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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(ON_EVALUATE_NURBS_INC_)</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span>&#160;<span class="preprocessor">#define ON_EVALUATE_NURBS_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">bool</span> ON_IncreaseBezierDegree(</div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// dimension </span></div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160; <span class="keywordtype">bool</span>, <span class="comment">// true if Bezier is rational</span></div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv_stride (&gt;=dim+1)</span></div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160; <span class="keywordtype">double</span>* <span class="comment">// cv[(order+1)*cv_stride] array</span></div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160; );</div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160;</div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160;ON_DECL</div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160;<span class="keywordtype">bool</span> ON_RemoveBezierSingAt0( <span class="comment">// input bezier is rational with 0/0 at start</span></div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// dimension </span></div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv_stride (&gt;=dim+1)</span></div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <span class="keywordtype">double</span>* <span class="comment">// cv[order*cv_stride] array</span></div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; );</div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160;</div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160;ON_DECL</div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160;<span class="keywordtype">bool</span> ON_RemoveBezierSingAt1( <span class="comment">// input bezier is rational with 0/0 at end</span></div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// dimension </span></div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv_stride (&gt;=dim+1)</span></div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <span class="keywordtype">double</span>* <span class="comment">// cv[order*cv_stride] array</span></div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; );</div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160;</div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160;ON_DECL</div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160;<span class="keywordtype">double</span> ON_EvaluateBernsteinBasis( <span class="comment">// returns (i choose d)*(1-t)^(d-i)*t^i</span></div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// degree, </span></div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// 0 &lt;= i &lt;= degree</span></div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <span class="keywordtype">double</span> <span class="comment">// t</span></div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; );</div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160;</div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160;ON_DECL</div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160;<span class="keywordtype">void</span> ON_EvaluatedeCasteljau(</div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// dim</span></div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order</span></div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// side &lt;= 0 return left side of bezier in cv array</span></div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <span class="comment">// &gt; 0 return right side of bezier in cv array</span></div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv_stride</span></div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <span class="keywordtype">double</span>*, <span class="comment">// cv</span></div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="keywordtype">double</span> <span class="comment">// t 0 &lt;= t &lt;= 1</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_EvaluateBezier(</div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// dimension</span></div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="keywordtype">bool</span>, <span class="comment">// true if Bezier is rational</span></div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv_stride &gt;= (is_rat)?dim+1:dim</span></div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// cv[order*cv_stride] array</span></div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; <span class="keywordtype">double</span>, <span class="keywordtype">double</span>, <span class="comment">// t0,t1 = domain of bezier</span></div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// number of derivatives to compute (&gt;=0)</span></div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <span class="keywordtype">double</span>, <span class="comment">// evaluation parameter</span></div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// v_stride (&gt;=dimension)</span></div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; <span class="keywordtype">double</span>* <span class="comment">// v[(der_count+1)*v_stride] array</span></div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; );</div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; </div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160;<span class="comment">Description:</span></div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160;<span class="comment"> Evaluate B-spline basis functions</span></div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160;<span class="comment"> </span></div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160;<span class="comment">Parameters:</span></div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160;<span class="comment"> order - [in]</span></div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160;<span class="comment"> order &gt;= 1 </span></div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160;<span class="comment"> d = degree = order - 1</span></div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160;<span class="comment"> knot - [in]</span></div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160;<span class="comment"> array of length 2*d. </span></div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160;<span class="comment"> Generally, knot[0] &lt;= ... &lt;= knot[d-1] &lt; knot[d] &lt;= ... &lt;= knot[2*d-1].