution is calculated.</span></div><div class="line"><a name="l01205"></a><span class="lineno"> 1205</span> <span class="comment"> If you need to preserve M for future use,</span></div><div class="line"><a name="l01206"></a><span class="lineno"> 1206</span> <span class="comment"> pass in a copy.</span></div><div class="line"><a name="l01207"></a><span class="lineno"> 1207</span> <span class="comment"> B - [in] n-dimensional vector. The values in</span></div><div class="line"><a name="l01208"></a><span class="lineno"> 1208</span> <span class="comment"> B are changed as the solution is calculated.</span></div><div class="line"><a name="l01209"></a><span class="lineno"> 1209</span> <span class="comment"> If you need to preserve B for future use,</span></div><div class="line"><a name="l01210"></a><span class="lineno"> 1210</span> <span class="comment"> pass in a copy.</span></div><div class="line"><a name="l01211"></a><span class="lineno"> 1211</span> <span class="comment"> X - [out] solution to M*X = B.</span></div><div class="line"><a name="l01212"></a><span class="lineno"> 1212</span> <span class="comment">Returns:</span></div><div class="line"><a name="l01213"></a><span class="lineno"> 1213</span> <span class="comment"> If the returned value is <= 0.0, the input matrix</span></div><div class="line"><a name="l01214"></a><span class="lineno"> 1214</span> <span class="comment"> has rank < n and no solution is returned in X.</span></div><div class="line"><a name="l01215"></a><span class="lineno"> 1215</span> <span class="comment"> If the returned value is > 0.0, then a solution is</span></div><div class="line"><a name="l01216"></a><span class="lineno"> 1216</span> <span class="comment"> returned in X and the returned value is the ratio</span></div><div class="line"><a name="l01217"></a><span class="lineno"> 1217</span> <span class="comment"> (minimum pivot)/(maximum pivot). This value is</span></div><div class="line"><a name="l01218"></a><span class="lineno"> 1218</span> <span class="comment"> called the pivot ratio and will be denoted "pr"</span></div><div class="line"><a name="l01219"></a><span class="lineno"> 1219</span> <span class="comment"> the discussion below. If pr <= 1e-15, then</span></div><div class="line"><a name="l01220"></a><span class="lineno"> 1220</span> <span class="comment"> M was nearly degenerate and the solution should be</span></div><div class="line"><a name="l01221"></a><span class="lineno"> 1221</span> <span class="comment"> used with caution. If an accurate solution is</span></div><div class="line"><a name="l01222"></a><span class="lineno"> 1222</span> <span class="comment"> critcial, then check the solution anytime pr <= 1e-10</span></div><div class="line"><a name="l01223"></a><span class="lineno"> 1223</span> <span class="comment"> In general, the difference between M*X and B will be</span></div><div class="line"><a name="l01224"></a><span class="lineno"> 1224</span> <span class="comment"> reasonably small. However, when the pr is small</span></div><div class="line"><a name="l01225"></a><span class="lineno"> 1225</span> <span class="comment"> there tend to be vector E, substantually different</span></div><div class="line"><a name="l01226"></a><span class="lineno"> 1226</span> <span class="comment"> from zero, such that M*(X+E) - B is also reasonably</span></div><div class="line"><a name="l01227"></a><span class="lineno"> 1227</span> <span class="comment"> small.</span></div><div class="line"><a name="l01228"></a><span class="lineno"> 1228</span> <span class="comment">See Also:</span></div><div class="line"><a name="l01229"></a><span class="lineno"> 1229</span> <span class="comment"> ON_Solve2x2</span></div><div class="line"><a name="l01230"></a><span class="lineno"> 1230</span> <span class="comment"> ON_Solve3x3</span></div><div class="line"><a name="l01231"></a><span class="lineno"> 1231</span> <span class="comment"> ON_Solve4x4</span></div><div class="line"><a name="l01232"></a><span class="lineno"> 1232</span> <span class="comment"> ON_Solve3x2</span></div><div class="line"><a name="l01233"></a><span class="lineno"> 1233</span> <span class="comment">*/</span></div><div class="line"><a name="l01234"></a><span class="lineno"> 1234</span> ON_DECL</div><div class="line"><a name="l01235"></a><span class="lineno"> 1235</span> <span class="keywordtype">double</span> ON_SolveNxN(<span class="keywordtype">bool</span> bFullPivot, <span class="keywordtype">bool</span> bNormalize, <span class="keywordtype">int</span> n, <span class="keywordtype">double</span>* M[], <span class="keywordtype">double</span> B[], <span class="keywordtype">double</span> X[]);</div><div class="line"><a name="l01236"></a><span class="lineno"> 1236</span> </div><div class="line"><a name="l01237"></a><span class="lineno"> 1237</span> </div><div class="line"><a name="l01238"></a><span class="lineno"> 1238</span> <span class="comment">/*</span></div><div class="line"><a name="l01239"></a><span class="lineno"> 1239</span> <span class="comment">Description:</span></div><div class="line"><a name="l01240"></a><span class="lineno"> 1240</span> <span class="comment">Find the eigen values and eigen vectors of a real symmetric</span></div><div class="line"><a name="l01241"></a><span class="lineno"> 1241</span> <span class="comment">3x3 matrix</span></div><div class="line"><a name="l01242"></a><span class="lineno"> 1242</span> <span class="comment"></span></div><div class="line"><a name="l01243"></a><span class="lineno"> 1243</span> <span class="comment">A D F</span></div><div class="line"><a name="l01244"></a><span class="lineno"> 1244</span> <span class="comment">D B E</span></div><div class="line"><a name="l01245"></a><span class="lineno"> 1245</span> <span class="comment">F E C</span></div><div class="line"><a name="l01246"></a><span class="lineno"> 1246</span> <span class="comment"></span></div><div class="line"><a name="l01247"></a><span class="lineno"> 1247</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l01248"></a><span class="lineno"> 1248</span> <span class="comment">A - [in] matrix entry</span></div><div class="line"><a name="l01249"></a><span class="lineno"> 1249</span> <span class="comment">B - [in] matrix entry</span></div><div class="line"><a name="l01250"></a><span class="lineno"> 1250</span> <span class="comment">C - [in] matrix entry</span></div><div class="line"><a name="l01251"></a><span class="lineno"> 1251</span> <span class="comment">D - [in] matrix entry</span></div><div class="line"><a name="l01252"></a><span class="lineno"> 1252</span> <span class="comment">E - [in] matrix entry</span></div><div class="line"><a name="l01253"></a><span class="lineno"> 1253</span> <span class="comment">F - [in] matrix entry</span></div><div class="line"><a name="l01254"></a><span class="lineno"> 1254</span> <span class="comment">e1 - [out] eigen value</span></div><div class="line"><a name="l01255"></a><span class="lineno"> 1255</span> <span class="comment">E1 - [out] eigen vector with eigen value e1</span></div><div class="line"><a name="l01256"></a><span class="lineno"> 1256</span> <span class="comment">e2 - [out] eigen value</span></div><div class="line"><a name="l01257"></a><span class="lineno"> 1257</span> <span class="comment">E2 - [out] eigen vector with eigen value e2</span></div><div class="line"><a name="l01258"></a><span class="lineno"> 1258</span> <span class="comment">e3 - [out] eigen value</span></div><div class="line"><a name="l01259"></a><span class="lineno"> 1259</span> <span class="comment">E3 - [out] eigen vector with eigen value e3</span></div><div class="line"><a name="l01260"></a><span class="lineno"> 1260</span> <span class="comment">Returns:</span></div><div class="line"><a name="l01261"></a><span class="lineno"> 1261</span> <span class="comment">True if successful.</span></div><div class="line"><a name="l01262"></a><span class="lineno"> 1262</span> <span class="comment">*/</span></div><div class="line"><a name="l01263"></a><span class="lineno"> 1263</span> ON_DECL</div><div class="line"><a name="l01264"></a><span class="lineno"> 1264</span> <span class="keywordtype">bool</span> ON_Sym3x3EigenSolver(<span class="keywordtype">double</span> A, <span class="keywordtype">double</span> B, <span class="keywordtype">double</span> C,</div><div class="line"><a name="l01265"></a><span class="lineno"> 1265</span>  <span class="keywordtype">double</span> D, <span class="keywordtype">double</span> E, <span class="keywordtype">double</span> F,</div><div class="line"><a name="l01266"></a><span class="lineno"> 1266</span>  <span class="keywordtype">double</span>* e1, <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& E1,</div><div class="line"><a name="l01267"></a><span class="lineno"> 1267</span>  <span class="keywordtype">double</span>* e2, <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& E2,</div><div class="line"><a name="l01268"></a><span class="lineno"> 1268</span>  <span class="keywordtype">double</span>* e3, <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& E3 );</div><div class="line"><a name="l01269"></a><span class="lineno"> 1269</span> </div><div class="line"><a name="l01270"></a><span class="lineno"> 1270</span> <span class="comment">// return false if determinant is (nearly) singular</span></div><div class="line"><a name="l01271"></a><span class="lineno"> 1271</span> ON_DECL</div><div class="line"><a name="l01272"></a><span class="lineno"> 1272</span> <span class="keywordtype">bool</span> ON_EvJacobian( </div><div class="line"><a name="l01273"></a><span class="lineno"> 1273</span>  <span class="keywordtype">double</span>, <span class="comment">// ds o ds</span></div><div class="line"><a name="l01274"></a><span class="lineno"> 1274</span>  <span class="keywordtype">double</span>, <span class="comment">// ds o dt</span></div><div class="line"><a name="l01275"></a><span class="lineno"> 1275</span>  <span class="keywordtype">double</span>, <span class="comment">// dt o dt</span></div><div class="line"><a name="l01276"></a><span class="lineno"> 1276</span>  <span class="keywordtype">double</span>* <span class="comment">// jacobian = determinant ( ds_o_ds dt_o_dt / ds_o_dt ds_o_dt )</span></div><div class="line"><a name="l01277"></a><span class="lineno"> 1277</span>  );</div><div class="line"><a name="l01278"></a><span class="lineno"> 1278</span> </div><div class="line"><a name="l01279"></a><span class="lineno"> 1279</span> <span class="comment">/*</span></div><div class="line"><a name="l01280"></a><span class="lineno"> 1280</span> <span class="comment">Description:</span></div><div class="line"><a name="l01281"></a><span class="lineno"> 1281</span> <span class="comment"> Finds scalars x and y so that the component of V in the plane</span></div><div class="line"><a name="l01282"></a><span class="lineno"> 1282</span> <span class="comment"> of A and B is x*A + y*B.</span></div><div class="line"><a name="l01283"></a><span class="lineno"> 1283</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l01284"></a><span class="lineno"> 1284</span> <span class="comment"> V - [in]</span></div><div class="line"><a name="l01285"></a><span class="lineno"> 1285</span> <span class="comment"> A - [in] nonzero and not parallel to B</span></div><div class="line"><a name="l01286"></a><span class="lineno"> 1286</span> <span class="comment"> B - [in] nonzero and not parallel to A</span></div><div class="line"><a name="l01287"></a><span class="lineno"> 1287</span> <span class="comment"> x - [out]</span></div><div class="line"><a name="l01288"></a><span class="lineno"> 1288</span> <span class="comment"> y - [out]</span></div><div class="line"><a name="l01289"></a><span class="lineno"> 1289</span> <span class="comment">Returns:</span></div><div class="line"><a name="l01290"></a><span class="lineno"> 1290</span> <span class="comment"> 1 - The rank of the problem is 2. The decomposition is unique.</span></div><div class="line"><a name="l01291"></a><span class="lineno"> 1291</span> <span class="comment"> 0 - The rank less than 2. Either there is no solution or there</span></div><div class="line"><a name="l01292"></a><span class="lineno"> 1292</span> <span class="comment"> are infinitely many solutions.</span></div><div class="line"><a name="l01293"></a><span class="lineno"> 1293</span> <span class="comment"></span></div><div class="line"><a name="l01294"></a><span class="lineno"> 1294</span> <span class="comment">See Also:</span></div><div class="line"><a name="l01295"></a><span class="lineno"> 1295</span> <span class="comment"> ON_Solve2x2</span></div><div class="line"><a name="l01296"></a><span class="lineno"> 1296</span> <span class="comment">*/</span></div><div class="line"><a name="l01297"></a><span class="lineno"> 1297</span> ON_DECL</div><div class="line"><a name="l01298"></a><span class="lineno"> 1298</span> <span class="keywordtype">int</span> ON_DecomposeVector(</div><div class="line"><a name="l01299"></a><span class="lineno"> 1299</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& V,</div><div class="line"><a name="l01300"></a><span class="lineno"> 1300</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& A,</div><div class="line"><a name="l01301"></a><span class="lineno"> 1301</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& B,</div><div class="line"><a name="l01302"></a><span class="lineno"> 1302</span>  <span class="keywordtype">double</span>* x, <span class="keywordtype">double</span>* y</div><div class="line"><a name="l01303"></a><span class="lineno"> 1303</span>  );</div><div class="line"><a name="l01304"></a><span class="lineno"> 1304</span> </div><div class="line"><a name="l01305"></a><span class="lineno"> 1305</span> </div><div class="line"><a name="l01306"></a><span class="lineno"> 1306</span> <span class="comment">/*</span></div><div class="line"><a name="l01307"></a><span class="lineno"> 1307</span> <span class="comment">Description:</span></div><div class="line"><a name="l01308"></a><span class="lineno"> 1308</span> <span class="comment"> Evaluate partial derivatives of surface unit normal</span></div><div class="line"><a name="l01309"></a><span class="lineno"> 1309</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l01310"></a><span class="lineno"> 1310</span> <span class="comment"> ds - [in]</span></div><div class="line"><a name="l01311"></a><span class="lineno"> 1311</span> <span class="comment"> dt - [in] surface first partial derivatives</span></div><div class="line"><a name="l01312"></a><span class="lineno"> 1312</span> <span class="comment"> dss - [in]</span></div><div class="line"><a name="l01313"></a><span class="lineno"> 1313</span> <span class="comment"> dst - [in]</span></div><div class="line"><a name="l01314"></a><span class="lineno"> 1314</span> <span class="comment"> dtt - [in] surface second partial derivatives</span></div><div class="line"><a name="l01315"></a><span class="lineno"> 1315</span> <span class="comment"> ns - [out]</span></div><div class="line"><a name="l01316"></a><span class="lineno"> 1316</span> <span class="comment"> nt - [out] First partial derivatives of surface unit normal</span></div><div class="line"><a name="l01317"></a><span class="lineno"> 1317</span> <span class="comment"> (If the Jacobian is degenerate, ns and nt are set to zero.)</span></div><div class="line"><a name="l01318"></a><span class="lineno"> 1318</span> <span class="comment">Returns:</span></div><div class="line"><a name="l01319"></a><span class="lineno"> 1319</span> <span class="comment"> true if Jacobian is nondegenerate</span></div><div class="line"><a name="l01320"></a><span class="lineno"> 1320</span> <span class="comment"> false if Jacobian is degenerate</span></div><div class="line"><a name="l01321"></a><span class="lineno"> 1321</span> <span class="comment">*/</span></div><div class="line"><a name="l01322"></a><span class="lineno"> 1322</span> ON_DECL</div><div class="line"><a name="l01323"></a><span class="lineno"> 1323</span> <span class="keywordtype">bool</span> ON_EvNormalPartials(</div><div class="line"><a name="l01324"></a><span class="lineno"> 1324</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& ds,</div><div class="line"><a name="l01325"></a><span class="lineno"> 1325</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& dt,</div><div class="line"><a name="l01326"></a><span class="lineno"> 1326</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& dss,</div><div class="line"><a name="l01327"></a><span class="lineno"> 1327</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& dst,</div><div class="line"><a name="l01328"></a><span class="lineno"> 1328</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& dtt,</div><div class="line"><a name="l01329"></a><span class="lineno"> 1329</span>  <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& ns,</div><div class="line"><a name="l01330"></a><span class="lineno"> 1330</span>  <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& nt</div><div class="line"><a name="l01331"></a><span class="lineno"> 1331</span>  );</div><div class="line"><a name="l01332"></a><span class="lineno"> 1332</span> </div><div class="line"><a name="l01333"></a><span class="lineno"> 1333</span> ON_DECL</div><div class="line"><a name="l01334"></a><span class="lineno"> 1334</span> <span class="keywordtype">bool</span> </div><div class="line"><a name="l01335"></a><span class="lineno"> 1335</span> ON_Pullback3dVector( <span class="comment">// use to pull 3d vector back to surface parameter space</span></div><div class="line"><a name="l01336"></a><span class="lineno"> 1336</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// 3d vector</span></div><div class="line"><a name="l01337"></a><span class="lineno"> 1337</span>  <span class="keywordtype">double</span>, <span class="comment">// signed distance from vector location to closet point on surface</span></div><div class="line"><a name="l01338"></a><span class="lineno"> 1338</span>  <span class="comment">// < 0 if point is below with respect to Du x Dv</span></div><div class="line"><a name="l01339"></a><span class="lineno"> 1339</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// ds surface first partials</span></div><div class="line"><a name="l01340"></a><span class="lineno"> 1340</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// dt</span></div><div class="line"><a name="l01341"></a><span class="lineno"> 1341</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// dss surface 2nd partials</span></div><div class="line"><a name="l01342"></a><span class="lineno"> 1342</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// dst (used only when dist != 0)</span></div><div class="line"><a name="l01343"></a><span class="lineno"> 1343</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// dtt</span></div><div class="line"><a name="l01344"></a><span class="lineno"> 1344</span>  <a class="code" href="class_o_n__2d_vector.html">ON_2dVector</a>& <span class="comment">// pullback</span></div><div class="line"><a name="l01345"></a><span class="lineno"> 1345</span>  );</div><div class="line"><a name="l01346"></a><span class="lineno"> 1346</span> </div><div class="line"><a name="l01347"></a><span class="lineno"> 1347</span> ON_DECL</div><div class="line"><a name="l01348"></a><span class="lineno"> 1348</span> <span class="keywordtype">bool</span> </div><div class="line"><a name="l01349"></a><span class="lineno"> 1349</span> ON_GetParameterTolerance(</div><div class="line"><a name="l01350"></a><span class="lineno"> 1350</span>  <span class="keywordtype">double</span>, <span class="comment">// t0 domain</span></div><div class="line"><a name="l01351"></a><span class="lineno"> 1351</span>  <span class="keywordtype">double</span>, <span class="comment">// t1 </span></div><div class="line"><a name="l01352"></a><span class="lineno"> 1352</span>  <span class="keywordtype">double</span>, <span class="comment">// t parameter in domain</span></div><div class="line"><a name="l01353"></a><span class="lineno"> 1353</span>  <span class="keywordtype">double</span>*, <span class="comment">// tminus parameter tolerance (tminus, tplus) returned here</span></div><div class="line"><a name="l01354"></a><span class="lineno"> 1354</span>  <span class="keywordtype">double</span>* <span class="comment">// tplus</span></div><div class="line"><a name="l01355"></a><span class="lineno"> 1355</span>  );</div><div class="line"><a name="l01356"></a><span class="lineno"> 1356</span> </div><div class="line"><a name="l01357"></a><span class="lineno"> 1357</span> </div><div class="line"><a name="l01358"></a><span class="lineno"> 1358</span> ON_DECL</div><div class="line"><a name="l01359"></a><span class="lineno"> 1359</span> <span class="keywordtype">bool</span> ON_EvNormal(</div><div class="line"><a name="l01360"></a><span class="lineno"> 1360</span>  <span class="keywordtype">int</span>, <span class="comment">// limit_dir 0=default,1=from quadrant I, 2 = from quadrant II, ...