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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span>&#160;<span class="comment">/* $NoKeywords: $ */</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span>&#160;<span class="comment">//</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span>&#160;<span class="comment">// Copyright (c) 1993-2012 Robert McNeel &amp; Associates. All rights reserved.</span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span>&#160;<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>&#160;<span class="comment">// McNeel &amp; Associates.</span></div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span>&#160;<span class="comment">//</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span>&#160;<span class="comment">// THIS SOFTWARE IS PROVIDED &quot;AS IS&quot; WITHOUT EXPRESS OR IMPLIED WARRANTY.</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span>&#160;<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>&#160;<span class="comment">// MERCHANTABILITY ARE HEREBY DISCLAIMED.</span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span>&#160;<span class="comment">// </span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span>&#160;<span class="comment">// For complete openNURBS copyright information see &lt;http://www.opennurbs.org&gt;.</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span>&#160;<span class="comment">//</span><span class="comment"></span></div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span>&#160;<span class="comment">////////////////////////////////////////////////////////////////</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span>&#160;<span class="comment"></span>*/</div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span>&#160;</div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span>&#160;<span class="preprocessor">#if !defined(OPENNURBS_KNOT_INC_)</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span>&#160;<span class="preprocessor">#define OPENNURBS_KNOT_INC_</span></div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span>&#160;</div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span>&#160;ON_DECL</div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160;<span class="keywordtype">double</span> ON_DomainTolerance(</div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160; <span class="keywordtype">double</span>, <span class="comment">// start of domain</span></div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160; <span class="keywordtype">double</span> <span class="comment">// end of domain</span></div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160; );</div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160;</div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160;ON_DECL</div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160;<span class="keywordtype">double</span> ON_KnotTolerance(</div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv count</span></div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// knot[] array</span></div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; <span class="keywordtype">int</span> <span class="comment">// knot index</span></div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; );</div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160;</div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160;ON_DECL</div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160;<span class="keywordtype">double</span> ON_SpanTolerance(</div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv count</span></div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// knot[] array</span></div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <span class="keywordtype">int</span> <span class="comment">// span index</span></div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; );</div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160;</div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160;ON_DECL</div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160;<span class="keywordtype">int</span> ON_KnotCount( <span class="comment">// returns (order + cv_count - 2)</span></div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="keywordtype">int</span> <span class="comment">// cv_count (&gt;=order)</span></div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; );</div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160;</div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160;ON_DECL</div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160;<span class="keywordtype">int</span> ON_KnotMultiplicity(</div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv_count (&gt;=order)</span></div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// knot[]</span></div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <span class="keywordtype">int</span> <span class="comment">// knot_index</span></div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; );</div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160;</div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160;ON_DECL</div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160;<span class="keywordtype">int</span> ON_KnotVectorSpanCount(</div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv count</span></div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* <span class="comment">// knot[] array</span></div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; );</div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160;</div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160;ON_DECL</div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160;<span class="keywordtype">bool</span> ON_GetKnotVectorSpanVector(</div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv count</span></div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// knot[] array</span></div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="keywordtype">double</span>* <span class="comment">// s[] array</span></div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; );</div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160;</div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160;<span class="comment">Description:</span></div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160;<span class="comment"> Given an evaluation parameter t in the domain of a NURBS curve,</span></div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160;<span class="comment"> ON_NurbsSpanIndex(order,cv_count,knot,t,0,0) returns the integer</span></div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160;<span class="comment"> i such that (knot[i],...,knot[i+2*degree-1]), and </span></div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160;<span class="comment"> (cv[i],...,cv[i+degree]) are the knots and control points that</span></div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160;<span class="comment"> define the span of the NURBS that are used for evaluation at t.