</span></div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160;<span class="comment"> These are the knots that are active for the span being evaluated.</span></div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160;<span class="comment"> t - [in]</span></div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160;<span class="comment"> Evaluation parameter. </span></div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160;<span class="comment"> Typically knot[d-1] &lt;= t &lt;= knot[d].</span></div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160;<span class="comment"> In general t may be outside the interval knot[d-1],knot[d]. This can happen </span></div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160;<span class="comment"> when some type of extrapolation is being used and is almost always a bad</span></div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160;<span class="comment"> idea in practical situations.</span></div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160;<span class="comment"> N - [out]</span></div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160;<span class="comment"> double array with capacity order*order.</span></div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160;<span class="comment"> The returned values are:</span></div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160;<span class="comment"> If &quot;N&quot; were declared as double N[order][order], then</span></div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160;<span class="comment"> k</span></div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160;<span class="comment"> N[d-k][i] = N (t) = value of i-th degree k basis function at t.</span></div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160;<span class="comment"> i</span></div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160;<span class="comment"> where 0 &lt;= k &lt;= d and k &lt;= i &lt;= d.</span></div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160;<span class="comment"> In particular, N[0], ..., N[d] - values of degree d basis functions.</span></div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160;<span class="comment"> The &quot;lower left&quot; triangle is not initialized.</span></div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160;<span class="comment"> Actually, the above is true when knot[d-1] &lt;= t &lt; knot[d]. Otherwise, the</span></div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160;<span class="comment"> value returned is the value of the polynomial that agrees with N_i^k on the</span></div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160;<span class="comment"> half open domain [ knot[d-1], knot[d] )</span></div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160;<span class="comment">COMMENTS:</span></div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160;<span class="comment"> If a degree d NURBS has n control points, then the OpenNURBS knot vector </span></div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160;<span class="comment"> for the entire NURBS curve has length d+n-1. The knot[] paramter to this</span></div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160;<span class="comment"> function points to the 2*d knots active for the span being evaluated.</span></div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160;<span class="comment"> </span></div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>&#160;<span class="comment"> Most literature, including DeBoor and The NURBS Book,</span></div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160;<span class="comment"> duplicate the Opennurbs start and end knot values and have knot vectors</span></div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160;<span class="comment"> of length d+n+1. The extra two knot values are completely superfluous </span></div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160;<span class="comment"> when degree &gt;= 1.</span></div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160;<span class="comment"> </span></div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>&#160;<span class="comment"> Assume C is a B-spline of degree d (order=d+1) with n control vertices</span></div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160;<span class="comment"> (n&gt;=d+1) and knot[] is its knot vector. Then</span></div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160;<span class="comment"> C(t) = Sum( 0 &lt;= i &lt; n, N_{i}(t) * C_{i} )</span></div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160;<span class="comment"> where N_{i} are the degree d b-spline basis functions and C_{i} are the control</span></div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160;<span class="comment"> vertices. The knot[] array length d+n-1 and satisfies</span></div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160;<span class="comment"> knot[0] &lt;= ... &lt;= knot[d-1] &lt; knot[d]</span></div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160;<span class="comment"> knot[n-2] &lt; knot[n-1] &lt;= ... &lt;= knot[n+d-2]</span></div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160;<span class="comment"> knot[i] &lt; knot[d+i] for 0 &lt;= i &lt; n-1</span></div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160;<span class="comment"> knot[i] &lt;= knot[i+1] for 0 &lt;= i &lt; n+d-2</span></div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span>&#160;<span class="comment"> The domain of C is [ knot[d-1], knot[n-1] ].</span></div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span>&#160;<span class="comment"> The support of N_{i} is [ knot[i-1], knot[i+d] ).