</span></div><div class="line"><a name="l01361"></a><span class="lineno"> 1361</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// first partials (Du,Dv)</span></div><div class="line"><a name="l01362"></a><span class="lineno"> 1362</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// optional second partials (Duu, Duv, Dvv)</span></div><div class="line"><a name="l01363"></a><span class="lineno"> 1363</span>  <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& <span class="comment">// unit normal returned here</span></div><div class="line"><a name="l01364"></a><span class="lineno"> 1364</span>  );</div><div class="line"><a name="l01365"></a><span class="lineno"> 1365</span> </div><div class="line"><a name="l01366"></a><span class="lineno"> 1366</span> <span class="comment">// returns false if the returned tangent is zero</span></div><div class="line"><a name="l01367"></a><span class="lineno"> 1367</span> ON_DECL</div><div class="line"><a name="l01368"></a><span class="lineno"> 1368</span> <span class="keywordtype">bool</span> ON_EvTangent(</div><div class="line"><a name="l01369"></a><span class="lineno"> 1369</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// first derivative</span></div><div class="line"><a name="l01370"></a><span class="lineno"> 1370</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// second derivative</span></div><div class="line"><a name="l01371"></a><span class="lineno"> 1371</span>  <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& <span class="comment">// Unit tangent returned here</span></div><div class="line"><a name="l01372"></a><span class="lineno"> 1372</span>  );</div><div class="line"><a name="l01373"></a><span class="lineno"> 1373</span> </div><div class="line"><a name="l01374"></a><span class="lineno"> 1374</span> <span class="comment">// returns false if first derivtive is zero</span></div><div class="line"><a name="l01375"></a><span class="lineno"> 1375</span> ON_DECL</div><div class="line"><a name="l01376"></a><span class="lineno"> 1376</span> <span class="keywordtype">bool</span> ON_EvCurvature(</div><div class="line"><a name="l01377"></a><span class="lineno"> 1377</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// first derivative</span></div><div class="line"><a name="l01378"></a><span class="lineno"> 1378</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// second derivative</span></div><div class="line"><a name="l01379"></a><span class="lineno"> 1379</span>  <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// Unit tangent returned here</span></div><div class="line"><a name="l01380"></a><span class="lineno"> 1380</span>  <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& <span class="comment">// Curvature returned here</span></div><div class="line"><a name="l01381"></a><span class="lineno"> 1381</span>  );</div><div class="line"><a name="l01382"></a><span class="lineno"> 1382</span> </div><div class="line"><a name="l01383"></a><span class="lineno"> 1383</span> ON_DECL</div><div class="line"><a name="l01384"></a><span class="lineno"> 1384</span> <span class="keywordtype">bool</span> ON_EvPrincipalCurvatures( </div><div class="line"><a name="l01385"></a><span class="lineno"> 1385</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// Ds,</span></div><div class="line"><a name="l01386"></a><span class="lineno"> 1386</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// Dt,</span></div><div class="line"><a name="l01387"></a><span class="lineno"> 1387</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// Dss,</span></div><div class="line"><a name="l01388"></a><span class="lineno"> 1388</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// Dst,</span></div><div class="line"><a name="l01389"></a><span class="lineno"> 1389</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// Dtt,</span></div><div class="line"><a name="l01390"></a><span class="lineno"> 1390</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// N, // unit normal to surface (use ON_EvNormal())</span></div><div class="line"><a name="l01391"></a><span class="lineno"> 1391</span>  <span class="keywordtype">double</span>*, <span class="comment">// gauss, // = Gaussian curvature = kappa1*kappa2</span></div><div class="line"><a name="l01392"></a><span class="lineno"> 1392</span>  <span class="keywordtype">double</span>*, <span class="comment">// mean, // = mean curvature = (kappa1+kappa2)/2</span></div><div class="line"><a name="l01393"></a><span class="lineno"> 1393</span>  <span class="keywordtype">double</span>*, <span class="comment">// kappa1, // = largest principal curvature value (may be negative)</span></div><div class="line"><a name="l01394"></a><span class="lineno"> 1394</span>  <span class="keywordtype">double</span>*, <span class="comment">// kappa2, // = smallest principal curvature value (may be negative)</span></div><div class="line"><a name="l01395"></a><span class="lineno"> 1395</span>  <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// K1, // kappa1 unit principal curvature direction</span></div><div class="line"><a name="l01396"></a><span class="lineno"> 1396</span>  <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& <span class="comment">// K2 // kappa2 unit principal curvature direction</span></div><div class="line"><a name="l01397"></a><span class="lineno"> 1397</span>  <span class="comment">// output K1,K2,N is right handed frame</span></div><div class="line"><a name="l01398"></a><span class="lineno"> 1398</span>  );</div><div class="line"><a name="l01399"></a><span class="lineno"> 1399</span> </div><div class="line"><a name="l01400"></a><span class="lineno"> 1400</span> ON_DECL</div><div class="line"><a name="l01401"></a><span class="lineno"> 1401</span> <span class="keywordtype">bool</span> ON_EvPrincipalCurvatures( </div><div class="line"><a name="l01402"></a><span class="lineno"> 1402</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// Ds,</span></div><div class="line"><a name="l01403"></a><span class="lineno"> 1403</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// Dt,</span></div><div class="line"><a name="l01404"></a><span class="lineno"> 1404</span>  <span class="keywordtype">double</span> l, <span class="comment">// Dss*N Second fundamental form coefficients</span></div><div class="line"><a name="l01405"></a><span class="lineno"> 1405</span>  <span class="keywordtype">double</span> m, <span class="comment">// Dst*N,</span></div><div class="line"><a name="l01406"></a><span class="lineno"> 1406</span>  <span class="keywordtype">double</span> n, <span class="comment">// Dtt*N,</span></div><div class="line"><a name="l01407"></a><span class="lineno"> 1407</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// N, // unit normal to surface (use ON_EvNormal())</span></div><div class="line"><a name="l01408"></a><span class="lineno"> 1408</span>  <span class="keywordtype">double</span>*, <span class="comment">// gauss, // = Gaussian curvature = kappa1*kappa2</span></div><div class="line"><a name="l01409"></a><span class="lineno"> 1409</span>  <span class="keywordtype">double</span>*, <span class="comment">// mean, // = mean curvature = (kappa1+kappa2)/2</span></div><div class="line"><a name="l01410"></a><span class="lineno"> 1410</span>  <span class="keywordtype">double</span>*, <span class="comment">// kappa1, // = largest principal curvature value (may be negative)</span></div><div class="line"><a name="l01411"></a><span class="lineno"> 1411</span>  <span class="keywordtype">double</span>*, <span class="comment">// kappa2, // = smallest principal curvature value (may be negative)</span></div><div class="line"><a name="l01412"></a><span class="lineno"> 1412</span>  <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// K1, // kappa1 unit principal curvature direction</span></div><div class="line"><a name="l01413"></a><span class="lineno"> 1413</span>  <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& <span class="comment">// K2 // kappa2 unit principal curvature direction</span></div><div class="line"><a name="l01414"></a><span class="lineno"> 1414</span>  <span class="comment">// output K1,K2,N is right handed frame</span></div><div class="line"><a name="l01415"></a><span class="lineno"> 1415</span>  );</div><div class="line"><a name="l01416"></a><span class="lineno"> 1416</span> </div><div class="line"><a name="l01417"></a><span class="lineno"> 1417</span> <span class="comment">/*</span></div><div class="line"><a name="l01418"></a><span class="lineno"> 1418</span> <span class="comment">Description:</span></div><div class="line"><a name="l01419"></a><span class="lineno"> 1419</span> <span class="comment"> Evaluate sectional curvature from surface derivatives and </span></div><div class="line"><a name="l01420"></a><span class="lineno"> 1420</span> <span class="comment"> section plane normal.</span></div><div class="line"><a name="l01421"></a><span class="lineno"> 1421</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l01422"></a><span class="lineno"> 1422</span> <span class="comment"> S10, S01 - [in]</span></div><div class="line"><a name="l01423"></a><span class="lineno"> 1423</span> <span class="comment"> surface 1st partial derivatives</span></div><div class="line"><a name="l01424"></a><span class="lineno"> 1424</span> <span class="comment"> S20, S11, S02 - [in]</span></div><div class="line"><a name="l01425"></a><span class="lineno"> 1425</span> <span class="comment"> surface 2nd partial derivatives</span></div><div class="line"><a name="l01426"></a><span class="lineno"> 1426</span> <span class="comment"> planeNormal - [in]</span></div><div class="line"><a name="l01427"></a><span class="lineno"> 1427</span> <span class="comment"> unit normal to section plane</span></div><div class="line"><a name="l01428"></a><span class="lineno"> 1428</span> <span class="comment"> K - [out] Sectional curvature</span></div><div class="line"><a name="l01429"></a><span class="lineno"> 1429</span> <span class="comment"> Curvature of the intersection curve of the surface</span></div><div class="line"><a name="l01430"></a><span class="lineno"> 1430</span> <span class="comment"> and plane through the surface point where the partial</span></div><div class="line"><a name="l01431"></a><span class="lineno"> 1431</span> <span class="comment"> derivatives were evaluationed.</span></div><div class="line"><a name="l01432"></a><span class="lineno"> 1432</span> <span class="comment">Returns:</span></div><div class="line"><a name="l01433"></a><span class="lineno"> 1433</span> <span class="comment"> True if successful.</span></div><div class="line"><a name="l01434"></a><span class="lineno"> 1434</span> <span class="comment"> False if first partials are not linearly independent, in</span></div><div class="line"><a name="l01435"></a><span class="lineno"> 1435</span> <span class="comment"> which case the K is set to zero.</span></div><div class="line"><a name="l01436"></a><span class="lineno"> 1436</span> <span class="comment">*/</span></div><div class="line"><a name="l01437"></a><span class="lineno"> 1437</span> ON_DECL</div><div class="line"><a name="l01438"></a><span class="lineno"> 1438</span> <span class="keywordtype">bool</span> ON_EvSectionalCurvature( </div><div class="line"><a name="l01439"></a><span class="lineno"> 1439</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& S10, </div><div class="line"><a name="l01440"></a><span class="lineno"> 1440</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& S01,</div><div class="line"><a name="l01441"></a><span class="lineno"> 1441</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& S20, </div><div class="line"><a name="l01442"></a><span class="lineno"> 1442</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& S11, </div><div class="line"><a name="l01443"></a><span class="lineno"> 1443</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& S02,</div><div class="line"><a name="l01444"></a><span class="lineno"> 1444</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& planeNormal,</div><div class="line"><a name="l01445"></a><span class="lineno"> 1445</span>  <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& K </div><div class="line"><a name="l01446"></a><span class="lineno"> 1446</span>  );</div><div class="line"><a name="l01447"></a><span class="lineno"> 1447</span> </div><div class="line"><a name="l01448"></a><span class="lineno"> 1448</span> </div><div class="line"><a name="l01449"></a><span class="lineno"> 1449</span> ON_DECL</div><div class="line"><a name="l01450"></a><span class="lineno"> 1450</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a> ON_NormalCurvature( </div><div class="line"><a name="l01451"></a><span class="lineno"> 1451</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// surface 1rst partial (Ds)</span></div><div class="line"><a name="l01452"></a><span class="lineno"> 1452</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// surface 1rst partial (Dt)</span></div><div class="line"><a name="l01453"></a><span class="lineno"> 1453</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// surface 1rst partial (Dss)</span></div><div class="line"><a name="l01454"></a><span class="lineno"> 1454</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// surface 1rst partial (Dst)</span></div><div class="line"><a name="l01455"></a><span class="lineno"> 1455</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// surface 1rst partial (Dtt)</span></div><div class="line"><a name="l01456"></a><span class="lineno"> 1456</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>&, <span class="comment">// surface unit normal</span></div><div class="line"><a name="l01457"></a><span class="lineno"> 1457</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a>& <span class="comment">// unit tangent direction</span></div><div class="line"><a name="l01458"></a><span class="lineno"> 1458</span>  );</div><div class="line"><a name="l01459"></a><span class="lineno"> 1459</span> </div><div class="line"><a name="l01460"></a><span class="lineno"> 1460</span> <span class="comment">/*</span></div><div class="line"><a name="l01461"></a><span class="lineno"> 1461</span> <span class="comment">Description:</span></div><div class="line"><a name="l01462"></a><span class="lineno"> 1462</span> <span class="comment"> Determing if two curvatrues are different enough</span></div><div class="line"><a name="l01463"></a><span class="lineno"> 1463</span> <span class="comment"> to qualify as a curvature discontinuity.</span></div><div class="line"><a name="l01464"></a><span class="lineno"> 1464</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l01465"></a><span class="lineno"> 1465</span> <span class="comment"> Km - [in]</span></div><div class="line"><a name="l01466"></a><span class="lineno"> 1466</span> <span class="comment"> Kp - [in]</span></div><div class="line"><a name="l01467"></a><span class="lineno"> 1467</span> <span class="comment"> Km and Kp should be curvatures evaluated at the same</span></div><div class="line"><a name="l01468"></a><span class="lineno"> 1468</span> <span class="comment"> parameters using limits from below (minus) and above (plus).</span></div><div class="line"><a name="l01469"></a><span class="lineno"> 1469</span> <span class="comment"> The assumption is that you have already compared the</span></div><div class="line"><a name="l01470"></a><span class="lineno"> 1470</span> <span class="comment"> points and tangents and consider to curve to be G1 at the</span></div><div class="line"><a name="l01471"></a><span class="lineno"> 1471</span> <span class="comment"> point in question.</span></div><div class="line"><a name="l01472"></a><span class="lineno"> 1472</span> <span class="comment"> cos_angle_tolerance - [in]</span></div><div class="line"><a name="l01473"></a><span class="lineno"> 1473</span> <span class="comment"> If the inut value of cos_angle_tolerance >= -1.0</span></div><div class="line"><a name="l01474"></a><span class="lineno"> 1474</span> <span class="comment"> and cos_angle_tolerance <= 1.0 and</span></div><div class="line"><a name="l01475"></a><span class="lineno"> 1475</span> <span class="comment"> Km o Kp < cos_angle_tolerance*|Km|*|Kp|, then</span></div><div class="line"><a name="l01476"></a><span class="lineno"> 1476</span> <span class="comment"> true is returned. Otherwise it is assumed Km and Kp</span></div><div class="line"><a name="l01477"></a><span class="lineno"> 1477</span> <span class="comment"> are parallel. If the curve being tested is nonplanar,</span></div><div class="line"><a name="l01478"></a><span class="lineno"> 1478</span> <span class="comment"> then use something like cos(2*tangent angle tolerance)</span></div><div class="line"><a name="l01479"></a><span class="lineno"> 1479</span> <span class="comment"> for this parameter. If the curve being tested is planar,</span></div><div class="line"><a name="l01480"></a><span class="lineno"> 1480</span> <span class="comment"> then 0.0 will work fine.