</span></div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160;<span class="comment">Parameters:</span></div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160;<span class="comment"> order - [in] order &gt;= 2</span></div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160;<span class="comment"> cv_count - [in] cv_count &gt;= order</span></div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160;<span class="comment"> knot - [in] valid knot vector</span></div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160;<span class="comment"> t - [in] evaluation parameter</span></div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160;<span class="comment"> side - [in] determines which span is used when t is at a knot</span></div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160;<span class="comment"> value; side = 0 for the default (from above),</span></div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160;<span class="comment"> side = -1 means from below, and </span></div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160;<span class="comment"> side = +1 means from above.</span></div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160;<span class="comment"> hint - [in] Search hint, or 0 if not hint is available.</span></div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160;<span class="comment"> Returns the index described above.</span></div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160;ON_DECL</div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160;<span class="keywordtype">int</span> ON_NurbsSpanIndex(</div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; <span class="keywordtype">int</span> order,</div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <span class="keywordtype">int</span> cv_count,</div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* knot,</div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; <span class="keywordtype">double</span> t,</div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; <span class="keywordtype">int</span> side,</div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; <span class="keywordtype">int</span> hint</div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; );</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160;</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160;ON_DECL</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160;<span class="keywordtype">int</span> ON_NextNurbsSpanIndex(</div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; <span class="comment">// returns 0: input span_index &lt; 0</span></div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; <span class="comment">// cv_count-order: input span_index = cv_count-order</span></div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; <span class="comment">// -1: input span_index &gt; cv_count-order;</span></div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160; <span class="comment">// otherwise next span index</span></div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; <span class="keywordtype">int</span> order,</div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; <span class="keywordtype">int</span> cv_count,</div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* knot,</div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; <span class="keywordtype">int</span> <span class="comment">// current span_index </span></div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; );</div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160;</div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160;ON_DECL</div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160;<span class="keywordtype">int</span> ON_GetSpanIndices( <span class="comment">// returns span count, which is one less than length of span_indices[]</span></div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160; <span class="keywordtype">int</span> order,</div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160; <span class="keywordtype">int</span> cv_count,</div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* knot,</div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160; <span class="keywordtype">int</span>* <span class="comment">// span_indices[cv_count-order+2]. </span></div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>&#160; <span class="comment">//Indices of knots at end of group of mult knots </span></div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160; <span class="comment">//at start of span, and knot at start of group of mult knots</span></div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160; <span class="comment">//at end of spline.</span></div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160; );</div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160;</div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>&#160;ON_DECL</div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160;<span class="keywordtype">double</span> ON_SuperfluousKnot( </div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160; <span class="keywordtype">int</span> order,</div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160; <span class="keywordtype">int</span> cv_count,</div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* knot,</div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160; <span class="keywordtype">int</span> <span class="comment">// 0 = first superfluous knot </span></div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160; <span class="comment">// 1 = last superfluous knot</span></div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span>&#160; );</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160;</div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160;ON_DECL</div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160;<span class="keywordtype">bool</span> ON_IsKnotVectorPeriodic(</div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160; <span class="keywordtype">int</span> order,</div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span>&#160; <span class="keywordtype">int</span> cv_count,</div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* knot</div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span>&#160; );</div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span>&#160;</div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>&#160;ON_DECL</div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span>&#160;<span class="keywordtype">bool</span> ON_IsKnotVectorClamped(</div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span>&#160; <span class="keywordtype">int</span> order,</div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span>&#160; <span