</span></div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span>&#160;<span class="comment"> If d-1 &lt;= k &lt; n-1 and knot[k] &lt;= t &lt; knot[k+1], then </span></div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span>&#160;<span class="comment"> N_{i}(t) = 0 if i &lt;= k-d</span></div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span>&#160;<span class="comment"> = 0 if i &gt;= k+2</span></div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span>&#160;<span class="comment"> = B[i-k+d-1] if k-d+1 &lt;= i &lt;= k+1, where B[] is computed by the call</span></div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span>&#160;<span class="comment"> ON_EvaluateNurbsBasis( d+1, knot+k-d+1, t, B );</span></div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span>&#160;<span class="comment"> If 0 &lt;= j &lt; n-d, 0 &lt;= m &lt;= d, knot[j+d-1] &lt;= t &lt; knot[j+d], and B[] is </span></div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>&#160;<span class="comment"> computed by the call</span></div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>&#160;<span class="comment"> ON_EvaluateNurbsBasis( d+1, knot+j, t, B ),</span></div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>&#160;<span class="comment"> then </span></div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span>&#160;<span class="comment"> N_{j+m}(t) = B[m].</span></div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span>&#160;ON_DECL</div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span>&#160;<span class="keywordtype">bool</span> ON_EvaluateNurbsBasis( </div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span>&#160; <span class="keywordtype">int</span> order,</div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* knot,</div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span>&#160; <span class="keywordtype">double</span> t,</div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span>&#160; <span class="keywordtype">double</span>* N</div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span>&#160; );</div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span>&#160;</div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span>&#160;<span class="comment">Description:</span></div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span>&#160;<span class="comment"> Calculate derivatives of B-spline basis functions.</span></div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span>&#160;<span class="comment">INPUT:</span></div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span>&#160;<span class="comment"> order - [in]</span></div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span>&#160;<span class="comment"> order &gt;= 1 </span></div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span>&#160;<span class="comment"> d = degree = order - 1</span></div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span>&#160;<span class="comment"> knot - [in]</span></div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span>&#160;<span class="comment"> array of length 2*d. </span></div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span>&#160;<span class="comment"> Generally, knot[0] &lt;= ... &lt;= knot[d-1] &lt; knot[d] &lt;= ... &lt;= knot[2*d-1].</span></div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span>&#160;<span class="comment"> These are the knots that are active for the span being evaluated.</span></div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span>&#160;<span class="comment"> der_count - [in]</span></div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span>&#160;<span class="comment"> 1 &lt;= der_count &lt; order</span></div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span>&#160;<span class="comment"> Number of derivatives. </span></div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span>&#160;<span class="comment"> Note all B-spline basis derivatives with der_coutn &gt;= order are identically zero.</span></div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span>&#160;<span class="comment"> N - [in]</span></div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span>&#160;<span class="comment"> The input value of N[] should be the results of the call</span></div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span>&#160;<span class="comment"> ON_EvaluateNurbsBasis( order, knot, t, N );</span></div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span>&#160;<span class="comment"> </span></div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span>&#160;<span class="comment"> N - [out]</span></div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160;<span class="comment"> If &quot;N&quot; were declared as double N[order][order], then</span></div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span>&#160;<span class="comment"> </span></div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span>&#160;<span class="comment"> d</span></div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span>&#160;<span class="comment"> N[d-k][i] = k-th derivative of N (t)</span></div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span>&#160;<span class="comment"> i</span></div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>&#160;<span class="comment"> </span></div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>&#160;<span class="comment"> where 0 &lt;= k &lt;= d and 0 &lt;= i &lt;= d.</span></div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span>&#160;<span class="comment"> </span></div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span>&#160;<span class="comment"> In particular, </span></div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span>&#160;<span class="comment"> N[0], ..., N[d] - values of degree d basis functions.</span></div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span>&#160;<span class="comment"> N[order], ..., N[order_d] - values of first derivative.</span></div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span>&#160;ON_DECL</div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span>&#160;<span class="keywordtype">bool</span> ON_EvaluateNurbsBasisDerivatives(</div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span>&#160; <span class="keywordtype">int</span> order,</div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* knot,</div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>&#160; <span class="keywordtype">int</span> der_count,</div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>&#160; <span class="keywordtype">double</span>* N</div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span>&#160; );</div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span>&#160;</div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span>&#160;<span class="comment">Description:</span></div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span>&#160;<span class="comment"> Evaluate a NURBS curve span.