</span></div><div class="line"><a name="l01481"></a><span class="lineno"> 1481</span> <span class="comment"> curvature_tolerance - [in]</span></div><div class="line"><a name="l01482"></a><span class="lineno"> 1482</span> <span class="comment"> If |Kp-Km| <= curvature_tolerance,</span></div><div class="line"><a name="l01483"></a><span class="lineno"> 1483</span> <span class="comment"> then false is returned, otherwise other tests are used</span></div><div class="line"><a name="l01484"></a><span class="lineno"> 1484</span> <span class="comment"> to determing continuity.</span></div><div class="line"><a name="l01485"></a><span class="lineno"> 1485</span> <span class="comment"> zero_curvature - [in] (ignored if < 2^-110 = 7.7037197787136e-34)</span></div><div class="line"><a name="l01486"></a><span class="lineno"> 1486</span> <span class="comment"> If |K| <= zero_curvature, then K is treated as zero.</span></div><div class="line"><a name="l01487"></a><span class="lineno"> 1487</span> <span class="comment"> When in doubt, use ON_ZERO_CURVATURE_TOLERANCE.</span></div><div class="line"><a name="l01488"></a><span class="lineno"> 1488</span> <span class="comment"> radius_tolerance - [in]</span></div><div class="line"><a name="l01489"></a><span class="lineno"> 1489</span> <span class="comment"> If radius_tolerance >= 0.0 and the difference between the</span></div><div class="line"><a name="l01490"></a><span class="lineno"> 1490</span> <span class="comment"> radii of curvature is >= radius_tolerance, then true </span></div><div class="line"><a name="l01491"></a><span class="lineno"> 1491</span> <span class="comment"> is returned.</span></div><div class="line"><a name="l01492"></a><span class="lineno"> 1492</span> <span class="comment"> relative_tolerance - [in]</span></div><div class="line"><a name="l01493"></a><span class="lineno"> 1493</span> <span class="comment"> If relative_tolerance > 0 and</span></div><div class="line"><a name="l01494"></a><span class="lineno"> 1494</span> <span class="comment"> |(|Km| - |Kp|)|/max(|Km|,|Kp|) > relative_tolerance,</span></div><div class="line"><a name="l01495"></a><span class="lineno"> 1495</span> <span class="comment"> then true is returned. Note that if the curvatures are</span></div><div class="line"><a name="l01496"></a><span class="lineno"> 1496</span> <span class="comment"> nonzero and rm and rp are the radii of curvature, then</span></div><div class="line"><a name="l01497"></a><span class="lineno"> 1497</span> <span class="comment"> |(|Km| - |Kp|)|/max(|Km|,|Kp|) = |rm-rp|/max(rm,rp).</span></div><div class="line"><a name="l01498"></a><span class="lineno"> 1498</span> <span class="comment"> This means the relative_tolerance insures both the scalar</span></div><div class="line"><a name="l01499"></a><span class="lineno"> 1499</span> <span class="comment"> curvature and the radii of curvature agree to the specified</span></div><div class="line"><a name="l01500"></a><span class="lineno"> 1500</span> <span class="comment"> number of decimal places.</span></div><div class="line"><a name="l01501"></a><span class="lineno"> 1501</span> <span class="comment"> When in doubt, use ON_RELATIVE_CURVATURE_TOLERANCE, which</span></div><div class="line"><a name="l01502"></a><span class="lineno"> 1502</span> <span class="comment"> is currently 0.05.</span></div><div class="line"><a name="l01503"></a><span class="lineno"> 1503</span> <span class="comment">Returns:</span></div><div class="line"><a name="l01504"></a><span class="lineno"> 1504</span> <span class="comment"> False if the curvatures should be considered G2.</span></div><div class="line"><a name="l01505"></a><span class="lineno"> 1505</span> <span class="comment"> True if the curvatures are different enough that the curve should be</span></div><div class="line"><a name="l01506"></a><span class="lineno"> 1506</span> <span class="comment"> considered not G2. </span></div><div class="line"><a name="l01507"></a><span class="lineno"> 1507</span> <span class="comment"> In addition to the tests described under the curvature_tolerance and </span></div><div class="line"><a name="l01508"></a><span class="lineno"> 1508</span> <span class="comment"> radius_tolerance checks, other hurestic tests are used.</span></div><div class="line"><a name="l01509"></a><span class="lineno"> 1509</span> <span class="comment">*/</span></div><div class="line"><a name="l01510"></a><span class="lineno"> 1510</span> ON_DECL</div><div class="line"><a name="l01511"></a><span class="lineno"> 1511</span> <span class="keywordtype">bool</span> ON_IsCurvatureDiscontinuity( </div><div class="line"><a name="l01512"></a><span class="lineno"> 1512</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a> Km, </div><div class="line"><a name="l01513"></a><span class="lineno"> 1513</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a> Kp,</div><div class="line"><a name="l01514"></a><span class="lineno"> 1514</span>  <span class="keywordtype">double</span> cos_angle_tolerance,</div><div class="line"><a name="l01515"></a><span class="lineno"> 1515</span>  <span class="keywordtype">double</span> curvature_tolerance,</div><div class="line"><a name="l01516"></a><span class="lineno"> 1516</span>  <span class="keywordtype">double</span> zero_curvature,</div><div class="line"><a name="l01517"></a><span class="lineno"> 1517</span>  <span class="keywordtype">double</span> radius_tolerance,</div><div class="line"><a name="l01518"></a><span class="lineno"> 1518</span>  <span class="keywordtype">double</span> relative_tolerance</div><div class="line"><a name="l01519"></a><span class="lineno"> 1519</span>  );</div><div class="line"><a name="l01520"></a><span class="lineno"> 1520</span> </div><div class="line"><a name="l01521"></a><span class="lineno"> 1521</span> ON_DECL</div><div class="line"><a name="l01522"></a><span class="lineno"> 1522</span> <span class="keywordtype">bool</span> ON_IsCurvatureDiscontinuity( </div><div class="line"><a name="l01523"></a><span class="lineno"> 1523</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a> Km, </div><div class="line"><a name="l01524"></a><span class="lineno"> 1524</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a> Kp,</div><div class="line"><a name="l01525"></a><span class="lineno"> 1525</span>  <span class="keywordtype">double</span> cos_angle_tolerance,</div><div class="line"><a name="l01526"></a><span class="lineno"> 1526</span>  <span class="keywordtype">double</span> curvature_tolerance,</div><div class="line"><a name="l01527"></a><span class="lineno"> 1527</span>  <span class="keywordtype">double</span> zero_curvature,</div><div class="line"><a name="l01528"></a><span class="lineno"> 1528</span>  <span class="keywordtype">double</span> radius_tolerance</div><div class="line"><a name="l01529"></a><span class="lineno"> 1529</span>  );</div><div class="line"><a name="l01530"></a><span class="lineno"> 1530</span> </div><div class="line"><a name="l01531"></a><span class="lineno"> 1531</span> </div><div class="line"><a name="l01532"></a><span class="lineno"> 1532</span> <span class="comment">/*</span></div><div class="line"><a name="l01533"></a><span class="lineno"> 1533</span> <span class="comment">Description:</span></div><div class="line"><a name="l01534"></a><span class="lineno"> 1534</span> <span class="comment"> This function is used to test curvature continuity</span></div><div class="line"><a name="l01535"></a><span class="lineno"> 1535</span> <span class="comment"> in IsContinuous and GetNextDiscontinuity functions</span></div><div class="line"><a name="l01536"></a><span class="lineno"> 1536</span> <span class="comment"> when the continuity parameter is ON::continuity::G2_continuous.</span></div><div class="line"><a name="l01537"></a><span class="lineno"> 1537</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l01538"></a><span class="lineno"> 1538</span> <span class="comment"> Km - [in]</span></div><div class="line"><a name="l01539"></a><span class="lineno"> 1539</span> <span class="comment"> Curve's vector curvature evaluated from below</span></div><div class="line"><a name="l01540"></a><span class="lineno"> 1540</span> <span class="comment"> Kp - [in]</span></div><div class="line"><a name="l01541"></a><span class="lineno"> 1541</span> <span class="comment"> Curve's vector curvature evaluated from below</span></div><div class="line"><a name="l01542"></a><span class="lineno"> 1542</span> <span class="comment">Returns:</span></div><div class="line"><a name="l01543"></a><span class="lineno"> 1543</span> <span class="comment"> True if the change from Km to Kp should be considered</span></div><div class="line"><a name="l01544"></a><span class="lineno"> 1544</span> <span class="comment"> G2 continuous.</span></div><div class="line"><a name="l01545"></a><span class="lineno"> 1545</span> <span class="comment">*/</span></div><div class="line"><a name="l01546"></a><span class="lineno"> 1546</span> ON_DECL</div><div class="line"><a name="l01547"></a><span class="lineno"> 1547</span> <span class="keywordtype">bool</span> ON_IsG2CurvatureContinuous(</div><div class="line"><a name="l01548"></a><span class="lineno"> 1548</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a> Km, </div><div class="line"><a name="l01549"></a><span class="lineno"> 1549</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a> Kp,</div><div class="line"><a name="l01550"></a><span class="lineno"> 1550</span>  <span class="keywordtype">double</span> cos_angle_tolerance,</div><div class="line"><a name="l01551"></a><span class="lineno"> 1551</span>  <span class="keywordtype">double</span> curvature_tolerance</div><div class="line"><a name="l01552"></a><span class="lineno"> 1552</span>  );</div><div class="line"><a name="l01553"></a><span class="lineno"> 1553</span> </div><div class="line"><a name="l01554"></a><span class="lineno"> 1554</span> <span class="comment">/*</span></div><div class="line"><a name="l01555"></a><span class="lineno"> 1555</span> <span class="comment">Description:</span></div><div class="line"><a name="l01556"></a><span class="lineno"> 1556</span> <span class="comment"> This function is used to test curvature continuity</span></div><div class="line"><a name="l01557"></a><span class="lineno"> 1557</span> <span class="comment"> in IsContinuous and GetNextDiscontinuity functions</span></div><div class="line"><a name="l01558"></a><span class="lineno"> 1558</span> <span class="comment"> when the continuity parameter is ON::continuity::Gsmooth_continuous.</span></div><div class="line"><a name="l01559"></a><span class="lineno"> 1559</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l01560"></a><span class="lineno"> 1560</span> <span class="comment"> Km - [in]</span></div><div class="line"><a name="l01561"></a><span class="lineno"> 1561</span> <span class="comment"> Curve's vector curvature evaluated from below</span></div><div class="line"><a name="l01562"></a><span class="lineno"> 1562</span> <span class="comment"> Kp - [in]</span></div><div class="line"><a name="l01563"></a><span class="lineno"> 1563</span> <span class="comment"> Curve's vector curvature evaluated from below</span></div><div class="line"><a name="l01564"></a><span class="lineno"> 1564</span> <span class="comment">Returns:</span></div><div class="line"><a name="l01565"></a><span class="lineno"> 1565</span> <span class="comment"> True if the change from Km to Kp should be considered</span></div><div class="line"><a name="l01566"></a><span class="lineno"> 1566</span> <span class="comment"> Gsmooth continuous.</span></div><div class="line"><a name="l01567"></a><span class="lineno"> 1567</span> <span class="comment">*/</span></div><div class="line"><a name="l01568"></a><span class="lineno"> 1568</span> ON_DECL</div><div class="line"><a name="l01569"></a><span class="lineno"> 1569</span> <span class="keywordtype">bool</span> ON_IsGsmoothCurvatureContinuous(</div><div class="line"><a name="l01570"></a><span class="lineno"> 1570</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a> Km, </div><div class="line"><a name="l01571"></a><span class="lineno"> 1571</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a> Kp,</div><div class="line"><a name="l01572"></a><span class="lineno"> 1572</span>  <span class="keywordtype">double</span> cos_angle_tolerance,</div><div class="line"><a name="l01573"></a><span class="lineno"> 1573</span>  <span class="keywordtype">double</span> curvature_tolerance</div><div class="line"><a name="l01574"></a><span class="lineno"> 1574</span>  );</div><div class="line"><a name="l01575"></a><span class="lineno"> 1575</span> </div><div class="line"><a name="l01576"></a><span class="lineno"> 1576</span> <span class="comment">/*</span></div><div class="line"><a name="l01577"></a><span class="lineno"> 1577</span> <span class="comment">Description:</span></div><div class="line"><a name="l01578"></a><span class="lineno"> 1578</span> <span class="comment"> Test curve continuity from derivative values.</span></div><div class="line"><a name="l01579"></a><span class="lineno"> 1579</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l01580"></a><span class="lineno"> 1580</span> <span class="comment"> c - [in] type of continuity to test for. Read ON::continuity</span></div><div class="line"><a name="l01581"></a><span class="lineno"> 1581</span> <span class="comment"> comments for details.</span></div><div class="line"><a name="l01582"></a><span class="lineno"> 1582</span> <span class="comment"> Pa - [in] point on curve A.</span></div><div class="line"><a name="l01583"></a><span class="lineno"> 1583</span> <span class="comment"> D1a - [in] first derviative of curve A.</span></div><div class="line"><a name="l01584"></a><span class="lineno"> 1584</span> <span class="comment"> D2a - [in] second derviative of curve A.</span></div><div class="line"><a name="l01585"></a><span class="lineno"> 1585</span> <span class="comment"> Pb - [in] point on curve B.</span></div><div class="line"><a name="l01586"></a><span class="lineno"> 1586</span> <span class="comment"> D1b - [in] first derviative of curve B.</span></div><div class="line"><a name="l01587"></a><span class="lineno"> 1587</span> <span class="comment"> D3b - [in] second derviative of curve B.</span></div><div class="line"><a name="l01588"></a><span class="lineno"> 1588</span> <span class="comment"> point_tolerance - [in] if the distance between two points is</span></div><div class="line"><a name="l01589"></a><span class="lineno"> 1589</span> <span class="comment"> greater than point_tolerance, then the curve is not C0.</span></div><div class="line"><a name="l01590"></a><span class="lineno"> 1590</span> <span class="comment"> d1_tolerance - [in] if the difference between two first derivatives is</span></div><div class="line"><a name="l01591"></a><span class="lineno"> 1591</span> <span class="comment"> greater than d1_tolerance, then the curve is not C1.</span></div><div class="line"><a name="l01592"></a><span class="lineno"> 1592</span> <span class="comment"> d2_tolerance - [in] if the difference between two second derivatives is</span></div><div class="line"><a name="l01593"></a><span class="lineno"> 1593</span> <span class="comment"> greater than d2_tolerance, then the curve is not C2.</span></div><div class="line"><a name="l01594"></a><span class="lineno"> 1594</span> <span class="comment"> cos_angle_tolerance - [in] default = cos(1 degree) Used only when</span></div><div class="line"><a name="l01595"></a><span class="lineno"> 1595</span> <span class="comment"> c is ON::continuity::G1_continuous or ON::continuity::G2_continuous. If the cosine</span></div><div class="line"><a name="l01596"></a><span class="lineno"> 1596</span> <span class="comment"> of the angle between two tangent vectors </span></div><div class="line"><a name="l01597"></a><span class="lineno"> 1597</span> <span class="comment"> is <= cos_angle_tolerance, then a G1 discontinuity is reported.</span></div><div class="line"><a name="l01598"></a><span class="lineno"> 1598</span> <span class="comment"> curvature_tolerance - [in] (default = ON_SQRT_EPSILON) Used only when</span></div><div class="line"><a name="l01599"></a><span class="lineno"> 1599</span> <span class="comment"> c is ON::continuity::G2_continuous. If K0 and K1 are curvatures evaluated</span></div><div class="line"><a name="l01600"></a><span class="lineno"> 1600</span> <span class="comment"> from above and below and |K0 - K1| > curvature_tolerance,</span></div><div class="line"><a name="l01601"></a><span class="lineno"> 1601</span> <span class="comment"> then a curvature discontinuity is reported.</span></div><div class="line"><a name="l01602"></a><span class="lineno"> 1602</span> <span class="comment">Returns:</span></div><div class="line"><a name="l01603"></a><span class="lineno"> 1603</span> <span class="comment"> true if the curve has at least the c type continuity at </span></div><div class="line"><a name="l01604"></a><span class="lineno"> 1604</span> <span class="comment"> the parameter t.