class="keywordtype">int</span> cv_count,</div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* knot,</div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span>&#160; <span class="keywordtype">int</span> = 2 <span class="comment">// 0 = check left end, 1 = check right end, 2 = check both</span></div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span>&#160; );</div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span>&#160;</div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>&#160;ON_DECL</div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>&#160;<span class="keywordtype">bool</span> ON_IsKnotVectorUniform(</div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>&#160; <span class="keywordtype">int</span> order,</div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span>&#160; <span class="keywordtype">int</span> cv_count,</div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* knot </div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span>&#160; );</div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span>&#160;<span class="comment">//////////</span></div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span>&#160;<span class="comment"></span><span class="comment">// returns true if all knots have multiplicity = degree</span></div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span>&#160;ON_DECL</div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span>&#160;<span class="keywordtype">bool</span> ON_KnotVectorHasBezierSpans(</div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span>&#160; <span class="keywordtype">int</span> order,</div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span>&#160; <span class="keywordtype">int</span> cv_count,</div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* knot</div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span>&#160; );</div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span>&#160;</div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span>&#160;</div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span>&#160;ON_DECL</div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span>&#160;ON::knot_style ON_KnotVectorStyle( </div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span>&#160; <span class="keywordtype">int</span> order,</div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span>&#160; <span class="keywordtype">int</span> cv_count,</div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* knot</div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span>&#160; );</div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span>&#160;</div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span>&#160;<span class="comment">Description:</span></div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span>&#160;<span class="comment"> Set the domain of a knot vector.</span></div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span>&#160;<span class="comment">Parameters:</span></div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span>&#160;<span class="comment"> order - [in] order &gt;= 2</span></div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span>&#160;<span class="comment"> cv_count - [in] cv_count &gt;= order</span></div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span>&#160;<span class="comment"> knot - [in/out] input existing knots and returns knots with new domain.</span></div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span>&#160;<span class="comment"> t0 - [in]</span></div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span>&#160;<span class="comment"> t1 - [in] New domain will be the interval (t0,t1).</span></div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160;<span class="comment"> True if input is valid and the returned knot vector </span></div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span>&#160;<span class="comment"> has the requested domain. False if the input is</span></div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span>&#160;<span class="comment"> invalid, in which case the input knot vector is not</span></div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span>&#160;<span class="comment"> changed.</span></div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>&#160;ON_DECL</div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>&#160;<span class="keywordtype">bool</span> ON_SetKnotVectorDomain( </div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span>&#160; <span class="keywordtype">int</span> order, </div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span>&#160; <span class="keywordtype">int</span> cv_count, </div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span>&#160; <span class="keywordtype">double</span>* knot, </div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span>&#160; <span class="keywordtype">double</span> t0, </div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span>&#160; <span class="keywordtype">double</span> t1 </div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span>&#160; );</div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span>&#160;</div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span>&#160;ON_DECL</div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span>&#160;<span class="keywordtype">bool</span> ON_GetKnotVectorDomain(</div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv count</span></div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// knot[] array</span></div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span>&#160; <span class="keywordtype">double</span>*, <span class="keywordtype">double</span>*</div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span>&#160; );</div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span>&#160;</div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span>&#160;ON_DECL</div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span>&#160;<span class="keywordtype">bool</span> ON_ReverseKnotVector(</div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv count</span></div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span>&#160; <span class="keywordtype">double</span>* <span class="comment">// knot[] array</span></div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span>&#160; );</div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>&#160;</div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span>&#160;ON_DECL</div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span>&#160;<span class="keywordtype">int</span> ON_CompareKnotVector( <span class="comment">// returns </span></div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span>&#160; <span class="comment">// -1: first &lt; second</span></div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span>&#160; <span class="comment">// 0: first == second</span></div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span>&#160; <span class="comment">// +1: first &gt; second</span></div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span>&#160; <span class="comment">// first knot vector</span></div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv count</span></div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// knot[] array</span></div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span>&#160; <span class="comment">// second knot vector</span></div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv count</span></div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* <span class="comment">// knot[] array</span></div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span>&#160; );</div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span>&#160;</div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span>&#160;ON_DECL</div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span>&#160;<span class="keywordtype">bool</span> ON_IsValidKnotVector(</div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span>&#160; <span class="keywordtype">int</span> order,</div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span>&#160; <span class="keywordtype">int</span> cv_count, </div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* knot, </div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span>&#160; <a class="code" href="../../d2/da3/class_o_n___text_log.html">ON_TextLog</a>* text_log = 0</div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span>&#160; );</div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span>&#160;</div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span>&#160;ON_DECL</div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span>&#160;<span class="keywordtype">bool</span> ON_ClampKnotVector(</div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span>&#160; <span class="comment">// Sets inital/final order-2 knots to values in</span></div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span>&#160; <span class="comment">// knot[order-2]/knot[cv_count-1].</span></div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv count</span></div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span>&#160; <span class="keywordtype">double</span>*, <span class="comment">// knot[] array</span></div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span>&#160; <span class="keywordtype">int</span> <span class="comment">// 0 = clamp left end, 1 = right end, 2 = clamp both ends</span></div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span>&#160; );</div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>&#160;</div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span>&#160;ON_DECL</div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span>&#160;<span class="keywordtype">bool</span> ON_MakeKnotVectorPeriodic(</div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span>&#160; <span class="comment">// Sets inital and final order-2 knots to values</span></div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span>&#160; <span class="comment">// that make the knot vector periodic</span></div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv count</span></div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span>&#160; <span class="keywordtype">double</span>* <span class="comment">// knot[] array</span></div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span>&#160; );</div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span>&#160;</div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span>&#160;<span class="comment"> Description:</span></div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span>&#160;<span class="comment"> Fill in knot values for a clamped uniform knot</span></div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span>&#160;<span class="comment"> vector.</span></div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span>&#160;<span class="comment"> Parameters:</span></div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span>&#160;<span class="comment"> order - [in] (&gt;=2) order (degree+1) of the NURBS</span></div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span>&#160;<span class="comment"> cv_count - [in] (&gt;=order) total number of control points</span></div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span>&#160;<span class="comment"> in the NURBS.</span></div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span>&#160;<span class="comment"> knot - [in/out] Input is an array with room for </span></div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span>&#160;<span class="comment"> ON_KnotCount(order,cv_count) doubles. Output is</span></div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span>&#160;<span class="comment"> a clamped uniform knot vector with domain</span></div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span>&#160;<span class="comment"> (0, (1+cv_count-order)*delta).</span></div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span>&#160;<span class="comment"> delta - [in] (&gt;0, default=1.0) spacing between knots.</span></div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span>&#160;<span class="comment"> true if successful</span></div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span>&#160;<span class="comment"> See Also:</span></div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span>&#160;<span class="comment"> ON_NurbsCurve::MakeClampedUniformKnotVector</span></div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span>&#160;ON_DECL</div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span>&#160;<span class="keywordtype">bool</span> ON_MakeClampedUniformKnotVector(</div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span>&#160; <span class="keywordtype">int</span> order,</div><div class="line"><a name="l00274"></a><span class="lineno"> 274</span>&#160; <span class="keywordtype">int</span> cv_count,</div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span>&#160; <span class="keywordtype">double</span>* knot,</div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span>&#160; <span class="keywordtype">double</span> delta = 1.0</div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span>&#160; );</div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span>&#160;</div><div class="line"><a name="l00279"></a><span class="lineno"> 279</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00280"></a><span class="lineno"> 280</span>&#160;<span class="comment"> Description:</span></div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span>&#160;<span class="comment"> Fill in knot values for a clamped uniform knot</span></div><div class="line"><a name="l00282"></a><span class="lineno"> 282</span>&#160;<span class="comment"> vector.