</span></div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span>&#160;<span class="comment">Parameters:</span></div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span>&#160;<span class="comment"> dim - [in]</span></div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span>&#160;<span class="comment"> dimension (&gt; 0).</span></div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span>&#160;<span class="comment"> is_rat - [in] </span></div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span>&#160;<span class="comment"> true or false.</span></div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>&#160;<span class="comment"> order - [in]</span></div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span>&#160;<span class="comment"> order=degree+1 (order&gt;=2)</span></div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span>&#160;<span class="comment"> knot - [in] NURBS knot vector.</span></div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span>&#160;<span class="comment"> NURBS knot vector with 2*(order-1) knots, knot[order-2] != knot[order-1]</span></div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span>&#160;<span class="comment"> cv_stride - [in]</span></div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span>&#160;<span class="comment"> cv - [in]</span></div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span>&#160;<span class="comment"> For 0 &lt;= i &lt; order the i-th control vertex is</span></div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span>&#160;<span class="comment"> cv[n],...,cv[n+(is_rat?dim:dim+1)], </span></div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span>&#160;<span class="comment"> where n = i*cv_stride. If is_rat is true the cv is</span></div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>&#160;<span class="comment"> in homogeneous form.</span></div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span>&#160;<span class="comment"> der_count - [in] </span></div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span>&#160;<span class="comment"> number of derivatives to evaluate (&gt;=0)</span></div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span>&#160;<span class="comment"> t - [in] </span></div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span>&#160;<span class="comment"> evaluation parameter</span></div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span>&#160;<span class="comment"> v_stride - [in]</span></div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span>&#160;<span class="comment"> v - [out]</span></div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span>&#160;<span class="comment"> An array of length v_stride*(der_count+1). The evaluation </span></div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span>&#160;<span class="comment"> results are returned in this array.</span></div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span>&#160;<span class="comment"> P = v[0],...,v[m_dim-1]</span></div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span>&#160;<span class="comment"> Dt = v[v_stride],...</span></div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span>&#160;<span class="comment"> Dtt = v[2*v_stride],...</span></div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span>&#160;<span class="comment"> ...</span></div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span>&#160;<span class="comment"> In general, Dt^i returned in v[n],...,v[n+m_dim-1], where</span></div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span>&#160;<span class="comment"> n = v_stride*i.</span></div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span>&#160;<span class="comment"> </span></div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span>&#160;<span class="comment"> True if successful.</span></div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span>&#160;<span class="comment">See Also:</span></div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>&#160;<span class="comment"> ON_NurbsCurve::Evaluate</span></div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span>&#160;<span class="comment"> ON_EvaluateNurbsSurfaceSpan</span></div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span>&#160;<span class="comment"> ON_EvaluateNurbsCageSpan</span></div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span>&#160;ON_DECL</div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span>&#160;<span class="keywordtype">bool</span> ON_EvaluateNurbsSpan( </div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span>&#160; <span class="keywordtype">int</span> dim,</div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span>&#160; <span class="keywordtype">bool</span> is_rat,</div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span>&#160; <span class="keywordtype">int</span> order,</div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* knot,</div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span>&#160; <span class="keywordtype">int</span> cv_stride,</div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* cv,</div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span>&#160; <span class="keywordtype">int</span> der_count,</div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span>&#160; <span class="keywordtype">double</span> t,</div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span>&#160; <span class="keywordtype">int</span> v_stride,</div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span>&#160; <span class="keywordtype">double</span>* v</div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span>&#160; );</div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span>&#160;</div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span>&#160;<span class="comment">Description:</span></div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span>&#160;<span class="comment"> Evaluate a NURBS surface bispan.