</span></div><div class="line"><a name="l01605"></a><span class="lineno"> 1605</span> <span class="comment">*/</span></div><div class="line"><a name="l01606"></a><span class="lineno"> 1606</span> ON_DECL</div><div class="line"><a name="l01607"></a><span class="lineno"> 1607</span> <span class="keywordtype">bool</span> ON_IsContinuous(</div><div class="line"><a name="l01608"></a><span class="lineno"> 1608</span>  ON::continuity c,</div><div class="line"><a name="l01609"></a><span class="lineno"> 1609</span>  <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a> Pa,</div><div class="line"><a name="l01610"></a><span class="lineno"> 1610</span>  <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a> D1a,</div><div class="line"><a name="l01611"></a><span class="lineno"> 1611</span>  <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a> D2a,</div><div class="line"><a name="l01612"></a><span class="lineno"> 1612</span>  <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a> Pb,</div><div class="line"><a name="l01613"></a><span class="lineno"> 1613</span>  <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a> D1b,</div><div class="line"><a name="l01614"></a><span class="lineno"> 1614</span>  <a class="code" href="class_o_n__3d_vector.html">ON_3dVector</a> D2b,</div><div class="line"><a name="l01615"></a><span class="lineno"> 1615</span>  <span class="keywordtype">double</span> point_tolerance=ON_ZERO_TOLERANCE,</div><div class="line"><a name="l01616"></a><span class="lineno"> 1616</span>  <span class="keywordtype">double</span> d1_tolerance=ON_ZERO_TOLERANCE,</div><div class="line"><a name="l01617"></a><span class="lineno"> 1617</span>  <span class="keywordtype">double</span> d2_tolerance=ON_ZERO_TOLERANCE,</div><div class="line"><a name="l01618"></a><span class="lineno"> 1618</span>  <span class="keywordtype">double</span> cos_angle_tolerance=ON_DEFAULT_ANGLE_TOLERANCE_COSINE,</div><div class="line"><a name="l01619"></a><span class="lineno"> 1619</span>  <span class="keywordtype">double</span> curvature_tolerance=ON_SQRT_EPSILON</div><div class="line"><a name="l01620"></a><span class="lineno"> 1620</span>  );</div><div class="line"><a name="l01621"></a><span class="lineno"> 1621</span> </div><div class="line"><a name="l01622"></a><span class="lineno"> 1622</span> </div><div class="line"><a name="l01623"></a><span class="lineno"> 1623</span> ON_DECL</div><div class="line"><a name="l01624"></a><span class="lineno"> 1624</span> <span class="keywordtype">bool</span> ON_TuneupEvaluationParameter( </div><div class="line"><a name="l01625"></a><span class="lineno"> 1625</span>  <span class="keywordtype">int</span> side,</div><div class="line"><a name="l01626"></a><span class="lineno"> 1626</span>  <span class="keywordtype">double</span> s0, <span class="keywordtype">double</span> s1, <span class="comment">// segment domain</span></div><div class="line"><a name="l01627"></a><span class="lineno"> 1627</span>  <span class="keywordtype">double</span> *s <span class="comment">// segment parameter</span></div><div class="line"><a name="l01628"></a><span class="lineno"> 1628</span>  );</div><div class="line"><a name="l01629"></a><span class="lineno"> 1629</span> </div><div class="line"><a name="l01630"></a><span class="lineno"> 1630</span> </div><div class="line"><a name="l01631"></a><span class="lineno"> 1631</span> ON_DECL</div><div class="line"><a name="l01632"></a><span class="lineno"> 1632</span> <span class="keywordtype">int</span> ON_Compare2dex( <span class="keyword">const</span> ON_2dex* a, <span class="keyword">const</span> ON_2dex* b);</div><div class="line"><a name="l01633"></a><span class="lineno"> 1633</span> </div><div class="line"><a name="l01634"></a><span class="lineno"> 1634</span> ON_DECL</div><div class="line"><a name="l01635"></a><span class="lineno"> 1635</span> <span class="keywordtype">int</span> ON_Compare3dex( <span class="keyword">const</span> ON_3dex* a, <span class="keyword">const</span> ON_3dex* b);</div><div class="line"><a name="l01636"></a><span class="lineno"> 1636</span> </div><div class="line"><a name="l01637"></a><span class="lineno"> 1637</span> ON_DECL</div><div class="line"><a name="l01638"></a><span class="lineno"> 1638</span> <span class="keywordtype">int</span> ON_Compare4dex( <span class="keyword">const</span> ON_4dex* a, <span class="keyword">const</span> ON_4dex* b);</div><div class="line"><a name="l01639"></a><span class="lineno"> 1639</span> </div><div class="line"><a name="l01640"></a><span class="lineno"> 1640</span> ON_DECL</div><div class="line"><a name="l01641"></a><span class="lineno"> 1641</span> <span class="keyword">const</span> ON_2dex* ON_BinarySearch2dexArray( </div><div class="line"><a name="l01642"></a><span class="lineno"> 1642</span>  <span class="keywordtype">int</span> key_i, </div><div class="line"><a name="l01643"></a><span class="lineno"> 1643</span>  <span class="keyword">const</span> ON_2dex* base, </div><div class="line"><a name="l01644"></a><span class="lineno"> 1644</span>  <span class="keywordtype">size_t</span> nel</div><div class="line"><a name="l01645"></a><span class="lineno"> 1645</span>  );</div><div class="line"><a name="l01646"></a><span class="lineno"> 1646</span> </div><div class="line"><a name="l01647"></a><span class="lineno"> 1647</span> <span class="comment">// These simple intersectors are fast and detect transverse intersections.</span></div><div class="line"><a name="l01648"></a><span class="lineno"> 1648</span> <span class="comment">// If the intersection is not a simple transverse case, then they</span></div><div class="line"><a name="l01649"></a><span class="lineno"> 1649</span> <span class="comment">// return false and you will have to use one of the slower but fancier</span></div><div class="line"><a name="l01650"></a><span class="lineno"> 1650</span> <span class="comment">// models.</span></div><div class="line"><a name="l01651"></a><span class="lineno"> 1651</span> </div><div class="line"><a name="l01652"></a><span class="lineno"> 1652</span> <span class="comment">// returns closest points between the two infinite lines</span></div><div class="line"><a name="l01653"></a><span class="lineno"> 1653</span> ON_DECL</div><div class="line"><a name="l01654"></a><span class="lineno"> 1654</span> <span class="keywordtype">bool</span> ON_Intersect( </div><div class="line"><a name="l01655"></a><span class="lineno"> 1655</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___line.html">ON_Line</a>&, </div><div class="line"><a name="l01656"></a><span class="lineno"> 1656</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___line.html">ON_Line</a>&, </div><div class="line"><a name="l01657"></a><span class="lineno"> 1657</span>  <span class="keywordtype">double</span>*, <span class="comment">// parameter on first line</span></div><div class="line"><a name="l01658"></a><span class="lineno"> 1658</span>  <span class="keywordtype">double</span>* <span class="comment">// parameter on second line</span></div><div class="line"><a name="l01659"></a><span class="lineno"> 1659</span>  );</div><div class="line"><a name="l01660"></a><span class="lineno"> 1660</span> </div><div class="line"><a name="l01661"></a><span class="lineno"> 1661</span> <span class="comment">// Returns false unless intersection is a single point</span></div><div class="line"><a name="l01662"></a><span class="lineno"> 1662</span> <span class="comment">// If returned parameter is < 0 or > 1, then the line</span></div><div class="line"><a name="l01663"></a><span class="lineno"> 1663</span> <span class="comment">// segment between line.m_point[0] and line.m_point[1]</span></div><div class="line"><a name="l01664"></a><span class="lineno"> 1664</span> <span class="comment">// does not intersect the plane</span></div><div class="line"><a name="l01665"></a><span class="lineno"> 1665</span> ON_DECL</div><div class="line"><a name="l01666"></a><span class="lineno"> 1666</span> <span class="keywordtype">bool</span> ON_Intersect( </div><div class="line"><a name="l01667"></a><span class="lineno"> 1667</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___line.html">ON_Line</a>&, </div><div class="line"><a name="l01668"></a><span class="lineno"> 1668</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___plane.html">ON_Plane</a>&, </div><div class="line"><a name="l01669"></a><span class="lineno"> 1669</span>  <span class="keywordtype">double</span>* <span class="comment">// parameter on line</span></div><div class="line"><a name="l01670"></a><span class="lineno"> 1670</span>  );</div><div class="line"><a name="l01671"></a><span class="lineno"> 1671</span> </div><div class="line"><a name="l01672"></a><span class="lineno"> 1672</span> ON_DECL</div><div class="line"><a name="l01673"></a><span class="lineno"> 1673</span> <span class="keywordtype">bool</span> ON_Intersect( </div><div class="line"><a name="l01674"></a><span class="lineno"> 1674</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___plane.html">ON_Plane</a>&, </div><div class="line"><a name="l01675"></a><span class="lineno"> 1675</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___plane.html">ON_Plane</a>&, </div><div class="line"><a name="l01676"></a><span class="lineno"> 1676</span>  <a class="code" href="class_o_n___line.html">ON_Line</a>& <span class="comment">// intersection line is returned here</span></div><div class="line"><a name="l01677"></a><span class="lineno"> 1677</span>  );</div><div class="line"><a name="l01678"></a><span class="lineno"> 1678</span> </div><div class="line"><a name="l01679"></a><span class="lineno"> 1679</span> ON_DECL</div><div class="line"><a name="l01680"></a><span class="lineno"> 1680</span> <span class="keywordtype">bool</span> ON_Intersect( </div><div class="line"><a name="l01681"></a><span class="lineno"> 1681</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___plane.html">ON_Plane</a>&, </div><div class="line"><a name="l01682"></a><span class="lineno"> 1682</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___plane.html">ON_Plane</a>&, </div><div class="line"><a name="l01683"></a><span class="lineno"> 1683</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___plane.html">ON_Plane</a>&,</div><div class="line"><a name="l01684"></a><span class="lineno"> 1684</span>  <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a>& <span class="comment">// intersection point is returned here</span></div><div class="line"><a name="l01685"></a><span class="lineno"> 1685</span>  );</div><div class="line"><a name="l01686"></a><span class="lineno"> 1686</span> </div><div class="line"><a name="l01687"></a><span class="lineno"> 1687</span> <span class="comment">// returns 0 = no intersections, </span></div><div class="line"><a name="l01688"></a><span class="lineno"> 1688</span> <span class="comment">// 1 = intersection = single point, </span></div><div class="line"><a name="l01689"></a><span class="lineno"> 1689</span> <span class="comment">// 2 = intersection = circle</span></div><div class="line"><a name="l01690"></a><span class="lineno"> 1690</span> <span class="comment">// If 0 is returned, returned circle has radius=0</span></div><div class="line"><a name="l01691"></a><span class="lineno"> 1691</span> <span class="comment">// and center = point on sphere closest to plane.</span></div><div class="line"><a name="l01692"></a><span class="lineno"> 1692</span> <span class="comment">// If 1 is returned, intersection is a single</span></div><div class="line"><a name="l01693"></a><span class="lineno"> 1693</span> <span class="comment">// point and returned circle has radius=0</span></div><div class="line"><a name="l01694"></a><span class="lineno"> 1694</span> <span class="comment">// and center = intersection point on sphere.</span></div><div class="line"><a name="l01695"></a><span class="lineno"> 1695</span> ON_DECL</div><div class="line"><a name="l01696"></a><span class="lineno"> 1696</span> <span class="keywordtype">int</span> ON_Intersect( </div><div class="line"><a name="l01697"></a><span class="lineno"> 1697</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___plane.html">ON_Plane</a>&, <span class="keyword">const</span> <a class="code" href="class_o_n___sphere.html">ON_Sphere</a>&, <a class="code" href="class_o_n___circle.html">ON_Circle</a>&</div><div class="line"><a name="l01698"></a><span class="lineno"> 1698</span>  );</div><div class="line"><a name="l01699"></a><span class="lineno"> 1699</span> </div><div class="line"><a name="l01700"></a><span class="lineno"> 1700</span> <span class="comment">// Intersects an infinte line and sphere and returns </span></div><div class="line"><a name="l01701"></a><span class="lineno"> 1701</span> <span class="comment">// 0 = no intersections, </span></div><div class="line"><a name="l01702"></a><span class="lineno"> 1702</span> <span class="comment">// 1 = one intersection, </span></div><div class="line"><a name="l01703"></a><span class="lineno"> 1703</span> <span class="comment">// 2 = 2 intersections</span></div><div class="line"><a name="l01704"></a><span class="lineno"> 1704</span> <span class="comment">// If 0 is returned, first point is point </span></div><div class="line"><a name="l01705"></a><span class="lineno"> 1705</span> <span class="comment">// on line closest to sphere and 2nd point is the point</span></div><div class="line"><a name="l01706"></a><span class="lineno"> 1706</span> <span class="comment">// on the sphere closest to the line.</span></div><div class="line"><a name="l01707"></a><span class="lineno"> 1707</span> <span class="comment">// If 1 is returned, first point is obtained by evaluating</span></div><div class="line"><a name="l01708"></a><span class="lineno"> 1708</span> <span class="comment">// the line and the second point is obtained by evaluating</span></div><div class="line"><a name="l01709"></a><span class="lineno"> 1709</span> <span class="comment">// the sphere.</span></div><div class="line"><a name="l01710"></a><span class="lineno"> 1710</span> ON_DECL</div><div class="line"><a name="l01711"></a><span class="lineno"> 1711</span> <span class="keywordtype">int</span> ON_Intersect( </div><div class="line"><a name="l01712"></a><span class="lineno"> 1712</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___line.html">ON_Line</a>&, </div><div class="line"><a name="l01713"></a><span class="lineno"> 1713</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___sphere.html">ON_Sphere</a>&,</div><div class="line"><a name="l01714"></a><span class="lineno"> 1714</span>  <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a>&, </div><div class="line"><a name="l01715"></a><span class="lineno"> 1715</span>  <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a>& <span class="comment">// intersection point(s) returned here</span></div><div class="line"><a name="l01716"></a><span class="lineno"> 1716</span>  );</div><div class="line"><a name="l01717"></a><span class="lineno"> 1717</span> </div><div class="line"><a name="l01718"></a><span class="lineno"> 1718</span> </div><div class="line"><a name="l01719"></a><span class="lineno"> 1719</span> <span class="comment">// Intersects an infinte line and cylinder and returns </span></div><div class="line"><a name="l01720"></a><span class="lineno"> 1720</span> <span class="comment">// 0 = no intersections, </span></div><div class="line"><a name="l01721"></a><span class="lineno"> 1721</span> <span class="comment">// 1 = one intersection, </span></div><div class="line"><a name="l01722"></a><span class="lineno"> 1722</span> <span class="comment">// 2 = 2 intersections</span></div><div class="line"><a name="l01723"></a><span class="lineno"> 1723</span> <span class="comment">// 3 = line lies on cylinder</span></div><div class="line"><a name="l01724"></a><span class="lineno"> 1724</span> <span class="comment">//</span></div><div class="line"><a name="l01725"></a><span class="lineno"> 1725</span> <span class="comment">// If 0 is returned, first point is point </span></div><div class="line"><a name="l01726"></a><span class="lineno"> 1726</span> <span class="comment">// on line closest to cylinder and 2nd point is the point</span></div><div class="line"><a name="l01727"></a><span class="lineno"> 1727</span> <span class="comment">// on the cylinder closest to the line.</span></div><div class="line"><a name="l01728"></a><span class="lineno"> 1728</span> <span class="comment">// If 1 is returned, first point is obtained by evaluating</span></div><div class="line"><a name="l01729"></a><span class="lineno"> 1729</span> <span class="comment">// the line and the second point is obtained by evaluating</span></div><div class="line"><a name="l01730"></a><span class="lineno"> 1730</span> <span class="comment">// the cylinder.</span></div><div class="line"><a name="l01731"></a><span class="lineno"> 1731</span> <span class="comment">//</span></div><div class="line"><a name="l01732"></a><span class="lineno"> 1732</span> <span class="comment">// The value of cylinder.IsFinite() determines if the</span></div><div class="line"><a name="l01733"></a><span class="lineno"> 1733</span> <span class="comment">// intersection is performed on the finite or infinite cylinder.</span></div><div class="line"><a name="l01734"></a><span class="lineno"> 1734</span> ON_DECL</div><div class="line"><a name="l01735"></a><span class="lineno"> 1735</span> <span class="keywordtype">int</span> ON_Intersect( </div><div class="line"><a name="l01736"></a><span class="lineno"> 1736</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___line.html">ON_Line</a>&, <span class="comment">// [in]</span></div><div class="line"><a name="l01737"></a><span class="lineno"> 1737</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___cylinder.html">ON_Cylinder</a>&, <span class="comment">// [in]</span></div><div class="line"><a name="l01738"></a><span class="lineno"> 1738</span>  <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a>&, <span class="comment">// [out] first intersection point</span></div><div class="line"><a name="l01739"></a><span class="lineno"> 1739</span>  <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a>& <span class="comment">// [out] second intersection point</span></div><div class="line"><a name="l01740"></a><span class="lineno"> 1740</span>  );</div><div class="line"><a name="l01741"></a><span class="lineno"> 1741</span> </div><div class="line"><a name="l01742"></a><span class="lineno"> 1742</span> <span class="comment">// Description:</span></div><div class="line"><a name="l01743"></a><span class="lineno"> 1743</span> <span class="comment">// Intersect an infinte line and circle.</span></div><div class="line"><a name="l01744"></a><span class="lineno"> 1744</span> <span class="comment">// Parameters:</span></div><div class="line"><a name="l01745"></a><span class="lineno"> 1745</span> <span class="comment">// line - [in]</span></div><div class="line"><a name="l01746"></a><span class="lineno"> 1746</span> <span class="comment">// circle - [in]</span></div><div class="line"><a name="l01747"></a><span class="lineno"> 1747</span> <span class="comment">// line_t0 - [out] line parameter of first intersection point</span></div><div class="line"><a name="l01748"></a><span class="lineno"> 1748</span> <span class="comment">// circle_point0 - [out] first intersection point on circle</span></div><div class="line"><a name="l01749"></a><span class="lineno"> 1749</span> <span class="comment">// line_t1 - [out] line parameter of second intersection point</span></div><div class="line"><a name="l01750"></a><span class="lineno"> 1750</span> <span class="comment">// circle_point1 - [out] second intersection point on circle</span></div><div class="line"><a name="l01751"></a><span class="lineno"> 1751</span> <span class="comment">// Returns:</span></div><div class="line"><a name="l01752"></a><span class="lineno"> 1752</span> <span class="comment">// 0 No intersection</span></div><div class="line"><a name="l01753"></a><span class="lineno"> 1753</span> <span class="comment">// 1 One intersection at line.PointAt(*line_t0)</span></div><div class="line"><a name="l01754"></a><span class="lineno"> 1754</span> <span class="comment">// 2 Two intersections at line.PointAt(*line_t0)</span></div><div class="line"><a name="l01755"></a><span class="lineno"> 1755</span> <span class="comment">// and line.PointAt(*line_t1).