</span></div><div class="line"><a name="l00283"></a><span class="lineno"> 283</span>&#160;<span class="comment"> Parameters:</span></div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span>&#160;<span class="comment"> order - [in] (&gt;=2) order (degree+1) of the NURBS</span></div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span>&#160;<span class="comment"> cv_count - [in] (&gt;=order) total number of control points</span></div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span>&#160;<span class="comment"> in the NURBS.</span></div><div class="line"><a name="l00287"></a><span class="lineno"> 287</span>&#160;<span class="comment"> knot - [in/out] Input is an array with room for </span></div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span>&#160;<span class="comment"> ON_KnotCount(order,cv_count) doubles. Output is</span></div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span>&#160;<span class="comment"> a periodic uniform knot vector with domain</span></div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span>&#160;<span class="comment"> (0, (1+cv_count-order)*delta).</span></div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span>&#160;<span class="comment"> delta - [in] (&gt;0, default=1.0) spacing between knots.</span></div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span>&#160;<span class="comment"> true if successful</span></div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span>&#160;<span class="comment"> See Also:</span></div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span>&#160;<span class="comment"> ON_NurbsCurve::MakePeriodicUniformKnotVector</span></div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span>&#160;ON_DECL</div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span>&#160;<span class="keywordtype">bool</span> ON_MakePeriodicUniformKnotVector(</div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span>&#160; <span class="keywordtype">int</span> order,</div><div class="line"><a name="l00300"></a><span class="lineno"> 300</span>&#160; <span class="keywordtype">int</span> cv_count,</div><div class="line"><a name="l00301"></a><span class="lineno"> 301</span>&#160; <span class="keywordtype">double</span>* knot,</div><div class="line"><a name="l00302"></a><span class="lineno"> 302</span>&#160; <span class="keywordtype">double</span> delta = 1.0</div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span>&#160; );</div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span>&#160;</div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span>&#160;ON_DECL</div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span>&#160;<span class="keywordtype">double</span> ON_GrevilleAbcissa( <span class="comment">// get Greville abcissae from knots</span></div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* <span class="comment">// knot[] array (length = order-1)</span></div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span>&#160; );</div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span>&#160;</div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span>&#160;ON_DECL</div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span>&#160;<span class="keywordtype">bool</span> ON_GetGrevilleAbcissae( <span class="comment">// get Greville abcissae from knots</span></div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00314"></a><span class="lineno"> 314</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv count</span></div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// knot[] array</span></div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span>&#160; <span class="keywordtype">bool</span>, <span class="comment">// true for periodic case</span></div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span>&#160; <span class="keywordtype">double</span>* <span class="comment">// g[] array has length cv_count in non-periodic case</span></div><div class="line"><a name="l00318"></a><span class="lineno"> 318</span>&#160; <span class="comment">// and cv_count-order+1 in periodic case</span></div><div class="line"><a name="l00319"></a><span class="lineno"> 319</span>&#160; );</div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span>&#160;</div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span>&#160;ON_DECL</div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span>&#160;<span class="keywordtype">bool</span> ON_GetGrevilleKnotVector( <span class="comment">// get knots from Greville abcissa</span></div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// g[] array stride (&gt;=1)</span></div><div class="line"><a name="l00324"></a><span class="lineno"> 324</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// g[] array</span></div><div class="line"><a name="l00325"></a><span class="lineno"> 325</span>&#160; <span class="comment">// if not periodic, length = cv_count</span></div><div class="line"><a name="l00326"></a><span class="lineno"> 326</span>&#160; <span class="comment">// if periodic, length = cv_count-order+2</span></div><div class="line"><a name="l00327"></a><span class="lineno"> 327</span>&#160; <span class="keywordtype">bool</span>, <span class="comment">// true for periodic knots</span></div><div class="line"><a name="l00328"></a><span class="lineno"> 328</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00329"></a><span class="lineno"> 329</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv_count (&gt;=order)</span></div><div class="line"><a name="l00330"></a><span class="lineno"> 330</span>&#160; <span class="keywordtype">double</span>* <span class="comment">// knot[cv_count+order-2]</span></div><div class="line"><a name="l00331"></a><span class="lineno"> 331</span>&#160; );</div><div class="line"><a name="l00332"></a><span class="lineno"> 332</span>&#160;</div><div class="line"><a name="l00333"></a><span class="lineno"> 333</span>&#160;ON_DECL</div><div class="line"><a name="l00334"></a><span class="lineno"> 334</span>&#160;<span class="keywordtype">bool</span> ON_ClampKnotVector(</div><div class="line"><a name="l00335"></a><span class="lineno"> 335</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv_dim ( = dim+1 for rational cvs )</span></div><div class="line"><a name="l00336"></a><span class="lineno"> 336</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00337"></a><span class="lineno"> 337</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv_count,</span></div><div class="line"><a name="l00338"></a><span class="lineno"> 338</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv_stride, </span></div><div class="line"><a name="l00339"></a><span class="lineno"> 339</span>&#160; <span class="keywordtype">double</span>*, <span class="comment">// cv[] nullptr or array of order many cvs</span></div><div class="line"><a name="l00340"></a><span class="lineno"> 340</span>&#160; <span class="keywordtype">double</span>*, <span class="comment">// knot[] array with room for at least knot_multiplicity new knots</span></div><div class="line"><a name="l00341"></a><span class="lineno"> 341</span>&#160; <span class="keywordtype">int</span> <span class="comment">// end 0 = clamp start, 1 = clamp end, 2 = clamp both ends</span></div><div class="line"><a name="l00342"></a><span class="lineno"> 342</span>&#160; );</div><div class="line"><a name="l00343"></a><span class="lineno"> 343</span>&#160;</div><div class="line"><a name="l00344"></a><span class="lineno"> 344</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00345"></a><span class="lineno"> 345</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00346"></a><span class="lineno"> 346</span>&#160;<span class="comment"> Number of knots added.