</span></div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span>&#160;<span class="comment">Parameters:</span></div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span>&#160;<span class="comment"> dim - [in] &gt;0</span></div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span>&#160;<span class="comment"> is_rat - [in] true of false</span></div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span>&#160;<span class="comment"> order0 - [in] &gt;= 2</span></div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span>&#160;<span class="comment"> order1 - [in] &gt;= 2</span></div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span>&#160;<span class="comment"> knot0 - [in] </span></div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span>&#160;<span class="comment"> NURBS knot vector with 2*(order0-1) knots, knot0[order0-2] != knot0[order0-1]</span></div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span>&#160;<span class="comment"> knot1 - [in]</span></div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span>&#160;<span class="comment"> NURBS knot vector with 2*(order1-1) knots, knot1[order1-2] != knot1[order1-1]</span></div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span>&#160;<span class="comment"> cv_stride0 - [in]</span></div><div class="line"><a name="l00274"></a><span class="lineno"> 274</span>&#160;<span class="comment"> cv_stride1 - [in]</span></div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span>&#160;<span class="comment"> cv - [in]</span></div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span>&#160;<span class="comment"> For 0 &lt;= i &lt; order0 and 0 &lt;= j &lt; order1, the (i,j) control vertex is</span></div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span>&#160;<span class="comment"> cv[n],...,cv[n+(is_rat?dim:dim+1)], </span></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"> where n = i*cv_stride0 + j*cv_stride1. If is_rat is true the cv is</span></div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span>&#160;<span class="comment"> in homogeneous form.</span></div><div class="line"><a name="l00282"></a><span class="lineno"> 282</span>&#160;<span class="comment"> </span></div><div class="line"><a name="l00283"></a><span class="lineno"> 283</span>&#160;<span class="comment"> der_count - [in] (&gt;=0)</span></div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span>&#160;<span class="comment"> s - [in]</span></div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span>&#160;<span class="comment"> t - [in] (s,t) is the evaluation parameter</span></div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span>&#160;<span class="comment"> v_stride - [in] (&gt;=dim)</span></div><div class="line"><a name="l00287"></a><span class="lineno"> 287</span>&#160;<span class="comment"> v - [out] An array of length v_stride*(der_count+1)*(der_count+2)/2.</span></div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span>&#160;<span class="comment"> The evaluation results are stored in this array.</span></div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span>&#160;<span class="comment"> P = v[0],...,v[m_dim-1]</span></div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span>&#160;<span class="comment"> Ds = v[v_stride],...</span></div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span>&#160;<span class="comment"> Dt = v[2*v_stride],...</span></div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span>&#160;<span class="comment"> Dss = v[3*v_stride],...</span></div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span>&#160;<span class="comment"> Dst = v[4*v_stride],...</span></div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span>&#160;<span class="comment"> Dtt = v[5*v_stride],...</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;<span class="comment"> In general, Ds^i Dt^j is returned in v[n],...,v[n+m_dim-1], where</span></div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span>&#160;<span class="comment"> n = v_stride*( (i+j)*(i+j+1)/2 + j).</span></div><div class="line"><a name="l00300"></a><span class="lineno"> 300</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00301"></a><span class="lineno"> 301</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00302"></a><span class="lineno"> 302</span>&#160;<span class="comment"> True if succcessful.</span></div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span>&#160;<span class="comment">See Also:</span></div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span>&#160;<span class="comment"> ON_NurbsSurface::Evaluate</span></div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span>&#160;<span class="comment"> ON_EvaluateNurbsSpan</span></div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span>&#160;<span class="comment"> ON_EvaluateNurbsCageSpan</span></div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span>&#160;ON_DECL</div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span>&#160;<span class="keywordtype">bool</span> ON_EvaluateNurbsSurfaceSpan(</div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span>&#160; <span class="keywordtype">int</span> dim,</div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span>&#160; <span class="keywordtype">bool</span> is_rat,</div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span>&#160; <span class="keywordtype">int</span> order0, </div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span>&#160; <span class="keywordtype">int</span> order1,</div><div class="line"><a name="l00314"></a><span class="lineno"> 314</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* knot0,</div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* knot1,</div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span>&#160; <span class="keywordtype">int</span> cv_stride0,</div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span>&#160; <span class="keywordtype">int</span> cv_stride1,</div><div class="line"><a name="l00318"></a><span class="lineno"> 318</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* cv,</div><div class="line"><a name="l00319"></a><span class="lineno"> 319</span>&#160; <span class="keywordtype">int</span> der_count,</div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span>&#160; <span class="keywordtype">double</span> s,</div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span>&#160; <span class="keywordtype">double</span> t,</div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span>&#160; <span class="keywordtype">int</span> v_stride,</div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span>&#160; <span class="keywordtype">double</span>* v</div><div class="line"><a name="l00324"></a><span class="lineno"> 324</span>&#160; );</div><div class="line"><a name="l00325"></a><span class="lineno"> 325</span>&#160; </div><div class="line"><a name="l00326"></a><span class="lineno"> 326</span>&#160;</div><div class="line"><a name="l00327"></a><span class="lineno"> 327</span>&#160;</div><div class="line"><a name="l00328"></a><span class="lineno"> 328</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00329"></a><span class="lineno"> 329</span>&#160;<span class="comment">Description:</span></div><div class="line"><a name="l00330"></a><span class="lineno"> 330</span>&#160;<span class="comment"> Evaluate a NURBS cage trispan.