</span></div><div class="line"><a name="l01756"></a><span class="lineno"> 1756</span> ON_DECL</div><div class="line"><a name="l01757"></a><span class="lineno"> 1757</span> <span class="keywordtype">int</span> ON_Intersect( </div><div class="line"><a name="l01758"></a><span class="lineno"> 1758</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___line.html">ON_Line</a>& line, </div><div class="line"><a name="l01759"></a><span class="lineno"> 1759</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___circle.html">ON_Circle</a>& circle,</div><div class="line"><a name="l01760"></a><span class="lineno"> 1760</span>  <span class="keywordtype">double</span>* line_t0,</div><div class="line"><a name="l01761"></a><span class="lineno"> 1761</span>  <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a>& circle_point0,</div><div class="line"><a name="l01762"></a><span class="lineno"> 1762</span>  <span class="keywordtype">double</span>* line_t1,</div><div class="line"><a name="l01763"></a><span class="lineno"> 1763</span>  <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a>& circle_point1</div><div class="line"><a name="l01764"></a><span class="lineno"> 1764</span>  );</div><div class="line"><a name="l01765"></a><span class="lineno"> 1765</span> </div><div class="line"><a name="l01766"></a><span class="lineno"> 1766</span> </div><div class="line"><a name="l01767"></a><span class="lineno"> 1767</span> </div><div class="line"><a name="l01768"></a><span class="lineno"> 1768</span> <span class="comment">// Description:</span></div><div class="line"><a name="l01769"></a><span class="lineno"> 1769</span> <span class="comment">// Intersect a infinte line and arc.</span></div><div class="line"><a name="l01770"></a><span class="lineno"> 1770</span> <span class="comment">// Parameters:</span></div><div class="line"><a name="l01771"></a><span class="lineno"> 1771</span> <span class="comment">// line - [in]</span></div><div class="line"><a name="l01772"></a><span class="lineno"> 1772</span> <span class="comment">// arc - [in]</span></div><div class="line"><a name="l01773"></a><span class="lineno"> 1773</span> <span class="comment">// line_t0 - [out] line parameter of first intersection point</span></div><div class="line"><a name="l01774"></a><span class="lineno"> 1774</span> <span class="comment">// arc_point0 - [out] first intersection point on arc</span></div><div class="line"><a name="l01775"></a><span class="lineno"> 1775</span> <span class="comment">// line_t1 - [out] line parameter of second intersection point</span></div><div class="line"><a name="l01776"></a><span class="lineno"> 1776</span> <span class="comment">// arc_point1 - [out] second intersection point on arc</span></div><div class="line"><a name="l01777"></a><span class="lineno"> 1777</span> <span class="comment">// Returns:</span></div><div class="line"><a name="l01778"></a><span class="lineno"> 1778</span> <span class="comment">// 0 No intersection</span></div><div class="line"><a name="l01779"></a><span class="lineno"> 1779</span> <span class="comment">// 1 One intersection at line.PointAt(*line_t0)</span></div><div class="line"><a name="l01780"></a><span class="lineno"> 1780</span> <span class="comment">// 2 Two intersections at line.PointAt(*line_t0)</span></div><div class="line"><a name="l01781"></a><span class="lineno"> 1781</span> <span class="comment">// and line.PointAt(*line_t1).</span></div><div class="line"><a name="l01782"></a><span class="lineno"> 1782</span> ON_DECL</div><div class="line"><a name="l01783"></a><span class="lineno"> 1783</span> <span class="keywordtype">int</span> ON_Intersect( </div><div class="line"><a name="l01784"></a><span class="lineno"> 1784</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___line.html">ON_Line</a>& line, </div><div class="line"><a name="l01785"></a><span class="lineno"> 1785</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___arc.html">ON_Arc</a>& arc,</div><div class="line"><a name="l01786"></a><span class="lineno"> 1786</span>  <span class="keywordtype">double</span>* line_t0,</div><div class="line"><a name="l01787"></a><span class="lineno"> 1787</span>  <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a>& arc_point0,</div><div class="line"><a name="l01788"></a><span class="lineno"> 1788</span>  <span class="keywordtype">double</span>* line_t1,</div><div class="line"><a name="l01789"></a><span class="lineno"> 1789</span>  <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a>& arc_point1</div><div class="line"><a name="l01790"></a><span class="lineno"> 1790</span>  );</div><div class="line"><a name="l01791"></a><span class="lineno"> 1791</span> </div><div class="line"><a name="l01792"></a><span class="lineno"> 1792</span> <span class="comment">// Description:</span></div><div class="line"><a name="l01793"></a><span class="lineno"> 1793</span> <span class="comment">// Intersect a plane and a circle.</span></div><div class="line"><a name="l01794"></a><span class="lineno"> 1794</span> <span class="comment">// Parameters:</span></div><div class="line"><a name="l01795"></a><span class="lineno"> 1795</span> <span class="comment">// plane - [in]</span></div><div class="line"><a name="l01796"></a><span class="lineno"> 1796</span> <span class="comment">// circle - [in]</span></div><div class="line"><a name="l01797"></a><span class="lineno"> 1797</span> <span class="comment">// point0 - [out] first intersection point </span></div><div class="line"><a name="l01798"></a><span class="lineno"> 1798</span> <span class="comment">// point1 - [out] second intersection point</span></div><div class="line"><a name="l01799"></a><span class="lineno"> 1799</span> <span class="comment">// Returns:</span></div><div class="line"><a name="l01800"></a><span class="lineno"> 1800</span> <span class="comment">// 0 No intersection</span></div><div class="line"><a name="l01801"></a><span class="lineno"> 1801</span> <span class="comment">// 1 One intersection at point0</span></div><div class="line"><a name="l01802"></a><span class="lineno"> 1802</span> <span class="comment">// 2 Two intersections at point0</span></div><div class="line"><a name="l01803"></a><span class="lineno"> 1803</span> <span class="comment">// and point1.</span></div><div class="line"><a name="l01804"></a><span class="lineno"> 1804</span> <span class="comment">// 3 Circle lies on plane</span></div><div class="line"><a name="l01805"></a><span class="lineno"> 1805</span> ON_DECL</div><div class="line"><a name="l01806"></a><span class="lineno"> 1806</span> <span class="keywordtype">int</span> ON_Intersect( </div><div class="line"><a name="l01807"></a><span class="lineno"> 1807</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___plane.html">ON_Plane</a>& plane, </div><div class="line"><a name="l01808"></a><span class="lineno"> 1808</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___circle.html">ON_Circle</a>& circle,</div><div class="line"><a name="l01809"></a><span class="lineno"> 1809</span>  <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a>& point0,</div><div class="line"><a name="l01810"></a><span class="lineno"> 1810</span>  <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a>& point1</div><div class="line"><a name="l01811"></a><span class="lineno"> 1811</span>  );</div><div class="line"><a name="l01812"></a><span class="lineno"> 1812</span> </div><div class="line"><a name="l01813"></a><span class="lineno"> 1813</span> <span class="comment">// Description:</span></div><div class="line"><a name="l01814"></a><span class="lineno"> 1814</span> <span class="comment">// Intersect a plane and an arc.</span></div><div class="line"><a name="l01815"></a><span class="lineno"> 1815</span> <span class="comment">// Parameters:</span></div><div class="line"><a name="l01816"></a><span class="lineno"> 1816</span> <span class="comment">// plane - [in]</span></div><div class="line"><a name="l01817"></a><span class="lineno"> 1817</span> <span class="comment">// arc - [in]</span></div><div class="line"><a name="l01818"></a><span class="lineno"> 1818</span> <span class="comment">// point0 - [out] first intersection point </span></div><div class="line"><a name="l01819"></a><span class="lineno"> 1819</span> <span class="comment">// point1 - [out] second intersection point</span></div><div class="line"><a name="l01820"></a><span class="lineno"> 1820</span> <span class="comment">// Returns:</span></div><div class="line"><a name="l01821"></a><span class="lineno"> 1821</span> <span class="comment">// 0 No intersection</span></div><div class="line"><a name="l01822"></a><span class="lineno"> 1822</span> <span class="comment">// 1 One intersection at point0</span></div><div class="line"><a name="l01823"></a><span class="lineno"> 1823</span> <span class="comment">// 2 Two intersections at point0</span></div><div class="line"><a name="l01824"></a><span class="lineno"> 1824</span> <span class="comment">// and point1.</span></div><div class="line"><a name="l01825"></a><span class="lineno"> 1825</span> <span class="comment">// 3 Arc lies on plane</span></div><div class="line"><a name="l01826"></a><span class="lineno"> 1826</span> ON_DECL</div><div class="line"><a name="l01827"></a><span class="lineno"> 1827</span> <span class="keywordtype">int</span> ON_Intersect( </div><div class="line"><a name="l01828"></a><span class="lineno"> 1828</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___plane.html">ON_Plane</a>& plane, </div><div class="line"><a name="l01829"></a><span class="lineno"> 1829</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___arc.html">ON_Arc</a>& arc,</div><div class="line"><a name="l01830"></a><span class="lineno"> 1830</span>  <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a>& point0,</div><div class="line"><a name="l01831"></a><span class="lineno"> 1831</span>  <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a>& point1</div><div class="line"><a name="l01832"></a><span class="lineno"> 1832</span>  );</div><div class="line"><a name="l01833"></a><span class="lineno"> 1833</span> </div><div class="line"><a name="l01834"></a><span class="lineno"> 1834</span> </div><div class="line"><a name="l01835"></a><span class="lineno"> 1835</span> <span class="comment">// returns 0 = no, 1 = yes, 2 = points are coincident and on line</span></div><div class="line"><a name="l01836"></a><span class="lineno"> 1836</span> ON_DECL</div><div class="line"><a name="l01837"></a><span class="lineno"> 1837</span> <span class="keywordtype">int</span> ON_ArePointsOnLine(</div><div class="line"><a name="l01838"></a><span class="lineno"> 1838</span>  <span class="keywordtype">int</span>, <span class="comment">// dimension of points</span></div><div class="line"><a name="l01839"></a><span class="lineno"> 1839</span>  <span class="keywordtype">bool</span>, <span class="comment">// is_rat = true if homogeneous rational</span></div><div class="line"><a name="l01840"></a><span class="lineno"> 1840</span>  <span class="keywordtype">int</span>, <span class="comment">// count = number of points</span></div><div class="line"><a name="l01841"></a><span class="lineno"> 1841</span>  <span class="keywordtype">int</span>, <span class="comment">// stride ( >= is_rat?(dim+1) :dim)</span></div><div class="line"><a name="l01842"></a><span class="lineno"> 1842</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// point array</span></div><div class="line"><a name="l01843"></a><span class="lineno"> 1843</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___bounding_box.html">ON_BoundingBox</a>&, <span class="comment">// if needed, use ON_GetBoundingBox(dim,is_rat,count,stride,point)</span></div><div class="line"><a name="l01844"></a><span class="lineno"> 1844</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___line.html">ON_Line</a>&,</div><div class="line"><a name="l01845"></a><span class="lineno"> 1845</span>  <span class="keywordtype">double</span> <span class="comment">// tolerance (if 0.0, a tolerance based on bounding box size is used)</span></div><div class="line"><a name="l01846"></a><span class="lineno"> 1846</span>  );</div><div class="line"><a name="l01847"></a><span class="lineno"> 1847</span> </div><div class="line"><a name="l01848"></a><span class="lineno"> 1848</span> <span class="comment">// returns 0 = no, 1 = yes, 2 = points are coincident and on line</span></div><div class="line"><a name="l01849"></a><span class="lineno"> 1849</span> ON_DECL</div><div class="line"><a name="l01850"></a><span class="lineno"> 1850</span> <span class="keywordtype">int</span> ON_ArePointsOnPlane(</div><div class="line"><a name="l01851"></a><span class="lineno"> 1851</span>  <span class="keywordtype">int</span>, <span class="comment">// dimension of points</span></div><div class="line"><a name="l01852"></a><span class="lineno"> 1852</span>  <span class="keywordtype">bool</span>, <span class="comment">// is_rat = true if homogeneous rational</span></div><div class="line"><a name="l01853"></a><span class="lineno"> 1853</span>  <span class="keywordtype">int</span>, <span class="comment">// count = number of points</span></div><div class="line"><a name="l01854"></a><span class="lineno"> 1854</span>  <span class="keywordtype">int</span>, <span class="comment">// stride ( >= is_rat?(dim+1) :dim)</span></div><div class="line"><a name="l01855"></a><span class="lineno"> 1855</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// point array</span></div><div class="line"><a name="l01856"></a><span class="lineno"> 1856</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___bounding_box.html">ON_BoundingBox</a>&, <span class="comment">// if needed, use ON_GetBoundingBox(dim,is_rat,count,stride,point)</span></div><div class="line"><a name="l01857"></a><span class="lineno"> 1857</span>  <span class="keyword">const</span> <a class="code" href="class_o_n___plane.html">ON_Plane</a>&,</div><div class="line"><a name="l01858"></a><span class="lineno"> 1858</span>  <span class="keywordtype">double</span> <span class="comment">// tolerance (if 0.0, a tolerance based on bounding box size is used)</span></div><div class="line"><a name="l01859"></a><span class="lineno"> 1859</span>  );</div><div class="line"><a name="l01860"></a><span class="lineno"> 1860</span> </div><div class="line"><a name="l01861"></a><span class="lineno"> 1861</span> <span class="comment">/*</span></div><div class="line"><a name="l01862"></a><span class="lineno"> 1862</span> <span class="comment">Description:</span></div><div class="line"><a name="l01863"></a><span class="lineno"> 1863</span> <span class="comment"> Use the quotient rule to compute derivatives of a one parameter</span></div><div class="line"><a name="l01864"></a><span class="lineno"> 1864</span> <span class="comment"> rational function F(t) = X(t)/W(t), where W is a scalar</span></div><div class="line"><a name="l01865"></a><span class="lineno"> 1865</span> <span class="comment"> and F and X are vectors of dimension dim.</span></div><div class="line"><a name="l01866"></a><span class="lineno"> 1866</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l01867"></a><span class="lineno"> 1867</span> <span class="comment"> dim - [in]</span></div><div class="line"><a name="l01868"></a><span class="lineno"> 1868</span> <span class="comment"> der_count - [in] number of derivative (>=0)</span></div><div class="line"><a name="l01869"></a><span class="lineno"> 1869</span> <span class="comment"> v_stride - [in] (>= dim+1)</span></div><div class="line"><a name="l01870"></a><span class="lineno"> 1870</span> <span class="comment"> v - [in/out]</span></div><div class="line"><a name="l01871"></a><span class="lineno"> 1871</span> <span class="comment"> v[] is an array of length (der_count+1)*v_stride.</span></div><div class="line"><a name="l01872"></a><span class="lineno"> 1872</span> <span class="comment"> The input v[] array contains derivatives of the numerator and</span></div><div class="line"><a name="l01873"></a><span class="lineno"> 1873</span> <span class="comment"> denominator functions in the order (X, W), (Xt, Wt), (Xtt, Wtt), ...</span></div><div class="line"><a name="l01874"></a><span class="lineno"> 1874</span> <span class="comment"> In general, the (dim+1) coordinates of the d-th derivative </span></div><div class="line"><a name="l01875"></a><span class="lineno"> 1875</span> <span class="comment"> are in (v[n],...,v[n+dim]) where n = d*v_stride.</span></div><div class="line"><a name="l01876"></a><span class="lineno"> 1876</span> <span class="comment"> In the output v[] array the derivatives of X are replaced with</span></div><div class="line"><a name="l01877"></a><span class="lineno"> 1877</span> <span class="comment"> the derivatives of F and the derivatives of W are divided by</span></div><div class="line"><a name="l01878"></a><span class="lineno"> 1878</span> <span class="comment"> w = v[dim].</span></div><div class="line"><a name="l01879"></a><span class="lineno"> 1879</span> <span class="comment">Returns:</span></div><div class="line"><a name="l01880"></a><span class="lineno"> 1880</span> <span class="comment"> True if input is valid; i.e., v[dim] != 0.</span></div><div class="line"><a name="l01881"></a><span class="lineno"> 1881</span> <span class="comment">See Also:</span></div><div class="line"><a name="l01882"></a><span class="lineno"> 1882</span> <span class="comment"> ON_EvaluateQuotientRule2</span></div><div class="line"><a name="l01883"></a><span class="lineno"> 1883</span> <span class="comment"> ON_EvaluateQuotientRule3</span></div><div class="line"><a name="l01884"></a><span class="lineno"> 1884</span> <span class="comment">*/</span></div><div class="line"><a name="l01885"></a><span class="lineno"> 1885</span> ON_DECL</div><div class="line"><a name="l01886"></a><span class="lineno"> 1886</span> <span class="keywordtype">bool</span> ON_EvaluateQuotientRule( </div><div class="line"><a name="l01887"></a><span class="lineno"> 1887</span>  <span class="keywordtype">int</span> dim, </div><div class="line"><a name="l01888"></a><span class="lineno"> 1888</span>  <span class="keywordtype">int</span> der_count,</div><div class="line"><a name="l01889"></a><span class="lineno"> 1889</span>  <span class="keywordtype">int</span> v_stride, </div><div class="line"><a name="l01890"></a><span class="lineno"> 1890</span>  <span class="keywordtype">double</span> *v </div><div class="line"><a name="l01891"></a><span class="lineno"> 1891</span>  );</div><div class="line"><a name="l01892"></a><span class="lineno"> 1892</span> </div><div class="line"><a name="l01893"></a><span class="lineno"> 1893</span> <span class="comment">/*</span></div><div class="line"><a name="l01894"></a><span class="lineno"> 1894</span> <span class="comment">Description:</span></div><div class="line"><a name="l01895"></a><span class="lineno"> 1895</span> <span class="comment"> Use the quotient rule to compute partial derivatives of a two parameter</span></div><div class="line"><a name="l01896"></a><span class="lineno"> 1896</span> <span class="comment"> rational function F(s,t) = X(s,t)/W(s,t), where W is a scalar</span></div><div class="line"><a name="l01897"></a><span class="lineno"> 1897</span> <span class="comment"> and F and X are vectors of dimension dim.