</span></div><div class="line"><a name="l00347"></a><span class="lineno"> 347</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00348"></a><span class="lineno"> 348</span>&#160;ON_DECL</div><div class="line"><a name="l00349"></a><span class="lineno"> 349</span>&#160;<span class="keywordtype">int</span> ON_InsertKnot(</div><div class="line"><a name="l00350"></a><span class="lineno"> 350</span>&#160; <span class="keywordtype">double</span>, <span class="comment">// knot_value,</span></div><div class="line"><a name="l00351"></a><span class="lineno"> 351</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// knot_multiplicity, (1 to order-1 including multiplicity of any existing knots)</span></div><div class="line"><a name="l00352"></a><span class="lineno"> 352</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv_dim ( = dim+1 for rational cvs )</span></div><div class="line"><a name="l00353"></a><span class="lineno"> 353</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00354"></a><span class="lineno"> 354</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv_count,</span></div><div class="line"><a name="l00355"></a><span class="lineno"> 355</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv_stride (&gt;=cv_dim)</span></div><div class="line"><a name="l00356"></a><span class="lineno"> 356</span>&#160; <span class="keywordtype">double</span>*, <span class="comment">// cv[] nullptr or cv array with room for at least knot_multiplicity new cvs</span></div><div class="line"><a name="l00357"></a><span class="lineno"> 357</span>&#160; <span class="keywordtype">double</span>*, <span class="comment">// knot[] knot array with room for at least knot_multiplicity new knots</span></div><div class="line"><a name="l00358"></a><span class="lineno"> 358</span>&#160; <span class="keywordtype">int</span>* <span class="comment">// hint, optional hint about where to search for span to add knots to</span></div><div class="line"><a name="l00359"></a><span class="lineno"> 359</span>&#160; <span class="comment">// pass nullptr if no hint is available</span></div><div class="line"><a name="l00360"></a><span class="lineno"> 360</span>&#160; );</div><div class="line"><a name="l00361"></a><span class="lineno"> 361</span>&#160;</div><div class="line"><a name="l00362"></a><span class="lineno"> 362</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00363"></a><span class="lineno"> 363</span>&#160;<span class="comment">Description:</span></div><div class="line"><a name="l00364"></a><span class="lineno"> 364</span>&#160;<span class="comment"> Reparameterize a rational Bezier curve.</span></div><div class="line"><a name="l00365"></a><span class="lineno"> 365</span>&#160;<span class="comment">Parameters:</span></div><div class="line"><a name="l00366"></a><span class="lineno"> 366</span>&#160;<span class="comment"> c - [in]</span></div><div class="line"><a name="l00367"></a><span class="lineno"> 367</span>&#160;<span class="comment"> reparameterization constant (generally speaking, c should be &gt; 0).</span></div><div class="line"><a name="l00368"></a><span class="lineno"> 368</span>&#160;<span class="comment"> The control points are adjusted so that </span></div><div class="line"><a name="l00369"></a><span class="lineno"> 369</span>&#160;<span class="comment"> output_bezier(t) = input_bezier(lambda(t)), where</span></div><div class="line"><a name="l00370"></a><span class="lineno"> 370</span>&#160;<span class="comment"> lambda(t) = c*t/( (c-1)*t + 1 ).</span></div><div class="line"><a name="l00371"></a><span class="lineno"> 371</span>&#160;<span class="comment"> Note that lambda(0) = 0, lambda(1) = 1, lambda&#39;(t) &gt; 0, </span></div><div class="line"><a name="l00372"></a><span class="lineno"> 372</span>&#160;<span class="comment"> lambda&#39;(0) = c and lambda&#39;(1) = 1/c.</span></div><div class="line"><a name="l00373"></a><span class="lineno"> 373</span>&#160;<span class="comment"> dim - [in]</span></div><div class="line"><a name="l00374"></a><span class="lineno"> 374</span>&#160;<span class="comment"> order - [in]</span></div><div class="line"><a name="l00375"></a><span class="lineno"> 375</span>&#160;<span class="comment"> cvstride - [in] (&gt;= dim+1)</span></div><div class="line"><a name="l00376"></a><span class="lineno"> 376</span>&#160;<span class="comment"> cv - [in/out] homogeneous rational control points</span></div><div class="line"><a name="l00377"></a><span class="lineno"> 377</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00378"></a><span class="lineno"> 378</span>&#160;<span class="comment"> The cv values are changed so that</span></div><div class="line"><a name="l00379"></a><span class="lineno"> 379</span>&#160;<span class="comment"> output_bezier(t) = input_bezier(lambda(t)).</span></div><div class="line"><a name="l00380"></a><span class="lineno"> 380</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00381"></a><span class="lineno"> 381</span>&#160;ON_DECL</div><div class="line"><a name="l00382"></a><span class="lineno"> 382</span>&#160;<span class="keywordtype">bool</span> ON_ReparameterizeRationalBezierCurve(</div><div class="line"><a name="l00383"></a><span class="lineno"> 383</span>&#160; <span class="keywordtype">double</span> c,</div><div class="line"><a name="l00384"></a><span class="lineno"> 384</span>&#160; <span class="keywordtype">int</span> dim,</div><div class="line"><a name="l00385"></a><span class="lineno"> 385</span>&#160; <span class="keywordtype">int</span> order,</div><div class="line"><a name="l00386"></a><span class="lineno"> 386</span>&#160; <span class="keywordtype">int</span> cvstride,</div><div class="line"><a name="l00387"></a><span class="lineno"> 387</span>&#160; <span class="keywordtype">double</span>* cv</div><div class="line"><a name="l00388"></a><span class="lineno"> 388</span>&#160; );</div><div class="line"><a name="l00389"></a><span class="lineno"> 389</span>&#160;</div><div class="line"><a name="l00390"></a><span class="lineno"> 390</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00391"></a><span class="lineno"> 391</span>&#160;<span class="comment">Description:</span></div><div class="line"><a name="l00392"></a><span class="lineno"> 392</span>&#160;<span class="comment"> Use a combination of scaling and reparameterization to set two rational</span></div><div class="line"><a name="l00393"></a><span class="lineno"> 393</span>&#160;<span class="comment"> Bezier weights to specified values.