</span></div><div class="line"><a name="l00331"></a><span class="lineno"> 331</span>&#160;<span class="comment">Parameters:</span></div><div class="line"><a name="l00332"></a><span class="lineno"> 332</span>&#160;<span class="comment"> dim - [in] &gt;0</span></div><div class="line"><a name="l00333"></a><span class="lineno"> 333</span>&#160;<span class="comment"> is_rat - [in] true of false</span></div><div class="line"><a name="l00334"></a><span class="lineno"> 334</span>&#160;<span class="comment"> order0 - [in] &gt;= 2</span></div><div class="line"><a name="l00335"></a><span class="lineno"> 335</span>&#160;<span class="comment"> order1 - [in] &gt;= 2</span></div><div class="line"><a name="l00336"></a><span class="lineno"> 336</span>&#160;<span class="comment"> order2 - [in] &gt;= 2</span></div><div class="line"><a name="l00337"></a><span class="lineno"> 337</span>&#160;<span class="comment"> knot0 - [in] </span></div><div class="line"><a name="l00338"></a><span class="lineno"> 338</span>&#160;<span class="comment"> NURBS knot vector with 2*(order0-1) knots, knot0[order0-2] != knot0[order0-1]</span></div><div class="line"><a name="l00339"></a><span class="lineno"> 339</span>&#160;<span class="comment"> knot1 - [in]</span></div><div class="line"><a name="l00340"></a><span class="lineno"> 340</span>&#160;<span class="comment"> NURBS knot vector with 2*(order1-1) knots, knot1[order1-2] != knot1[order1-1]</span></div><div class="line"><a name="l00341"></a><span class="lineno"> 341</span>&#160;<span class="comment"> knot2 - [in]</span></div><div class="line"><a name="l00342"></a><span class="lineno"> 342</span>&#160;<span class="comment"> NURBS knot vector with 2*(order1-1) knots, knot2[order2-2] != knot2[order2-1]</span></div><div class="line"><a name="l00343"></a><span class="lineno"> 343</span>&#160;<span class="comment"> cv_stride0 - [in]</span></div><div class="line"><a name="l00344"></a><span class="lineno"> 344</span>&#160;<span class="comment"> cv_stride1 - [in]</span></div><div class="line"><a name="l00345"></a><span class="lineno"> 345</span>&#160;<span class="comment"> cv_stride2 - [in]</span></div><div class="line"><a name="l00346"></a><span class="lineno"> 346</span>&#160;<span class="comment"> cv - [in]</span></div><div class="line"><a name="l00347"></a><span class="lineno"> 347</span>&#160;<span class="comment"> For 0 &lt;= i &lt; order0, 0 &lt;= j &lt; order1, and 0 &lt;= k &lt; order2, </span></div><div class="line"><a name="l00348"></a><span class="lineno"> 348</span>&#160;<span class="comment"> the (i,j,k)-th control vertex is</span></div><div class="line"><a name="l00349"></a><span class="lineno"> 349</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00350"></a><span class="lineno"> 350</span>&#160;<span class="comment"> cv[n],...,cv[n+(is_rat?dim:dim+1)], </span></div><div class="line"><a name="l00351"></a><span class="lineno"> 351</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00352"></a><span class="lineno"> 352</span>&#160;<span class="comment"> where n = i*cv_stride0 + j*cv_stride1 *k*cv_stride2. </span></div><div class="line"><a name="l00353"></a><span class="lineno"> 353</span>&#160;<span class="comment"> If is_rat is true the cv is in homogeneous form.</span></div><div class="line"><a name="l00354"></a><span class="lineno"> 354</span>&#160;<span class="comment"> </span></div><div class="line"><a name="l00355"></a><span class="lineno"> 355</span>&#160;<span class="comment"> der_count - [in] (&gt;=0)</span></div><div class="line"><a name="l00356"></a><span class="lineno"> 356</span>&#160;<span class="comment"> r - [in]</span></div><div class="line"><a name="l00357"></a><span class="lineno"> 357</span>&#160;<span class="comment"> s - [in]</span></div><div class="line"><a name="l00358"></a><span class="lineno"> 358</span>&#160;<span class="comment"> t - [in] (r,s,t) is the evaluation parameter</span></div><div class="line"><a name="l00359"></a><span class="lineno"> 359</span>&#160;<span class="comment"> v_stride - [in] (&gt;=dim)</span></div><div class="line"><a name="l00360"></a><span class="lineno"> 360</span>&#160;<span class="comment"> v - [out] An array of length v_stride*(der_count+1)*(der_count+2)*(der_count+3)/6.</span></div><div class="line"><a name="l00361"></a><span class="lineno"> 361</span>&#160;<span class="comment"> The evaluation results are stored in this array.</span></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"> P = v[0],...,v[m_dim-1]</span></div><div class="line"><a name="l00364"></a><span class="lineno"> 364</span>&#160;<span class="comment"> Dr = v[v_stride],...</span></div><div class="line"><a name="l00365"></a><span class="lineno"> 365</span>&#160;<span class="comment"> Ds = v[2*v_stride],...</span></div><div class="line"><a name="l00366"></a><span class="lineno"> 366</span>&#160;<span class="comment"> Dt = v[3*v_stride],...</span></div><div class="line"><a name="l00367"></a><span class="lineno"> 367</span>&#160;<span class="comment"> Drr = v[4*v_stride],...</span></div><div class="line"><a name="l00368"></a><span class="lineno"> 368</span>&#160;<span class="comment"> Drs = v[5*v_stride],...</span></div><div class="line"><a name="l00369"></a><span class="lineno"> 369</span>&#160;<span class="comment"> Drt = v[6*v_stride],...</span></div><div class="line"><a name="l00370"></a><span class="lineno"> 370</span>&#160;<span class="comment"> Dss = v[7*v_stride],...</span></div><div class="line"><a name="l00371"></a><span class="lineno"> 371</span>&#160;<span class="comment"> Dst = v[8*v_stride],...</span></div><div class="line"><a name="l00372"></a><span class="lineno"> 372</span>&#160;<span class="comment"> Dtt = v[9*v_stride],...