</span></div><div class="line"><a name="l01898"></a><span class="lineno"> 1898</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l01899"></a><span class="lineno"> 1899</span> <span class="comment"> dim - [in]</span></div><div class="line"><a name="l01900"></a><span class="lineno"> 1900</span> <span class="comment"> der_count - [in] number of derivative (>=0)</span></div><div class="line"><a name="l01901"></a><span class="lineno"> 1901</span> <span class="comment"> v_stride - [in] (>= dim+1)</span></div><div class="line"><a name="l01902"></a><span class="lineno"> 1902</span> <span class="comment"> v - [in/out]</span></div><div class="line"><a name="l01903"></a><span class="lineno"> 1903</span> <span class="comment"> v[] is an array of length (der_count+2)*(der_count+1)*v_stride.</span></div><div class="line"><a name="l01904"></a><span class="lineno"> 1904</span> <span class="comment"> The input array contains derivatives of the numerator and denominator</span></div><div class="line"><a name="l01905"></a><span class="lineno"> 1905</span> <span class="comment"> functions in the order X, W, Xs, Ws, Xt, Wt, Xss, Wss, Xst, Wst, Xtt, Wtt, ...</span></div><div class="line"><a name="l01906"></a><span class="lineno"> 1906</span> <span class="comment"> In general, the (i,j)-th derivatives are in the (dim+1) entries of v[]</span></div><div class="line"><a name="l01907"></a><span class="lineno"> 1907</span> <span class="comment"> v[k], ..., answer[k+dim], where k = ((i+j)*(i+j+1)/2 + j)*v_stride.</span></div><div class="line"><a name="l01908"></a><span class="lineno"> 1908</span> <span class="comment"> In the output v[] array the derivatives of X are replaced with</span></div><div class="line"><a name="l01909"></a><span class="lineno"> 1909</span> <span class="comment"> the derivatives of F and the derivatives of W are divided by</span></div><div class="line"><a name="l01910"></a><span class="lineno"> 1910</span> <span class="comment"> w = v[dim].</span></div><div class="line"><a name="l01911"></a><span class="lineno"> 1911</span> <span class="comment">Returns:</span></div><div class="line"><a name="l01912"></a><span class="lineno"> 1912</span> <span class="comment"> True if input is valid; i.e., v[dim] != 0.</span></div><div class="line"><a name="l01913"></a><span class="lineno"> 1913</span> <span class="comment">See Also:</span></div><div class="line"><a name="l01914"></a><span class="lineno"> 1914</span> <span class="comment"> ON_EvaluateQuotientRule</span></div><div class="line"><a name="l01915"></a><span class="lineno"> 1915</span> <span class="comment"> ON_EvaluateQuotientRule3</span></div><div class="line"><a name="l01916"></a><span class="lineno"> 1916</span> <span class="comment">*/</span></div><div class="line"><a name="l01917"></a><span class="lineno"> 1917</span> ON_DECL</div><div class="line"><a name="l01918"></a><span class="lineno"> 1918</span> <span class="keywordtype">bool</span> ON_EvaluateQuotientRule2( </div><div class="line"><a name="l01919"></a><span class="lineno"> 1919</span>  <span class="keywordtype">int</span> dim, </div><div class="line"><a name="l01920"></a><span class="lineno"> 1920</span>  <span class="keywordtype">int</span> der_count, </div><div class="line"><a name="l01921"></a><span class="lineno"> 1921</span>  <span class="keywordtype">int</span> v_stride, </div><div class="line"><a name="l01922"></a><span class="lineno"> 1922</span>  <span class="keywordtype">double</span> *v </div><div class="line"><a name="l01923"></a><span class="lineno"> 1923</span>  );</div><div class="line"><a name="l01924"></a><span class="lineno"> 1924</span> </div><div class="line"><a name="l01925"></a><span class="lineno"> 1925</span> <span class="comment">/*</span></div><div class="line"><a name="l01926"></a><span class="lineno"> 1926</span> <span class="comment">Description:</span></div><div class="line"><a name="l01927"></a><span class="lineno"> 1927</span> <span class="comment"> Use the quotient rule to compute partial derivatives of a 3 parameter</span></div><div class="line"><a name="l01928"></a><span class="lineno"> 1928</span> <span class="comment"> rational function F(r,s,t) = X(r,s,t)/W(r,s,t), where W is a scalar</span></div><div class="line"><a name="l01929"></a><span class="lineno"> 1929</span> <span class="comment"> and F and X are vectors of dimension dim.</span></div><div class="line"><a name="l01930"></a><span class="lineno"> 1930</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l01931"></a><span class="lineno"> 1931</span> <span class="comment"> dim - [in]</span></div><div class="line"><a name="l01932"></a><span class="lineno"> 1932</span> <span class="comment"> der_count - [in] number of derivative (>=0)</span></div><div class="line"><a name="l01933"></a><span class="lineno"> 1933</span> <span class="comment"> v_stride - [in] (>= dim+1)</span></div><div class="line"><a name="l01934"></a><span class="lineno"> 1934</span> <span class="comment"> v - [in/out]</span></div><div class="line"><a name="l01935"></a><span class="lineno"> 1935</span> <span class="comment"> v[] is an array of length </span></div><div class="line"><a name="l01936"></a><span class="lineno"> 1936</span> <span class="comment"> v_stride*(der_count+1)*(der_count+2)*(der_count+3)/6.</span></div><div class="line"><a name="l01937"></a><span class="lineno"> 1937</span> <span class="comment"> The input v[] array contains derivatives of the numerator and</span></div><div class="line"><a name="l01938"></a><span class="lineno"> 1938</span> <span class="comment"> denominator functions in the order (X, W), (Xr, Wr), (Xs, Ws),</span></div><div class="line"><a name="l01939"></a><span class="lineno"> 1939</span> <span class="comment"> (Xt, Wt), (Xrr, Wrr), (Xrs, Wrs), (Xrt, Wrt), (Xss, Wss), </span></div><div class="line"><a name="l01940"></a><span class="lineno"> 1940</span> <span class="comment"> (Xst, Wst), (Xtt, Wtt), ...</span></div><div class="line"><a name="l01941"></a><span class="lineno"> 1941</span> <span class="comment"> In general, the (dim+1) coordinates of the derivative </span></div><div class="line"><a name="l01942"></a><span class="lineno"> 1942</span> <span class="comment"> (Dr^i Ds^j Dt^k, i+j+k=d) are at v[n], ..., v[n+dim] where </span></div><div class="line"><a name="l01943"></a><span class="lineno"> 1943</span> <span class="comment"> n = v_stride*( d*(d+1)*(d+2)/6 + (d-i)*(d-i+1)/2 + k ).</span></div><div class="line"><a name="l01944"></a><span class="lineno"> 1944</span> <span class="comment"> In the output v[] array the derivatives of X are replaced with</span></div><div class="line"><a name="l01945"></a><span class="lineno"> 1945</span> <span class="comment"> the derivatives of F and the derivatives of W are divided by</span></div><div class="line"><a name="l01946"></a><span class="lineno"> 1946</span> <span class="comment"> w = v[dim].</span></div><div class="line"><a name="l01947"></a><span class="lineno"> 1947</span> <span class="comment">Returns:</span></div><div class="line"><a name="l01948"></a><span class="lineno"> 1948</span> <span class="comment"> True if input is valid; i.e., v[dim] != 0.</span></div><div class="line"><a name="l01949"></a><span class="lineno"> 1949</span> <span class="comment">See Also:</span></div><div class="line"><a name="l01950"></a><span class="lineno"> 1950</span> <span class="comment"> ON_EvaluateQuotientRule</span></div><div class="line"><a name="l01951"></a><span class="lineno"> 1951</span> <span class="comment"> ON_EvaluateQuotientRule2</span></div><div class="line"><a name="l01952"></a><span class="lineno"> 1952</span> <span class="comment">*/</span></div><div class="line"><a name="l01953"></a><span class="lineno"> 1953</span> ON_DECL</div><div class="line"><a name="l01954"></a><span class="lineno"> 1954</span> <span class="keywordtype">bool</span> ON_EvaluateQuotientRule3( </div><div class="line"><a name="l01955"></a><span class="lineno"> 1955</span>  <span class="keywordtype">int</span> dim, </div><div class="line"><a name="l01956"></a><span class="lineno"> 1956</span>  <span class="keywordtype">int</span> der_count, </div><div class="line"><a name="l01957"></a><span class="lineno"> 1957</span>  <span class="keywordtype">int</span> v_stride,</div><div class="line"><a name="l01958"></a><span class="lineno"> 1958</span>  <span class="keywordtype">double</span> *v </div><div class="line"><a name="l01959"></a><span class="lineno"> 1959</span>  );</div><div class="line"><a name="l01960"></a><span class="lineno"> 1960</span> </div><div class="line"><a name="l01961"></a><span class="lineno"> 1961</span> ON_DECL</div><div class="line"><a name="l01962"></a><span class="lineno"> 1962</span> <span class="keywordtype">bool</span> ON_GetPolylineLength(</div><div class="line"><a name="l01963"></a><span class="lineno"> 1963</span>  <span class="keywordtype">int</span>, <span class="comment">// dimension of points</span></div><div class="line"><a name="l01964"></a><span class="lineno"> 1964</span>  <span class="keywordtype">bool</span>, <span class="comment">// bIsRational true if points are homogeneous rational</span></div><div class="line"><a name="l01965"></a><span class="lineno"> 1965</span>  <span class="keywordtype">int</span>, <span class="comment">// number of points</span></div><div class="line"><a name="l01966"></a><span class="lineno"> 1966</span>  <span class="keywordtype">int</span>, <span class="comment">// stride between points</span></div><div class="line"><a name="l01967"></a><span class="lineno"> 1967</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// points</span></div><div class="line"><a name="l01968"></a><span class="lineno"> 1968</span>  <span class="keywordtype">double</span>* <span class="comment">// length returned here</span></div><div class="line"><a name="l01969"></a><span class="lineno"> 1969</span>  );</div><div class="line"><a name="l01970"></a><span class="lineno"> 1970</span> </div><div class="line"><a name="l01971"></a><span class="lineno"> 1971</span> </div><div class="line"><a name="l01972"></a><span class="lineno"> 1972</span> <span class="comment">/*</span></div><div class="line"><a name="l01973"></a><span class="lineno"> 1973</span> <span class="comment">Description:</span></div><div class="line"><a name="l01974"></a><span class="lineno"> 1974</span> <span class="comment"> Find the index of the point in the point_list that is closest to P.</span></div><div class="line"><a name="l01975"></a><span class="lineno"> 1975</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l01976"></a><span class="lineno"> 1976</span> <span class="comment"> point_count - [in]</span></div><div class="line"><a name="l01977"></a><span class="lineno"> 1977</span> <span class="comment"> point_list - [in]</span></div><div class="line"><a name="l01978"></a><span class="lineno"> 1978</span> <span class="comment"> P - [in]</span></div><div class="line"><a name="l01979"></a><span class="lineno"> 1979</span> <span class="comment"> closest_point_index - [out]</span></div><div class="line"><a name="l01980"></a><span class="lineno"> 1980</span> <span class="comment">Returns:</span></div><div class="line"><a name="l01981"></a><span class="lineno"> 1981</span> <span class="comment"> True if successful and *closest_point_index is set.</span></div><div class="line"><a name="l01982"></a><span class="lineno"> 1982</span> <span class="comment"> False if input is not valid, in which case *closest_point_index</span></div><div class="line"><a name="l01983"></a><span class="lineno"> 1983</span> <span class="comment"> is undefined.</span></div><div class="line"><a name="l01984"></a><span class="lineno"> 1984</span> <span class="comment">*/</span></div><div class="line"><a name="l01985"></a><span class="lineno"> 1985</span> ON_DECL</div><div class="line"><a name="l01986"></a><span class="lineno"> 1986</span> <span class="keywordtype">bool</span> ON_GetClosestPointInPointList( </div><div class="line"><a name="l01987"></a><span class="lineno"> 1987</span>  <span class="keywordtype">int</span> point_count,</div><div class="line"><a name="l01988"></a><span class="lineno"> 1988</span>  <span class="keyword">const</span> <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a>* point_list,</div><div class="line"><a name="l01989"></a><span class="lineno"> 1989</span>  <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a> P,</div><div class="line"><a name="l01990"></a><span class="lineno"> 1990</span>  <span class="keywordtype">int</span>* closest_point_index</div><div class="line"><a name="l01991"></a><span class="lineno"> 1991</span>  );</div><div class="line"><a name="l01992"></a><span class="lineno"> 1992</span> </div><div class="line"><a name="l01993"></a><span class="lineno"> 1993</span> <span class="comment">/*</span></div><div class="line"><a name="l01994"></a><span class="lineno"> 1994</span> <span class="comment">Description:</span></div><div class="line"><a name="l01995"></a><span class="lineno"> 1995</span> <span class="comment"> Test math library functions.</span></div><div class="line"><a name="l01996"></a><span class="lineno"> 1996</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l01997"></a><span class="lineno"> 1997</span> <span class="comment"> function_index - [in] Determines which math library function is called.</span></div><div class="line"><a name="l01998"></a><span class="lineno"> 1998</span> <span class="comment"></span></div><div class="line"><a name="l01999"></a><span class="lineno"> 1999</span> <span class="comment"> 1: z = x+y</span></div><div class="line"><a name="l02000"></a><span class="lineno"> 2000</span> <span class="comment"> 2: z = x-y</span></div><div class="line"><a name="l02001"></a><span class="lineno"> 2001</span> <span class="comment"> 3: z = x*y</span></div><div class="line"><a name="l02002"></a><span class="lineno"> 2002</span> <span class="comment"> 4: z = x/y</span></div><div class="line"><a name="l02003"></a><span class="lineno"> 2003</span> <span class="comment"> 5: z = fabs(x)</span></div><div class="line"><a name="l02004"></a><span class="lineno"> 2004</span> <span class="comment"> 6: z = exp(x)</span></div><div class="line"><a name="l02005"></a><span class="lineno"> 2005</span> <span class="comment"> 7: z = log(x)</span></div><div class="line"><a name="l02006"></a><span class="lineno"> 2006</span> <span class="comment"> 8: z = logb(x)</span></div><div class="line"><a name="l02007"></a><span class="lineno"> 2007</span> <span class="comment"> 9: z = log10(x)</span></div><div class="line"><a name="l02008"></a><span class="lineno"> 2008</span> <span class="comment"> 10: z = pow(x,y)</span></div><div class="line"><a name="l02009"></a><span class="lineno"> 2009</span> <span class="comment"> 11: z = sqrt(x)</span></div><div class="line"><a name="l02010"></a><span class="lineno"> 2010</span> <span class="comment"> 12: z = sin(x)</span></div><div class="line"><a name="l02011"></a><span class="lineno"> 2011</span> <span class="comment"> 13: z = cos(x)</span></div><div class="line"><a name="l02012"></a><span class="lineno"> 2012</span> <span class="comment"> 14: z = tan(x)</span></div><div class="line"><a name="l02013"></a><span class="lineno"> 2013</span> <span class="comment"> 15: z = sinh(x)</span></div><div class="line"><a name="l02014"></a><span class="lineno"> 2014</span> <span class="comment"> 16: z = cosh(x)</span></div><div class="line"><a name="l02015"></a><span class="lineno"> 2015</span> <span class="comment"> 17: z = tanh(x)</span></div><div class="line"><a name="l02016"></a><span class="lineno"> 2016</span> <span class="comment"> 18: z = asin(x)</span></div><div class="line"><a name="l02017"></a><span class="lineno"> 2017</span> <span class="comment"> 19: z = acos(x)</span></div><div class="line"><a name="l02018"></a><span class="lineno"> 2018</span> <span class="comment"> 20: z = atan(x)</span></div><div class="line"><a name="l02019"></a><span class="lineno"> 2019</span> <span class="comment"> 21: z = atan2(y,x)</span></div><div class="line"><a name="l02020"></a><span class="lineno"> 2020</span> <span class="comment"> 22: z = fmod(x,y)</span></div><div class="line"><a name="l02021"></a><span class="lineno"> 2021</span> <span class="comment"> 23: z = modf(x,&y)</span></div><div class="line"><a name="l02022"></a><span class="lineno"> 2022</span> <span class="comment"> 24: z = frexp(x,&y)</span></div><div class="line"><a name="l02023"></a><span class="lineno"> 2023</span> <span class="comment"></span></div><div class="line"><a name="l02024"></a><span class="lineno"> 2024</span> <span class="comment"> double x - [in]</span></div><div class="line"><a name="l02025"></a><span class="lineno"> 2025</span> <span class="comment"> double y - [in]</span></div><div class="line"><a name="l02026"></a><span class="lineno"> 2026</span> <span class="comment">Returns:</span></div><div class="line"><a name="l02027"></a><span class="lineno"> 2027</span> <span class="comment"> Returns the "z" value listed in the function_index parameter</span></div><div class="line"><a name="l02028"></a><span class="lineno"> 2028</span> <span class="comment"> description.</span></div><div class="line"><a name="l02029"></a><span class="lineno"> 2029</span> <span class="comment">Remarks:</span></div><div class="line"><a name="l02030"></a><span class="lineno"> 2030</span> <span class="comment"> This function is used to test the results of class floating</span></div><div class="line"><a name="l02031"></a><span class="lineno"> 2031</span> <span class="comment"> point functions. It is primarily used to see what happens</span></div><div class="line"><a name="l02032"></a><span class="lineno"> 2032</span> <span class="comment"> when opennurbs is used as a DLL and illegal operations are</span></div><div class="line"><a name="l02033"></a><span class="lineno"> 2033</span> <span class="comment"> performed.