</span></div><div class="line"><a name="l00394"></a><span class="lineno"> 394</span>&#160;<span class="comment">Parameters:</span></div><div class="line"><a name="l00395"></a><span class="lineno"> 395</span>&#160;<span class="comment"> dim - [in] </span></div><div class="line"><a name="l00396"></a><span class="lineno"> 396</span>&#160;<span class="comment"> order - [in]</span></div><div class="line"><a name="l00397"></a><span class="lineno"> 397</span>&#160;<span class="comment"> cvstride - [in] ( &gt;= dim+1)</span></div><div class="line"><a name="l00398"></a><span class="lineno"> 398</span>&#160;<span class="comment"> cv - [in/out] homogeneous rational control points</span></div><div class="line"><a name="l00399"></a><span class="lineno"> 399</span>&#160;<span class="comment"> i0 - [in] </span></div><div class="line"><a name="l00400"></a><span class="lineno"> 400</span>&#160;<span class="comment"> w0 - [in]</span></div><div class="line"><a name="l00401"></a><span class="lineno"> 401</span>&#160;<span class="comment"> i1 - [in]</span></div><div class="line"><a name="l00402"></a><span class="lineno"> 402</span>&#160;<span class="comment"> w1 - [in]</span></div><div class="line"><a name="l00403"></a><span class="lineno"> 403</span>&#160;<span class="comment"> The i0-th cv will have weight w0 and the i1-th cv will have weight w1.</span></div><div class="line"><a name="l00404"></a><span class="lineno"> 404</span>&#160;<span class="comment"> If v0 and v1 are the cv&#39;s input weights, then v0, v1, w0 and w1 must</span></div><div class="line"><a name="l00405"></a><span class="lineno"> 405</span>&#160;<span class="comment"> all be nonzero, and w0*v0 and w1*v1 must have the same sign.</span></div><div class="line"><a name="l00406"></a><span class="lineno"> 406</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00407"></a><span class="lineno"> 407</span>&#160;<span class="comment"> true if successful</span></div><div class="line"><a name="l00408"></a><span class="lineno"> 408</span>&#160;<span class="comment">Remarks:</span></div><div class="line"><a name="l00409"></a><span class="lineno"> 409</span>&#160;<span class="comment"> The equations</span></div><div class="line"><a name="l00410"></a><span class="lineno"> 410</span>&#160;<span class="comment"> s * r^i0 = w0/v0</span></div><div class="line"><a name="l00411"></a><span class="lineno"> 411</span>&#160;<span class="comment"> s * r^i1 = w1/v1</span></div><div class="line"><a name="l00412"></a><span class="lineno"> 412</span>&#160;<span class="comment"> determine the scaling and reparameterization necessary to change v0,v1 to</span></div><div class="line"><a name="l00413"></a><span class="lineno"> 413</span>&#160;<span class="comment"> w0,w1. </span></div><div class="line"><a name="l00414"></a><span class="lineno"> 414</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00415"></a><span class="lineno"> 415</span>&#160;<span class="comment"> If the input Bezier has control vertices {B_0, ..., B_d}, then the </span></div><div class="line"><a name="l00416"></a><span class="lineno"> 416</span>&#160;<span class="comment"> output Bezier has control vertices {s*B_0, ... s*r^i * B_i, ..., s*r^d * B_d}.</span></div><div class="line"><a name="l00417"></a><span class="lineno"> 417</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00418"></a><span class="lineno"> 418</span>&#160;ON_DECL</div><div class="line"><a name="l00419"></a><span class="lineno"> 419</span>&#160;<span class="keywordtype">bool</span> ON_ChangeRationalBezierCurveWeights(</div><div class="line"><a name="l00420"></a><span class="lineno"> 420</span>&#160; <span class="keywordtype">int</span> dim, <span class="keywordtype">int</span> order, <span class="keywordtype">int</span> cvstride, <span class="keywordtype">double</span>* cv,</div><div class="line"><a name="l00421"></a><span class="lineno"> 421</span>&#160; <span class="keywordtype">int</span> i0, <span class="keywordtype">double</span> w0, </div><div class="line"><a name="l00422"></a><span class="lineno"> 422</span>&#160; <span class="keywordtype">int</span> i1, <span class="keywordtype">double</span> w1</div><div class="line"><a name="l00423"></a><span class="lineno"> 423</span>&#160; );</div><div class="line"><a name="l00424"></a><span class="lineno"> 424</span>&#160;</div><div class="line"><a name="l00425"></a><span class="lineno"> 425</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00426"></a><span class="lineno"> 426</span>&#160;<span class="comment">Description:</span></div><div class="line"><a name="l00427"></a><span class="lineno"> 427</span>&#160;<span class="comment"> Reparameterize a rational NURBS curve.</span></div><div class="line"><a name="l00428"></a><span class="lineno"> 428</span>&#160;<span class="comment">Parameters:</span></div><div class="line"><a name="l00429"></a><span class="lineno"> 429</span>&#160;<span class="comment"> c - [in]</span></div><div class="line"><a name="l00430"></a><span class="lineno"> 430</span>&#160;<span class="comment"> reparameterization constant (generally speaking, c should be &gt; 0).</span></div><div class="line"><a name="l00431"></a><span class="lineno"> 431</span>&#160;<span class="comment"> The control points and knots are adjusted so that </span></div><div class="line"><a name="l00432"></a><span class="lineno"> 432</span>&#160;<span class="comment"> output_nurbs(t) = input_nurbs(lambda(t)), where</span></div><div class="line"><a name="l00433"></a><span class="lineno"> 433</span>&#160;<span class="comment"> lambda(t) = c*t/( (c-1)*t + 1 ).</span></div><div class="line"><a name="l00434"></a><span class="lineno"> 434</span>&#160;<span class="comment"> Note that lambda(0) = 0, lambda(1) = 1, lambda&#39;(t) &gt; 0, </span></div><div class="line"><a name="l00435"></a><span class="lineno"> 435</span>&#160;<span class="comment"> lambda&#39;(0) = c and lambda&#39;(1) = 1/c.</span></div><div class="line"><a name="l00436"></a><span class="lineno"> 436</span>&#160;<span class="comment"> dim - [in]</span></div><div class="line"><a name="l00437"></a><span class="lineno"> 437</span>&#160;<span class="comment"> order - [in]</span></div><div class="line"><a name="l00438"></a><span class="lineno"> 438</span>&#160;<span class="comment"> cvstride - [in] (&gt;=dim+1)</span></div><div class="line"><a name="l00439"></a><span class="lineno"> 439</span>&#160;<span class="comment"> cv - [in/out] homogeneous rational control points</span></div><div class="line"><a name="l00440"></a><span class="lineno"> 440</span>&#160;<span class="comment"> knot - [in/out]</span></div><div class="line"><a name="l00441"></a><span class="lineno"> 441</span>&#160;<span class="comment"> NURBS curve knots</span></div><div class="line"><a name="l00442"></a><span class="lineno"> 442</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00443"></a><span class="lineno"> 443</span>&#160;<span class="comment"> The cv values are changed so that</span></div><div class="line"><a name="l00444"></a><span class="lineno"> 444</span>&#160;<span class="comment"> output_bezier(t) = input_bezier(lambda(t)).