</span></div><div class="line"><a name="l00373"></a><span class="lineno"> 373</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00374"></a><span class="lineno"> 374</span>&#160;<span class="comment"> In general, Dr^i Ds^j Dt^k is returned in v[n],...,v[n+dim-1], where</span></div><div class="line"><a name="l00375"></a><span class="lineno"> 375</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00376"></a><span class="lineno"> 376</span>&#160;<span class="comment"> d = (i+j+k)</span></div><div class="line"><a name="l00377"></a><span class="lineno"> 377</span>&#160;<span class="comment"> n = v_stride*( d*(d+1)*(d+2)/6 + (j+k)*(j+k+1)/2 + k) </span></div><div class="line"><a name="l00378"></a><span class="lineno"> 378</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00379"></a><span class="lineno"> 379</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00380"></a><span class="lineno"> 380</span>&#160;<span class="comment"> True if succcessful.</span></div><div class="line"><a name="l00381"></a><span class="lineno"> 381</span>&#160;<span class="comment">See Also:</span></div><div class="line"><a name="l00382"></a><span class="lineno"> 382</span>&#160;<span class="comment"> ON_NurbsCage::Evaluate</span></div><div class="line"><a name="l00383"></a><span class="lineno"> 383</span>&#160;<span class="comment"> ON_EvaluateNurbsSpan</span></div><div class="line"><a name="l00384"></a><span class="lineno"> 384</span>&#160;<span class="comment"> ON_EvaluateNurbsSurfaceSpan</span></div><div class="line"><a name="l00385"></a><span class="lineno"> 385</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00386"></a><span class="lineno"> 386</span>&#160;ON_DECL</div><div class="line"><a name="l00387"></a><span class="lineno"> 387</span>&#160;<span class="keywordtype">bool</span> ON_EvaluateNurbsCageSpan(</div><div class="line"><a name="l00388"></a><span class="lineno"> 388</span>&#160; <span class="keywordtype">int</span> dim,</div><div class="line"><a name="l00389"></a><span class="lineno"> 389</span>&#160; <span class="keywordtype">bool</span> is_rat,</div><div class="line"><a name="l00390"></a><span class="lineno"> 390</span>&#160; <span class="keywordtype">int</span> order0, <span class="keywordtype">int</span> order1, <span class="keywordtype">int</span> order2,</div><div class="line"><a name="l00391"></a><span class="lineno"> 391</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* knot0,</div><div class="line"><a name="l00392"></a><span class="lineno"> 392</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* knot1,</div><div class="line"><a name="l00393"></a><span class="lineno"> 393</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* knot2,</div><div class="line"><a name="l00394"></a><span class="lineno"> 394</span>&#160; <span class="keywordtype">int</span> cv_stride0, <span class="keywordtype">int</span> cv_stride1, <span class="keywordtype">int</span> cv_stride2,</div><div class="line"><a name="l00395"></a><span class="lineno"> 395</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>* cv,</div><div class="line"><a name="l00396"></a><span class="lineno"> 396</span>&#160; <span class="keywordtype">int</span> der_count,</div><div class="line"><a name="l00397"></a><span class="lineno"> 397</span>&#160; <span class="keywordtype">double</span> t0, <span class="keywordtype">double</span> t1, <span class="keywordtype">double</span> t2,</div><div class="line"><a name="l00398"></a><span class="lineno"> 398</span>&#160; <span class="keywordtype">int</span> v_stride, </div><div class="line"><a name="l00399"></a><span class="lineno"> 399</span>&#160; <span class="keywordtype">double</span>* v</div><div class="line"><a name="l00400"></a><span class="lineno"> 400</span>&#160; );</div><div class="line"><a name="l00401"></a><span class="lineno"> 401</span>&#160;</div><div class="line"><a name="l00402"></a><span class="lineno"> 402</span>&#160;</div><div class="line"><a name="l00403"></a><span class="lineno"> 403</span>&#160;ON_DECL</div><div class="line"><a name="l00404"></a><span class="lineno"> 404</span>&#160;<span class="keywordtype">bool</span> ON_EvaluateNurbsDeBoor( <span class="comment">// for expert users only - no support available</span></div><div class="line"><a name="l00405"></a><span class="lineno"> 405</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv_dim ( dim+1 for rational cvs )</span></div><div class="line"><a name="l00406"></a><span class="lineno"> 406</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order (&gt;=2)</span></div><div class="line"><a name="l00407"></a><span class="lineno"> 407</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv_stride (&gt;=cv_dim)</span></div><div class="line"><a name="l00408"></a><span class="lineno"> 408</span>&#160; <span class="keywordtype">double</span>*, <span class="comment">// cv array - values changed to result of applying De Boor&#39;s algorithm</span></div><div class="line"><a name="l00409"></a><span class="lineno"> 409</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// knot array</span></div><div class="line"><a name="l00410"></a><span class="lineno"> 410</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// side,</span></div><div class="line"><a name="l00411"></a><span class="lineno"> 411</span>&#160; <span class="comment">// -1 return left side of B-spline span in cv array</span></div><div class="line"><a name="l00412"></a><span class="lineno"> 412</span>&#160; <span class="comment">// +1 return right side of B-spline span in cv array</span></div><div class="line"><a name="l00413"></a><span class="lineno"> 413</span>&#160; <span class="comment">// -2 return left side of B-spline span in cv array</span></div><div class="line"><a name="l00414"></a><span class="lineno"> 414</span>&#160; <span class="comment">// Ignore values of knots[0,...,order-3] and assume</span></div><div class="line"><a name="l00415"></a><span class="lineno"> 415</span>&#160; <span class="comment">// left end of span has a fully multiple knot with</span></div><div class="line"><a name="l00416"></a><span class="lineno"> 416</span>&#160; <span class="comment">// value &quot;mult_k&quot;.</span></div><div class="line"><a name="l00417"></a><span class="lineno"> 417</span>&#160; <span class="comment">// +2 return right side of B-spline span in cv array</span></div><div class="line"><a name="l00418"></a><span class="lineno"> 418</span>&#160; <span class="comment">// Ignore values of knots[order,...,2*order-2] and</span></div><div class="line"><a name="l00419"></a><span class="lineno"> 419</span>&#160; <span class="comment">// assume right end of span has a fully multiple</span></div><div class="line"><a name="l00420"></a><span class="lineno"> 420</span>&#160; <span class="comment">// knot with value &quot;mult_k&quot;.