</span></div><div class="line"><a name="l02034"></a><span class="lineno"> 2034</span> <span class="comment">*/</span></div><div class="line"><a name="l02035"></a><span class="lineno"> 2035</span> ON_DECL</div><div class="line"><a name="l02036"></a><span class="lineno"> 2036</span> <span class="keywordtype">double</span> ON_TestMathFunction( </div><div class="line"><a name="l02037"></a><span class="lineno"> 2037</span>  <span class="keywordtype">int</span> function_index, </div><div class="line"><a name="l02038"></a><span class="lineno"> 2038</span>  <span class="keywordtype">double</span> x, </div><div class="line"><a name="l02039"></a><span class="lineno"> 2039</span>  <span class="keywordtype">double</span> y </div><div class="line"><a name="l02040"></a><span class="lineno"> 2040</span>  );</div><div class="line"><a name="l02041"></a><span class="lineno"> 2041</span> </div><div class="line"><a name="l02042"></a><span class="lineno"> 2042</span> <span class="comment">// If performance is important, then</span></div><div class="line"><a name="l02043"></a><span class="lineno"> 2043</span> <span class="comment">// you are better off using ((b<a)?a:b)</span></div><div class="line"><a name="l02044"></a><span class="lineno"> 2044</span> ON_DECL <span class="keywordtype">double</span> ON_Max(<span class="keywordtype">double</span> a, <span class="keywordtype">double</span> b);</div><div class="line"><a name="l02045"></a><span class="lineno"> 2045</span> </div><div class="line"><a name="l02046"></a><span class="lineno"> 2046</span> <span class="comment">// If performance is important, then</span></div><div class="line"><a name="l02047"></a><span class="lineno"> 2047</span> <span class="comment">// you are better off using ((b<a)?a:b)</span></div><div class="line"><a name="l02048"></a><span class="lineno"> 2048</span> ON_DECL <span class="keywordtype">float</span> ON_Max(<span class="keywordtype">float</span> a, <span class="keywordtype">float</span> b);</div><div class="line"><a name="l02049"></a><span class="lineno"> 2049</span> </div><div class="line"><a name="l02050"></a><span class="lineno"> 2050</span> <span class="comment">// If performance is important, then</span></div><div class="line"><a name="l02051"></a><span class="lineno"> 2051</span> <span class="comment">// you are better off using ((b<a)?a:b)</span></div><div class="line"><a name="l02052"></a><span class="lineno"> 2052</span> ON_DECL <span class="keywordtype">int</span> ON_Max(<span class="keywordtype">int</span> a, <span class="keywordtype">int</span> b);</div><div class="line"><a name="l02053"></a><span class="lineno"> 2053</span> </div><div class="line"><a name="l02054"></a><span class="lineno"> 2054</span> <span class="comment">// If performance is important, then</span></div><div class="line"><a name="l02055"></a><span class="lineno"> 2055</span> <span class="comment">// you are better off using ((a<b)?a:b)</span></div><div class="line"><a name="l02056"></a><span class="lineno"> 2056</span> ON_DECL <span class="keywordtype">double</span> ON_Min(<span class="keywordtype">double</span> a, <span class="keywordtype">double</span> b);</div><div class="line"><a name="l02057"></a><span class="lineno"> 2057</span> </div><div class="line"><a name="l02058"></a><span class="lineno"> 2058</span> <span class="comment">// If performance is important, then</span></div><div class="line"><a name="l02059"></a><span class="lineno"> 2059</span> <span class="comment">// you are better off using ((a<b)?a:b)</span></div><div class="line"><a name="l02060"></a><span class="lineno"> 2060</span> ON_DECL <span class="keywordtype">float</span> ON_Min(<span class="keywordtype">float</span> a, <span class="keywordtype">float</span> b);</div><div class="line"><a name="l02061"></a><span class="lineno"> 2061</span> </div><div class="line"><a name="l02062"></a><span class="lineno"> 2062</span> <span class="comment">// If performance is important, then</span></div><div class="line"><a name="l02063"></a><span class="lineno"> 2063</span> <span class="comment">// you are better off using ((a<b)?a:b)</span></div><div class="line"><a name="l02064"></a><span class="lineno"> 2064</span> ON_DECL <span class="keywordtype">int</span> ON_Min(<span class="keywordtype">int</span> a, <span class="keywordtype">int</span> b);</div><div class="line"><a name="l02065"></a><span class="lineno"> 2065</span> </div><div class="line"><a name="l02066"></a><span class="lineno"> 2066</span> <span class="comment">// Do not call ON_Round() in any opennurbs code, tl code</span></div><div class="line"><a name="l02067"></a><span class="lineno"> 2067</span> <span class="comment">// or any other code that does critical calculations or</span></div><div class="line"><a name="l02068"></a><span class="lineno"> 2068</span> <span class="comment">// when there is any possibility that x is invalid or</span></div><div class="line"><a name="l02069"></a><span class="lineno"> 2069</span> <span class="comment">// fabs(x)>2147483647. Use floor(x+0.5) instead.</span></div><div class="line"><a name="l02070"></a><span class="lineno"> 2070</span> ON_DECL <span class="keywordtype">int</span> ON_Round(<span class="keywordtype">double</span> x);</div><div class="line"><a name="l02071"></a><span class="lineno"> 2071</span> </div><div class="line"><a name="l02072"></a><span class="lineno"> 2072</span> <span class="comment">/*</span></div><div class="line"><a name="l02073"></a><span class="lineno"> 2073</span> <span class="comment">Description:</span></div><div class="line"><a name="l02074"></a><span class="lineno"> 2074</span> <span class="comment"> Calculate the value of (1.0-t)*x + t*y so that, </span></div><div class="line"><a name="l02075"></a><span class="lineno"> 2075</span> <span class="comment"> if 0.0 <= t <= 1.0, then the result is between x and y and</span></div><div class="line"><a name="l02076"></a><span class="lineno"> 2076</span> <span class="comment"> if x == y and t is a valid double, the result is x.</span></div><div class="line"><a name="l02077"></a><span class="lineno"> 2077</span> <span class="comment">Returns:</span></div><div class="line"><a name="l02078"></a><span class="lineno"> 2078</span> <span class="comment"> (1.0-t)*x + t*y</span></div><div class="line"><a name="l02079"></a><span class="lineno"> 2079</span> <span class="comment">*/</span></div><div class="line"><a name="l02080"></a><span class="lineno"> 2080</span> ON_DECL <span class="keywordtype">double</span> ON_LinearInterpolation(</div><div class="line"><a name="l02081"></a><span class="lineno"> 2081</span>  <span class="keywordtype">double</span> t, </div><div class="line"><a name="l02082"></a><span class="lineno"> 2082</span>  <span class="keywordtype">double</span> x, </div><div class="line"><a name="l02083"></a><span class="lineno"> 2083</span>  <span class="keywordtype">double</span> y</div><div class="line"><a name="l02084"></a><span class="lineno"> 2084</span>  );</div><div class="line"><a name="l02085"></a><span class="lineno"> 2085</span> </div><div class="line"><a name="l02086"></a><span class="lineno"> 2086</span> <span class="comment">/*</span></div><div class="line"><a name="l02087"></a><span class="lineno"> 2087</span> <span class="comment">Description:</span></div><div class="line"><a name="l02088"></a><span class="lineno"> 2088</span> <span class="comment"> Find the equation of the parabola, ellipse or hyperbola </span></div><div class="line"><a name="l02089"></a><span class="lineno"> 2089</span> <span class="comment"> (non-degenerate conic) that passes through six distinct points.</span></div><div class="line"><a name="l02090"></a><span class="lineno"> 2090</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l02091"></a><span class="lineno"> 2091</span> <span class="comment"> stride - [in] (>=2) </span></div><div class="line"><a name="l02092"></a><span class="lineno"> 2092</span> <span class="comment"> points array stride</span></div><div class="line"><a name="l02093"></a><span class="lineno"> 2093</span> <span class="comment"> points2d - [in] (>=2) </span></div><div class="line"><a name="l02094"></a><span class="lineno"> 2094</span> <span class="comment"> i-th point is (points[i*stride],points[i*stride+1])</span></div><div class="line"><a name="l02095"></a><span class="lineno"> 2095</span> <span class="comment"> conic - [out]</span></div><div class="line"><a name="l02096"></a><span class="lineno"> 2096</span> <span class="comment"> Coefficients of the conic equation.</span></div><div class="line"><a name="l02097"></a><span class="lineno"> 2097</span> <span class="comment"> The points on the conic satisfy the equation</span></div><div class="line"><a name="l02098"></a><span class="lineno"> 2098</span> <span class="comment"> 0 = conic[0]*x^2 + conic[1]*xy + conic[2]*y^2 </span></div><div class="line"><a name="l02099"></a><span class="lineno"> 2099</span> <span class="comment"> + conic[3]*x + conic[4]*y + conic[5]</span></div><div class="line"><a name="l02100"></a><span class="lineno"> 2100</span> <span class="comment"> max_pivot - [out] (can be null)</span></div><div class="line"><a name="l02101"></a><span class="lineno"> 2101</span> <span class="comment"> min_pivot - [out] (can be null)</span></div><div class="line"><a name="l02102"></a><span class="lineno"> 2102</span> <span class="comment"> zero_pivot - [out] (can be null)</span></div><div class="line"><a name="l02103"></a><span class="lineno"> 2103</span> <span class="comment"> If there are some near duplicates in the input point set,</span></div><div class="line"><a name="l02104"></a><span class="lineno"> 2104</span> <span class="comment"> the calculation is not stable. If you want to get an</span></div><div class="line"><a name="l02105"></a><span class="lineno"> 2105</span> <span class="comment"> estimate of the validity of the solution, then inspect</span></div><div class="line"><a name="l02106"></a><span class="lineno"> 2106</span> <span class="comment"> the returned values. max_pivot should around 1, </span></div><div class="line"><a name="l02107"></a><span class="lineno"> 2107</span> <span class="comment"> min_pivot should be > 1e-4 or so, and zero_pivot should</span></div><div class="line"><a name="l02108"></a><span class="lineno"> 2108</span> <span class="comment"> be < 1e-10 or so. If the returned pivots don't satisify</span></div><div class="line"><a name="l02109"></a><span class="lineno"> 2109</span> <span class="comment"> these condtions, then exercise caution when using the</span></div><div class="line"><a name="l02110"></a><span class="lineno"> 2110</span> <span class="comment"> returned solution.</span></div><div class="line"><a name="l02111"></a><span class="lineno"> 2111</span> <span class="comment">Returns:</span></div><div class="line"><a name="l02112"></a><span class="lineno"> 2112</span> <span class="comment"> True if a there is an ellipse, parabola or hyperbola through the </span></div><div class="line"><a name="l02113"></a><span class="lineno"> 2113</span> <span class="comment"> six points.</span></div><div class="line"><a name="l02114"></a><span class="lineno"> 2114</span> <span class="comment"> False if the input is invalid or the conic degenerate (the</span></div><div class="line"><a name="l02115"></a><span class="lineno"> 2115</span> <span class="comment"> points lie on one or two lines).</span></div><div class="line"><a name="l02116"></a><span class="lineno"> 2116</span> <span class="comment"> If false is returned, then conic[0]=...=conic[5] = 0 and</span></div><div class="line"><a name="l02117"></a><span class="lineno"> 2117</span> <span class="comment"> *min_pivot = *max_pivot = *zero_pivot = 0.</span></div><div class="line"><a name="l02118"></a><span class="lineno"> 2118</span> <span class="comment">*/</span></div><div class="line"><a name="l02119"></a><span class="lineno"> 2119</span> ON_DECL <span class="keywordtype">bool</span> ON_GetConicEquationThrough6Points( </div><div class="line"><a name="l02120"></a><span class="lineno"> 2120</span>  <span class="keywordtype">int</span> stride, </div><div class="line"><a name="l02121"></a><span class="lineno"> 2121</span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* points2d, </div><div class="line"><a name="l02122"></a><span class="lineno"> 2122</span>  <span class="keywordtype">double</span> conic[6],</div><div class="line"><a name="l02123"></a><span class="lineno"> 2123</span>  <span class="keywordtype">double</span>* max_pivot,</div><div class="line"><a name="l02124"></a><span class="lineno"> 2124</span>  <span class="keywordtype">double</span>* min_pivot,</div><div class="line"><a name="l02125"></a><span class="lineno"> 2125</span>  <span class="keywordtype">double</span>* zero_pivot</div><div class="line"><a name="l02126"></a><span class="lineno"> 2126</span>  );</div><div class="line"><a name="l02127"></a><span class="lineno"> 2127</span> </div><div class="line"><a name="l02128"></a><span class="lineno"> 2128</span> <span class="comment">/*</span></div><div class="line"><a name="l02129"></a><span class="lineno"> 2129</span> <span class="comment">Description:</span></div><div class="line"><a name="l02130"></a><span class="lineno"> 2130</span> <span class="comment"> Test a conic equation to see if it defines and ellipse. If so,</span></div><div class="line"><a name="l02131"></a><span class="lineno"> 2131</span> <span class="comment"> return the center and axes of the ellipse.</span></div><div class="line"><a name="l02132"></a><span class="lineno"> 2132</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l02133"></a><span class="lineno"> 2133</span> <span class="comment"> conic - [in]</span></div><div class="line"><a name="l02134"></a><span class="lineno"> 2134</span> <span class="comment"> Coefficients of the conic equation.</span></div><div class="line"><a name="l02135"></a><span class="lineno"> 2135</span> <span class="comment"> The points on the conic satisfy the equation</span></div><div class="line"><a name="l02136"></a><span class="lineno"> 2136</span> <span class="comment"> 0 = conic[0]*x^2 + conic[1]*xy + conic[2]*y^2 </span></div><div class="line"><a name="l02137"></a><span class="lineno"> 2137</span> <span class="comment"> + conic[3]*x + conic[4]*y + conic[5]</span></div><div class="line"><a name="l02138"></a><span class="lineno"> 2138</span> <span class="comment"> center - [out]</span></div><div class="line"><a name="l02139"></a><span class="lineno"> 2139</span> <span class="comment"> major_axis - [out]</span></div><div class="line"><a name="l02140"></a><span class="lineno"> 2140</span> <span class="comment"> minor_axis - [out]</span></div><div class="line"><a name="l02141"></a><span class="lineno"> 2141</span> <span class="comment"> major_radius - [out]</span></div><div class="line"><a name="l02142"></a><span class="lineno"> 2142</span> <span class="comment"> minor_radius - [out]</span></div><div class="line"><a name="l02143"></a><span class="lineno"> 2143</span> <span class="comment">Returns:</span></div><div class="line"><a name="l02144"></a><span class="lineno"> 2144</span> <span class="comment"> True if the conic is an ellipse and the center and axes were found.</span></div><div class="line"><a name="l02145"></a><span class="lineno"> 2145</span> <span class="comment"> False if the conic is not an ellipse, in which case the input values</span></div><div class="line"><a name="l02146"></a><span class="lineno"> 2146</span> <span class="comment"> of center, major_axis, minor_axis, major_radius, and minor_radius</span></div><div class="line"><a name="l02147"></a><span class="lineno"> 2147</span> <span class="comment"> are not changed.</span></div><div class="line"><a name="l02148"></a><span class="lineno"> 2148</span> <span class="comment">*/</span></div><div class="line"><a name="l02149"></a><span class="lineno"> 2149</span> ON_DECL <span class="keywordtype">bool</span> ON_IsConicEquationAnEllipse( </div><div class="line"><a name="l02150"></a><span class="lineno"> 2150</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> conic[6], </div><div class="line"><a name="l02151"></a><span class="lineno"> 2151</span>  <a class="code" href="class_o_n__2d_point.html">ON_2dPoint</a>& center, </div><div class="line"><a name="l02152"></a><span class="lineno"> 2152</span>  <a class="code" href="class_o_n__2d_vector.html">ON_2dVector</a>& major_axis, </div><div class="line"><a name="l02153"></a><span class="lineno"> 2153</span>  <a class="code" href="class_o_n__2d_vector.html">ON_2dVector</a>& minor_axis, </div><div class="line"><a name="l02154"></a><span class="lineno"> 2154</span>  <span class="keywordtype">double</span>* major_radius, </div><div class="line"><a name="l02155"></a><span class="lineno"> 2155</span>  <span class="keywordtype">double</span>* minor_radius</div><div class="line"><a name="l02156"></a><span class="lineno"> 2156</span>  );</div><div class="line"><a name="l02157"></a><span class="lineno"> 2157</span> </div><div class="line"><a name="l02158"></a><span class="lineno"> 2158</span> <span class="comment">/*</span></div><div class="line"><a name="l02159"></a><span class="lineno"> 2159</span> <span class="comment">Description:</span></div><div class="line"><a name="l02160"></a><span class="lineno"> 2160</span> <span class="comment"> Get the conic equation of an ellipse.</span></div><div class="line"><a name="l02161"></a><span class="lineno"> 2161</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l02162"></a><span class="lineno"> 2162</span> <span class="comment"> a - [in] (a>0)</span></div><div class="line"><a name="l02163"></a><span class="lineno"> 2163</span> <span class="comment"> b - [in] (b>0)</span></div><div class="line"><a name="l02164"></a><span class="lineno"> 2164</span> <span class="comment"> a and b are the lengths of the axes. Either one</span></div><div class="line"><a name="l02165"></a><span class="lineno"> 2165</span> <span class="comment"> may be largest and they can be equal.</span></div><div class="line"><a name="l02166"></a><span class="lineno"> 2166</span> <span class="comment"> x0 - [in]</span></div><div class="line"><a name="l02167"></a><span class="lineno"> 2167</span> <span class="comment"> y0 - [in]</span></div><div class="line"><a name="l02168"></a><span class="lineno"> 2168</span> <span class="comment"> (x0,y0) is the enter of the ellipse.</span></div><div class="line"><a name="l02169"></a><span class="lineno"> 2169</span> <span class="comment"> alpha - [in] (angle in radians)</span></div><div class="line"><a name="l02170"></a><span class="lineno"> 2170</span> <span class="comment"> When alpha is 0, a corresponds to the x-axis and</span></div><div class="line"><a name="l02171"></a><span class="lineno"> 2171</span> <span class="comment"> b corresponds to the y axis. If alpha is non-zero</span></div><div class="line"><a name="l02172"></a><span class="lineno"> 2172</span> <span class="comment"> it specifies the rotation of these axes.</span></div><div class="line"><a name="l02173"></a><span class="lineno"> 2173</span> <span class="comment"> conic - [out]</span></div><div class="line"><a name="l02174"></a><span class="lineno"> 2174</span> <span class="comment"> Coefficients of the conic equation.