</span></div><div class="line"><a name="l00445"></a><span class="lineno"> 445</span>&#160;<span class="comment">See Also:</span></div><div class="line"><a name="l00446"></a><span class="lineno"> 446</span>&#160;<span class="comment"> ON_ChangeRationalNurbsCurveEndWeights</span></div><div class="line"><a name="l00447"></a><span class="lineno"> 447</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00448"></a><span class="lineno"> 448</span>&#160;ON_DECL</div><div class="line"><a name="l00449"></a><span class="lineno"> 449</span>&#160;<span class="keywordtype">bool</span> ON_ReparameterizeRationalNurbsCurve(</div><div class="line"><a name="l00450"></a><span class="lineno"> 450</span>&#160; <span class="keywordtype">double</span> c, </div><div class="line"><a name="l00451"></a><span class="lineno"> 451</span>&#160; <span class="keywordtype">int</span> dim, </div><div class="line"><a name="l00452"></a><span class="lineno"> 452</span>&#160; <span class="keywordtype">int</span> order, </div><div class="line"><a name="l00453"></a><span class="lineno"> 453</span>&#160; <span class="keywordtype">int</span> cv_count,</div><div class="line"><a name="l00454"></a><span class="lineno"> 454</span>&#160; <span class="keywordtype">int</span> cvstride,</div><div class="line"><a name="l00455"></a><span class="lineno"> 455</span>&#160; <span class="keywordtype">double</span>* cv,</div><div class="line"><a name="l00456"></a><span class="lineno"> 456</span>&#160; <span class="keywordtype">double</span>* knot</div><div class="line"><a name="l00457"></a><span class="lineno"> 457</span>&#160; );</div><div class="line"><a name="l00458"></a><span class="lineno"> 458</span>&#160;</div><div class="line"><a name="l00459"></a><span class="lineno"> 459</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00460"></a><span class="lineno"> 460</span>&#160;<span class="comment">Description:</span></div><div class="line"><a name="l00461"></a><span class="lineno"> 461</span>&#160;<span class="comment"> Use a combination of scaling and reparameterization to set the end</span></div><div class="line"><a name="l00462"></a><span class="lineno"> 462</span>&#160;<span class="comment"> weights to the specified values. This </span></div><div class="line"><a name="l00463"></a><span class="lineno"> 463</span>&#160;<span class="comment">Parameters:</span></div><div class="line"><a name="l00464"></a><span class="lineno"> 464</span>&#160;<span class="comment"> dim - [in]</span></div><div class="line"><a name="l00465"></a><span class="lineno"> 465</span>&#160;<span class="comment"> order - [in]</span></div><div class="line"><a name="l00466"></a><span class="lineno"> 466</span>&#160;<span class="comment"> cvstride - [in] (&gt;=dim+1)</span></div><div class="line"><a name="l00467"></a><span class="lineno"> 467</span>&#160;<span class="comment"> cv - [in/out] homogeneous rational control points</span></div><div class="line"><a name="l00468"></a><span class="lineno"> 468</span>&#160;<span class="comment"> knot - [in/out] (output knot vector will be clamped and internal</span></div><div class="line"><a name="l00469"></a><span class="lineno"> 469</span>&#160;<span class="comment"> knots may be shifted.)</span></div><div class="line"><a name="l00470"></a><span class="lineno"> 470</span>&#160;<span class="comment"> w0 - [in]</span></div><div class="line"><a name="l00471"></a><span class="lineno"> 471</span>&#160;<span class="comment"> w1 - [in]</span></div><div class="line"><a name="l00472"></a><span class="lineno"> 472</span>&#160;<span class="comment"> The first cv will have weight w0 and the last cv will have weight w1.</span></div><div class="line"><a name="l00473"></a><span class="lineno"> 473</span>&#160;<span class="comment"> If v0 and v1 are the cv&#39;s input weights, then v0, v1, w0 and w1 must</span></div><div class="line"><a name="l00474"></a><span class="lineno"> 474</span>&#160;<span class="comment"> all be nonzero, and w0*v0 and w1*v1 must have the same sign.</span></div><div class="line"><a name="l00475"></a><span class="lineno"> 475</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00476"></a><span class="lineno"> 476</span>&#160;<span class="comment"> true if successful</span></div><div class="line"><a name="l00477"></a><span class="lineno"> 477</span>&#160;<span class="comment">See Also:</span></div><div class="line"><a name="l00478"></a><span class="lineno"> 478</span>&#160;<span class="comment"> ON_ReparameterizeRationalNurbsCurve</span></div><div class="line"><a name="l00479"></a><span class="lineno"> 479</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00480"></a><span class="lineno"> 480</span>&#160;ON_DECL</div><div class="line"><a name="l00481"></a><span class="lineno"> 481</span>&#160;<span class="keywordtype">bool</span> ON_ChangeRationalNurbsCurveEndWeights(</div><div class="line"><a name="l00482"></a><span class="lineno"> 482</span>&#160; <span class="keywordtype">int</span> dim, </div><div class="line"><a name="l00483"></a><span class="lineno"> 483</span>&#160; <span class="keywordtype">int</span> order, </div><div class="line"><a name="l00484"></a><span class="lineno"> 484</span>&#160; <span class="keywordtype">int</span> cv_count,</div><div class="line"><a name="l00485"></a><span class="lineno"> 485</span>&#160; <span class="keywordtype">int</span> cvstride, </div><div class="line"><a name="l00486"></a><span class="lineno"> 486</span>&#160; <span class="keywordtype">double</span>* cv, </div><div class="line"><a name="l00487"></a><span class="lineno"> 487</span>&#160; <span class="keywordtype">double</span>* knot,</div><div class="line"><a name="l00488"></a><span class="lineno"> 488</span>&#160; <span class="keywordtype">double</span> w0, </div><div class="line"><a name="l00489"></a><span class="lineno"> 489</span>&#160; <span class="keywordtype">double</span> w1</div><div class="line"><a name="l00490"></a><span class="lineno"> 490</span>&#160; );</div><div class="line"><a name="l00491"></a><span class="lineno"> 491</span>&#160;</div><div class="line"><a name="l00492"></a><span class="lineno"> 492</span>&#160;<span class="preprocessor">#endif</span></div><div class="ttc" id="class_o_n___text_log_html"><div class="ttname"><a href="../../d2/da3/class_o_n___text_log.html">ON_TextLog</a></div><div class="ttdef"><b>Definition:</b> opennurbs_textlog.h:20</div></div>
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