</span></div><div class="line"><a name="l00421"></a><span class="lineno"> 421</span>&#160; <span class="keywordtype">double</span>, <span class="comment">// mult_k - used when side is +2 or -2. See above for usage.</span></div><div class="line"><a name="l00422"></a><span class="lineno"> 422</span>&#160; <span class="keywordtype">double</span> <span class="comment">// t</span></div><div class="line"><a name="l00423"></a><span class="lineno"> 423</span>&#160; <span class="comment">// If side &lt; 0, then the cv&#39;s for the portion of the NURB span to</span></div><div class="line"><a name="l00424"></a><span class="lineno"> 424</span>&#160; <span class="comment">// the LEFT of t are computed. If side &gt; 0, then the cv&#39;s for the</span></div><div class="line"><a name="l00425"></a><span class="lineno"> 425</span>&#160; <span class="comment">// portion the span to the RIGHT of t are computed. The following</span></div><div class="line"><a name="l00426"></a><span class="lineno"> 426</span>&#160; <span class="comment">// table summarizes the restrictions on t:</span></div><div class="line"><a name="l00427"></a><span class="lineno"> 427</span>&#160; <span class="comment">//</span></div><div class="line"><a name="l00428"></a><span class="lineno"> 428</span>&#160; <span class="comment">// value of side condition t must satisfy</span></div><div class="line"><a name="l00429"></a><span class="lineno"> 429</span>&#160; <span class="comment">// -2 mult_k &lt; t and mult_k &lt; knots[order-1]</span></div><div class="line"><a name="l00430"></a><span class="lineno"> 430</span>&#160; <span class="comment">// -1 knots[order-2] &lt; t</span></div><div class="line"><a name="l00431"></a><span class="lineno"> 431</span>&#160; <span class="comment">// +1 t &lt; knots[order-1]</span></div><div class="line"><a name="l00432"></a><span class="lineno"> 432</span>&#160; <span class="comment">// +2 t &lt; mult_k and knots[order-2] &lt; mult_k</span></div><div class="line"><a name="l00433"></a><span class="lineno"> 433</span>&#160; );</div><div class="line"><a name="l00434"></a><span class="lineno"> 434</span>&#160;</div><div class="line"><a name="l00435"></a><span class="lineno"> 435</span>&#160;</div><div class="line"><a name="l00436"></a><span class="lineno"> 436</span>&#160;ON_DECL</div><div class="line"><a name="l00437"></a><span class="lineno"> 437</span>&#160;<span class="keywordtype">bool</span> ON_EvaluateNurbsBlossom(<span class="keywordtype">int</span>, <span class="comment">// cvdim,</span></div><div class="line"><a name="l00438"></a><span class="lineno"> 438</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order, </span></div><div class="line"><a name="l00439"></a><span class="lineno"> 439</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cv_stride,</span></div><div class="line"><a name="l00440"></a><span class="lineno"> 440</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">//CV, size cv_stride*order</span></div><div class="line"><a name="l00441"></a><span class="lineno"> 441</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">//knot, nondecreasing, size 2*(order-1)</span></div><div class="line"><a name="l00442"></a><span class="lineno"> 442</span>&#160; <span class="comment">// knot[order-2] != knot[order-1]</span></div><div class="line"><a name="l00443"></a><span class="lineno"> 443</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">//t, input parameters size order-1</span></div><div class="line"><a name="l00444"></a><span class="lineno"> 444</span>&#160; <span class="keywordtype">double</span>* <span class="comment">// P</span></div><div class="line"><a name="l00445"></a><span class="lineno"> 445</span>&#160;</div><div class="line"><a name="l00446"></a><span class="lineno"> 446</span>&#160; <span class="comment">// DeBoor algorithm with different input at each step.</span></div><div class="line"><a name="l00447"></a><span class="lineno"> 447</span>&#160; <span class="comment">// returns false for bad input.</span></div><div class="line"><a name="l00448"></a><span class="lineno"> 448</span>&#160; );</div><div class="line"><a name="l00449"></a><span class="lineno"> 449</span>&#160;</div><div class="line"><a name="l00450"></a><span class="lineno"> 450</span>&#160;</div><div class="line"><a name="l00451"></a><span class="lineno"> 451</span>&#160;ON_DECL</div><div class="line"><a name="l00452"></a><span class="lineno"> 452</span>&#160;<span class="keywordtype">void</span> ON_ConvertNurbSpanToBezier(</div><div class="line"><a name="l00453"></a><span class="lineno"> 453</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cvdim (dim+1 for rational curves)</span></div><div class="line"><a name="l00454"></a><span class="lineno"> 454</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// order, </span></div><div class="line"><a name="l00455"></a><span class="lineno"> 455</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// cvstride (&gt;=cvdim)</span></div><div class="line"><a name="l00456"></a><span class="lineno"> 456</span>&#160; <span class="keywordtype">double</span>*, <span class="comment">// cv array - input has NURBS cvs, output has Bezier cvs</span></div><div class="line"><a name="l00457"></a><span class="lineno"> 457</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span>*, <span class="comment">// (2*order-2) knots for the NURBS span</span></div><div class="line"><a name="l00458"></a><span class="lineno"> 458</span>&#160; <span class="keywordtype">double</span>, <span class="comment">// t0, NURBS span parameter of start point</span></div><div class="line"><a name="l00459"></a><span class="lineno"> 459</span>&#160; <span class="keywordtype">double</span> <span class="comment">// t1, NURBS span parameter of end point</span></div><div class="line"><a name="l00460"></a><span class="lineno"> 460</span>&#160; );</div><div class="line"><a name="l00461"></a><span class="lineno"> 461</span>&#160;<span class="preprocessor">#endif</span></div></div><!-- fragment --></div><!-- contents -->
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