</span></div><div class="line"><a name="l02175"></a><span class="lineno"> 2175</span> <span class="comment"> The points on the conic satisfy the equation</span></div><div class="line"><a name="l02176"></a><span class="lineno"> 2176</span> <span class="comment"> 0 = conic[0]*x^2 + conic[1]*xy + conic[2]*y^2 </span></div><div class="line"><a name="l02177"></a><span class="lineno"> 2177</span> <span class="comment"> + conic[3]*x + conic[4]*y + conic[5]</span></div><div class="line"><a name="l02178"></a><span class="lineno"> 2178</span> <span class="comment"> center - [out]</span></div><div class="line"><a name="l02179"></a><span class="lineno"> 2179</span> <span class="comment"> major_axis - [out]</span></div><div class="line"><a name="l02180"></a><span class="lineno"> 2180</span> <span class="comment"> minor_axis - [out]</span></div><div class="line"><a name="l02181"></a><span class="lineno"> 2181</span> <span class="comment"> major_radius - [out]</span></div><div class="line"><a name="l02182"></a><span class="lineno"> 2182</span> <span class="comment"> minor_radius - [out]</span></div><div class="line"><a name="l02183"></a><span class="lineno"> 2183</span> <span class="comment">Remarks:</span></div><div class="line"><a name="l02184"></a><span class="lineno"> 2184</span> <span class="comment"> Here is the way to evaluate a point on the ellipse:</span></div><div class="line"><a name="l02185"></a><span class="lineno"> 2185</span> <span class="comment"></span></div><div class="line"><a name="l02186"></a><span class="lineno"> 2186</span> <span class="comment"> </span></div><div class="line"><a name="l02187"></a><span class="lineno"> 2187</span> <span class="comment"> double t = ellipse paramter in radians;</span></div><div class="line"><a name="l02188"></a><span class="lineno"> 2188</span> <span class="comment"> double x = a*cos(t);</span></div><div class="line"><a name="l02189"></a><span class="lineno"> 2189</span> <span class="comment"> double y = b*sin(t);</span></div><div class="line"><a name="l02190"></a><span class="lineno"> 2190</span> <span class="comment"> ON_2dPoint ellipse_point;</span></div><div class="line"><a name="l02191"></a><span class="lineno"> 2191</span> <span class="comment"> ellipse_point.x = x0 + x*cos(alpha) + y*sin(alpha);</span></div><div class="line"><a name="l02192"></a><span class="lineno"> 2192</span> <span class="comment"> ellipse_point.y = y0 - x*sin(alpha) + y*cos(alpha);</span></div><div class="line"><a name="l02193"></a><span class="lineno"> 2193</span> <span class="comment"></span></div><div class="line"><a name="l02194"></a><span class="lineno"> 2194</span> <span class="comment">Returns:</span></div><div class="line"><a name="l02195"></a><span class="lineno"> 2195</span> <span class="comment"> True if the input is valid and conic[] was filled in.</span></div><div class="line"><a name="l02196"></a><span class="lineno"> 2196</span> <span class="comment"> Falis if the input is not valid. In this case the values in conic[]</span></div><div class="line"><a name="l02197"></a><span class="lineno"> 2197</span> <span class="comment"> are not changed.</span></div><div class="line"><a name="l02198"></a><span class="lineno"> 2198</span> <span class="comment">*/</span></div><div class="line"><a name="l02199"></a><span class="lineno"> 2199</span> ON_DECL <span class="keywordtype">bool</span> ON_GetEllipseConicEquation( </div><div class="line"><a name="l02200"></a><span class="lineno"> 2200</span>  <span class="keywordtype">double</span> a, <span class="keywordtype">double</span> b, </div><div class="line"><a name="l02201"></a><span class="lineno"> 2201</span>  <span class="keywordtype">double</span> x0, <span class="keywordtype">double</span> y0, </div><div class="line"><a name="l02202"></a><span class="lineno"> 2202</span>  <span class="keywordtype">double</span> alpha,</div><div class="line"><a name="l02203"></a><span class="lineno"> 2203</span>  <span class="keywordtype">double</span> conic[6]</div><div class="line"><a name="l02204"></a><span class="lineno"> 2204</span>  );</div><div class="line"><a name="l02205"></a><span class="lineno"> 2205</span> </div><div class="line"><a name="l02206"></a><span class="lineno"> 2206</span> <span class="comment">/*</span></div><div class="line"><a name="l02207"></a><span class="lineno"> 2207</span> <span class="comment">Descripton:</span></div><div class="line"><a name="l02208"></a><span class="lineno"> 2208</span> <span class="comment"> Return the length of a 2d vector (x,y)</span></div><div class="line"><a name="l02209"></a><span class="lineno"> 2209</span> <span class="comment">Returns:</span></div><div class="line"><a name="l02210"></a><span class="lineno"> 2210</span> <span class="comment"> sqrt(x^2 + y^2) calculated in as precisely and safely as possible.</span></div><div class="line"><a name="l02211"></a><span class="lineno"> 2211</span> <span class="comment">*/</span></div><div class="line"><a name="l02212"></a><span class="lineno"> 2212</span> ON_DECL <span class="keywordtype">double</span> ON_Length2d( <span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y );</div><div class="line"><a name="l02213"></a><span class="lineno"> 2213</span> </div><div class="line"><a name="l02214"></a><span class="lineno"> 2214</span> <span class="comment">/*</span></div><div class="line"><a name="l02215"></a><span class="lineno"> 2215</span> <span class="comment">Descripton:</span></div><div class="line"><a name="l02216"></a><span class="lineno"> 2216</span> <span class="comment"> Return the length of a 3d vector (x,y,z)</span></div><div class="line"><a name="l02217"></a><span class="lineno"> 2217</span> <span class="comment">Returns:</span></div><div class="line"><a name="l02218"></a><span class="lineno"> 2218</span> <span class="comment"> sqrt(x^2 + y^2 + z^2) calculated in as precisely and safely as possible.</span></div><div class="line"><a name="l02219"></a><span class="lineno"> 2219</span> <span class="comment">*/</span></div><div class="line"><a name="l02220"></a><span class="lineno"> 2220</span> ON_DECL <span class="keywordtype">double</span> ON_Length3d( <span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y, <span class="keywordtype">double</span> z );</div><div class="line"><a name="l02221"></a><span class="lineno"> 2221</span> </div><div class="line"><a name="l02222"></a><span class="lineno"> 2222</span> </div><div class="line"><a name="l02223"></a><span class="lineno"> 2223</span> <span class="comment">/*</span></div><div class="line"><a name="l02224"></a><span class="lineno"> 2224</span> <span class="comment">Description:</span></div><div class="line"><a name="l02225"></a><span class="lineno"> 2225</span> <span class="comment"> Get the area of a 3d triangle.</span></div><div class="line"><a name="l02226"></a><span class="lineno"> 2226</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l02227"></a><span class="lineno"> 2227</span> <span class="comment"> A - [in]</span></div><div class="line"><a name="l02228"></a><span class="lineno"> 2228</span> <span class="comment"> B - [in]</span></div><div class="line"><a name="l02229"></a><span class="lineno"> 2229</span> <span class="comment"> C - [in]</span></div><div class="line"><a name="l02230"></a><span class="lineno"> 2230</span> <span class="comment"> Triangle corners</span></div><div class="line"><a name="l02231"></a><span class="lineno"> 2231</span> <span class="comment">Returns:</span></div><div class="line"><a name="l02232"></a><span class="lineno"> 2232</span> <span class="comment"> Area of a 3d triangle with corners at A, B, C.</span></div><div class="line"><a name="l02233"></a><span class="lineno"> 2233</span> <span class="comment">*/</span></div><div class="line"><a name="l02234"></a><span class="lineno"> 2234</span> ON_DECL</div><div class="line"><a name="l02235"></a><span class="lineno"> 2235</span> <span class="keywordtype">double</span> ON_TriangleArea3d(</div><div class="line"><a name="l02236"></a><span class="lineno"> 2236</span>  <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a> A,</div><div class="line"><a name="l02237"></a><span class="lineno"> 2237</span>  <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a> B, </div><div class="line"><a name="l02238"></a><span class="lineno"> 2238</span>  <a class="code" href="class_o_n__3d_point.html">ON_3dPoint</a> C</div><div class="line"><a name="l02239"></a><span class="lineno"> 2239</span>  );</div><div class="line"><a name="l02240"></a><span class="lineno"> 2240</span> </div><div class="line"><a name="l02241"></a><span class="lineno"> 2241</span> <span class="comment">/*</span></div><div class="line"><a name="l02242"></a><span class="lineno"> 2242</span> <span class="comment">Description:</span></div><div class="line"><a name="l02243"></a><span class="lineno"> 2243</span> <span class="comment"> Get the area of a 2d triangle.</span></div><div class="line"><a name="l02244"></a><span class="lineno"> 2244</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l02245"></a><span class="lineno"> 2245</span> <span class="comment"> A - [in]</span></div><div class="line"><a name="l02246"></a><span class="lineno"> 2246</span> <span class="comment"> B - [in]</span></div><div class="line"><a name="l02247"></a><span class="lineno"> 2247</span> <span class="comment"> C - [in]</span></div><div class="line"><a name="l02248"></a><span class="lineno"> 2248</span> <span class="comment"> Triangle corners</span></div><div class="line"><a name="l02249"></a><span class="lineno"> 2249</span> <span class="comment">Returns:</span></div><div class="line"><a name="l02250"></a><span class="lineno"> 2250</span> <span class="comment"> Area of a 2d triangle with corners at A, B, C.</span></div><div class="line"><a name="l02251"></a><span class="lineno"> 2251</span> <span class="comment">*/</span></div><div class="line"><a name="l02252"></a><span class="lineno"> 2252</span> ON_DECL</div><div class="line"><a name="l02253"></a><span class="lineno"> 2253</span> <span class="keywordtype">double</span> ON_TriangleArea2d(</div><div class="line"><a name="l02254"></a><span class="lineno"> 2254</span>  <a class="code" href="class_o_n__2d_point.html">ON_2dPoint</a> A,</div><div class="line"><a name="l02255"></a><span class="lineno"> 2255</span>  <a class="code" href="class_o_n__2d_point.html">ON_2dPoint</a> B,</div><div class="line"><a name="l02256"></a><span class="lineno"> 2256</span>  <a class="code" href="class_o_n__2d_point.html">ON_2dPoint</a> C</div><div class="line"><a name="l02257"></a><span class="lineno"> 2257</span>  );</div><div class="line"><a name="l02258"></a><span class="lineno"> 2258</span> </div><div class="line"><a name="l02259"></a><span class="lineno"> 2259</span> </div><div class="line"><a name="l02260"></a><span class="lineno"> 2260</span> <span class="comment">/*</span></div><div class="line"><a name="l02261"></a><span class="lineno"> 2261</span> <span class="comment">Description:</span></div><div class="line"><a name="l02262"></a><span class="lineno"> 2262</span> <span class="comment"> Convert a double x to the largest float f such that</span></div><div class="line"><a name="l02263"></a><span class="lineno"> 2263</span> <span class="comment"> the mathematical value of f is at most the value of x.</span></div><div class="line"><a name="l02264"></a><span class="lineno"> 2264</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l02265"></a><span class="lineno"> 2265</span> <span class="comment"> x - [in]</span></div><div class="line"><a name="l02266"></a><span class="lineno"> 2266</span> <span class="comment">Returns</span></div><div class="line"><a name="l02267"></a><span class="lineno"> 2267</span> <span class="comment"> The largest float f such that the mathematical value</span></div><div class="line"><a name="l02268"></a><span class="lineno"> 2268</span> <span class="comment"> of f is at most the value of x.</span></div><div class="line"><a name="l02269"></a><span class="lineno"> 2269</span> <span class="comment">*/</span></div><div class="line"><a name="l02270"></a><span class="lineno"> 2270</span> ON_DECL <span class="keywordtype">float</span> ON_FloatFloor(<span class="keywordtype">double</span> x);</div><div class="line"><a name="l02271"></a><span class="lineno"> 2271</span> </div><div class="line"><a name="l02272"></a><span class="lineno"> 2272</span> <span class="comment">/*</span></div><div class="line"><a name="l02273"></a><span class="lineno"> 2273</span> <span class="comment">Description:</span></div><div class="line"><a name="l02274"></a><span class="lineno"> 2274</span> <span class="comment"> Convert a double x to the smallest float f such that</span></div><div class="line"><a name="l02275"></a><span class="lineno"> 2275</span> <span class="comment"> the mathematical value of f is at least the value of x.</span></div><div class="line"><a name="l02276"></a><span class="lineno"> 2276</span> <span class="comment">Parameters:</span></div><div class="line"><a name="l02277"></a><span class="lineno"> 2277</span> <span class="comment"> x - [in]</span></div><div class="line"><a name="l02278"></a><span class="lineno"> 2278</span> <span class="comment">Returns</span></div><div class="line"><a name="l02279"></a><span class="lineno"> 2279</span> <span class="comment"> The smallest float f such that the mathematical value</span></div><div class="line"><a name="l02280"></a><span class="lineno"> 2280</span> <span class="comment"> of f is at least the value of x.</span></div><div class="line"><a name="l02281"></a><span class="lineno"> 2281</span> <span class="comment">*/</span></div><div class="line"><a name="l02282"></a><span class="lineno"> 2282</span> ON_DECL <span class="keywordtype">float</span> ON_FloatCeil(<span class="keywordtype">double</span> x);</div><div class="line"><a name="l02283"></a><span class="lineno"> 2283</span> </div><div class="line"><a name="l02284"></a><span class="lineno"> 2284</span> <span class="preprocessor">#endif</span></div><div class="ttc" id="class_o_n___sum_html"><div class="ttname"><a href="class_o_n___sum.html">ON_Sum</a></div><div class="ttdef"><b>Definition:</b> opennurbs_math.h:30</div></div>
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<div class="ttc" id="class_o_n___arc_html"><div class="ttname"><a href="class_o_n___arc.html">ON_Arc</a></div><div class="ttdef"><b>Definition:</b> opennurbs_arc.h:34</div></div>
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<div class="ttc" id="class_o_n___simple_array_html"><div class="ttname"><a href="class_o_n___simple_array.html">ON_SimpleArray< ON_Interval ></a></div></div>
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<div class="ttc" id="class_o_n___cylinder_html"><div class="ttname"><a href="class_o_n___cylinder.html">ON_Cylinder</a></div><div class="ttdef"><b>Definition:</b> opennurbs_cylinder.h:28</div></div>
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<div class="ttc" id="class_o_n__3f_point_html"><div class="ttname"><a href="class_o_n__3f_point.html">ON_3fPoint</a></div><div class="ttdef"><b>Definition:</b> opennurbs_fpoint.h:216</div></div>
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<div class="ttc" id="class_o_n___circle_html"><div class="ttname"><a href="class_o_n___circle.html">ON_Circle</a></div><div class="ttdef"><b>Definition:</b> opennurbs_circle.h:33</div></div>
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<div class="ttc" id="class_o_n___evaluator_html_a39ab8c1ebc601902f5a2ff8a0d21c6e4"><div class="ttname"><a href="class_o_n___evaluator.html#a39ab8c1ebc601902f5a2ff8a0d21c6e4">ON_Evaluator::m_bPeriodicParameter</a></div><div class="ttdeci">ON_SimpleArray< bool > m_bPeriodicParameter</div><div class="ttdef"><b>Definition:</b> opennurbs_math.h:326</div></div>
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<div class="ttc" id="class_o_n___evaluator_html_a9d8118ded2762c9e5f38be107e2a5d2d"><div class="ttname"><a href="class_o_n___evaluator.html#a9d8118ded2762c9e5f38be107e2a5d2d">ON_Evaluator::m_parameter_count</a></div><div class="ttdeci">const int m_parameter_count</div><div class="ttdef"><b>Definition:</b> opennurbs_math.h:264</div></div>
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<div class="ttc" id="class_o_n__2d_point_html"><div class="ttname"><a href="class_o_n__2d_point.html">ON_2dPoint</a></div><div class="ttdef"><b>Definition:</b> opennurbs_point.h:292</div></div>
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<div class="ttc" id="class_o_n___bounding_box_html"><div class="ttname"><a href="class_o_n___bounding_box.html">ON_BoundingBox</a></div><div class="ttdef"><b>Definition:</b> opennurbs_bounding_box.h:25</div></div>
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<div class="ttc" id="class_o_n___xform_html"><div class="ttname"><a href="class_o_n___xform.html">ON_Xform</a></div><div class="ttdef"><b>Definition:</b> opennurbs_xform.h:28</div></div>
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<div class="ttc" id="class_o_n___evaluator_html_a8e7e3d681c06c498b26529affd1d22f7"><div class="ttname"><a href="class_o_n___evaluator.html#a8e7e3d681c06c498b26529affd1d22f7">ON_Evaluator::m_domain</a></div><div class="ttdeci">ON_SimpleArray< ON_Interval > m_domain</div><div class="ttdef"><b>Definition:</b> opennurbs_math.h:319</div></div>
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<div class="ttc" id="class_o_n___evaluator_html"><div class="ttname"><a href="class_o_n___evaluator.html">ON_Evaluator</a></div><div class="ttdef"><b>Definition:</b> opennurbs_math.h:143</div></div>
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<div class="ttc" id="class_o_n___line_html"><div class="ttname"><a href="class_o_n___line.html">ON_Line</a></div><div class="ttdef"><b>Definition:</b> opennurbs_line.h:20</div></div>
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<div class="ttc" id="class_o_n__2f_point_html"><div class="ttname"><a href="class_o_n__2f_point.html">ON_2fPoint</a></div><div class="ttdef"><b>Definition:</b> opennurbs_fpoint.h:38</div></div>
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<div class="ttc" id="class_o_n__3d_point_html"><div class="ttname"><a href="class_o_n__3d_point.html">ON_3dPoint</a></div><div class="ttdef"><b>Definition:</b> opennurbs_point.h:480</div></div>
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<div class="ttc" id="class_o_n___plane_html"><div class="ttname"><a href="class_o_n___plane.html">ON_Plane</a></div><div class="ttdef"><b>Definition:</b> opennurbs_plane.h:20</div></div>
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<div class="ttc" id="class_o_n___plane_equation_html"><div class="ttname"><a href="class_o_n___plane_equation.html">ON_PlaneEquation</a></div><div class="ttdef"><b>Definition:</b> opennurbs_point.h:1465</div></div>
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<div class="ttc" id="class_o_n___evaluator_html_a61abf86c2c652d0ab38548f6eba4d482"><div class="ttname"><a href="class_o_n___evaluator.html#a61abf86c2c652d0ab38548f6eba4d482">ON_Evaluator::m_value_count</a></div><div class="ttdeci">const int m_value_count</div><div class="ttdef"><b>Definition:</b> opennurbs_math.h:268</div></div>
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<div class="ttc" id="class_o_n__2d_vector_html"><div class="ttname"><a href="class_o_n__2d_vector.html">ON_2dVector</a></div><div class="ttdef"><b>Definition:</b> opennurbs_point.h:868</div></div>
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<div class="ttc" id="class_o_n__3d_vector_html"><div class="ttname"><a href="class_o_n__3d_vector.html">ON_3dVector</a></div><div class="ttdef"><b>Definition:</b> opennurbs_point.h:1182</div></div>
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<div class="ttc" id="class_o_n___interval_html"><div class="ttname"><a href="class_o_n___interval.html">ON_Interval</a></div><div class="ttdef"><b>Definition:</b> opennurbs_point.h:46</div></div>
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<div class="ttc" id="class_o_n___sphere_html"><div class="ttname"><a href="class_o_n___sphere.html">ON_Sphere</a></div><div class="ttdef"><b>Definition:</b> opennurbs_sphere.h:22</div></div>
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