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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_INTERSECT_INC_)</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span>&#160;<span class="preprocessor">#define ON_INTERSECT_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;<span class="comment">// These simple intersectors are fast and detect transverse intersections.</span></div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160;<span class="comment">// If the intersection is not a simple transverse case, then they</span></div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160;<span class="comment">// return false and you will have to use one of the slower but fancier</span></div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160;<span class="comment">// models.</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;<span class="comment">/*</span></div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160;<span class="comment">Description:</span></div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160;<span class="comment"> Intersect two lines.</span></div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160;<span class="comment">Parameters:</span></div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160;<span class="comment"> lineA - [in]</span></div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160;<span class="comment"> lineB - [in]</span></div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160;<span class="comment"> double* a - [out]</span></div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160;<span class="comment"> double* b - [out] The shortest distance between the lines is the</span></div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160;<span class="comment"> chord from lineA.PointAt(*a) to lineB.PointAt(*b).</span></div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160;<span class="comment"> tolerance - [in] If &gt; 0.0, then an intersection is reported only</span></div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160;<span class="comment"> if the distance between the points is &lt;= tolerance.</span></div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160;<span class="comment"> If &lt;= 0.0, then the closest point between the lines</span></div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160;<span class="comment"> is reported.</span></div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160;<span class="comment"> bIntersectSegments - [in] if true, the input lines are treated</span></div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160;<span class="comment"> as finite segments. If false, the</span></div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160;<span class="comment"> input lines are treated as infinite lines.</span></div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160;<span class="comment"> True if a closest point can be calculated and the result passes</span></div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160;<span class="comment"> the tolerance parameter test.</span></div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160;<span class="comment">See Also:</span></div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160;<span class="comment"> ON_Intersect( const ON_Line&amp; lineA, const ON_Line&amp; line B)</span></div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160;<span class="comment">Remarks:</span></div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160;<span class="comment"> If the lines are exactly parallel, meaning the system of equations</span></div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160;<span class="comment"> used to find a and b has no numerical solution, then false is returned.</span></div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160;<span class="comment"> If the lines are nearly parallel, which is often numerically true</span></div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160;<span class="comment"> even if you think the lines look exactly parallel, then the</span></div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160;<span class="comment"> closest points are found and true is returned. So, if you</span></div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160;<span class="comment"> care about weeding out &quot;parallel&quot; lines, then you need to</span></div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160;<span class="comment"> do something like the following.</span></div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160;<span class="comment"> bool rc = ON_IntersectLineLine(lineA,lineB,</span></div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160;<span class="comment"> &amp;a,&amp;b,</span></div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160;<span class="comment"> tolerance,</span></div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160;<span class="comment"> bIntersectSegments);</span></div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160;<span class="comment"> if (rc)</span></div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160;<span class="comment"> {</span></div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160;<span class="comment"> double angle_tolerance_radians = 0.5*ON_PI/180.0; // or whatever</span></div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160;<span class="comment"> double parallel_tol = cos(angle_tolerance_radians);</span></div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160;<span class="comment"> if ( fabs(lineA.Tangent()*lineB.Tangent()) &gt;= parallel_tol )</span></div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160;<span class="comment"> {</span></div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160;<span class="comment"> ... do whatever you think is appropriate</span></div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160;<span class="comment"> }</span></div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160;<span class="comment"> }</span></div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160;ON_DECL</div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160;<span class="keywordtype">bool</span> ON_IntersectLineLine(</div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d4/d6f/class_o_n___line.html">ON_Line</a>&amp; lineA, </div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d4/d6f/class_o_n___line.html">ON_Line</a>&amp; lineB, </div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; <span class="keywordtype">double</span>* a,</div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <span class="keywordtype">double</span>* b,</div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <span class="keywordtype">double</span> tolerance,</div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; <span class="keywordtype">bool</span> bIntersectSegments</div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; );</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160;</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">Description:</span></div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160;<span class="comment"> Find the closest point between two infinte lines.</span></div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160;<span class="comment">Parameters:</span></div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160;<span class="comment"> lineA - [in]</span></div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160;<span class="comment"> lineB - [in]</span></div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160;<span class="comment"> double* a - [out]</span></div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160;<span class="comment"> double* b - [out] The shortest distance between the lines is the</span></div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160;<span class="comment"> chord from lineA.PointAt(*a) to lineB.PointAt(*b).</span></div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160;<span class="comment"> True if points are found and false if the lines are numerically parallel.</span></div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160;<span class="comment"> Numerically parallel means the 2x2 matrix</span></div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160;<span class="comment"> AoA -AoB</span></div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160;<span class="comment"> -AoB BoB</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"> is numerically singluar, where A = lineA.to-lineA.from </span></div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160;<span class="comment"> and B = lineB.to-lineB.from.</span></div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160;<span class="comment">See Also:</span></div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160;<span class="comment"> ON_IntersectLineLine</span></div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160;</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160;<span class="comment">/* 15 Sept 2016 - Already in opennurbs_math.h</span></div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160;<span class="comment">ON_DECL</span></div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160;<span class="comment">bool ON_Intersect(</span></div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160;<span class="comment"> const ON_Line&amp; lineA, </span></div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160;<span class="comment"> const ON_Line&amp; lineB, </span></div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160;<span class="comment"> double* a,</span></div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160;<span class="comment"> double* b</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"> */</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;<span class="comment">/* 15 Sept 2016 - Already in opennurbs_math.h</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">ON_DECL</span></div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160;<span class="comment">bool ON_Intersect( // Returns false unless intersection is a single point</span></div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160;<span class="comment"> // If returned parameter is &lt; 0 or &gt; 1, then the line</span></div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160;<span class="comment"> // segment between line.m_point[0] and line.m_point[1]</span></div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160;<span class="comment"> // does not intersect the plane</span></div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>&#160;<span class="comment"> const ON_Line&amp;, </span></div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160;<span class="comment"> const ON_Plane&amp;, </span></div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160;<span class="comment"> double* // parameter on line</span></div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160;<span class="comment"> );</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;</div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160;<span class="comment">Parameters:</span></div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160;<span class="comment"> line - [in]</span></div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160;<span class="comment"> plane_equation - [in]</span></div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160;<span class="comment"> line_parameter - [out]</span></div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160;<span class="comment"> If the returned parameter is &lt; 0 or &gt; 1, then the</span></div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span>&#160;<span class="comment"> line segment between line.from and line.to</span></div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160;<span class="comment"> does not intersect the plane.</span></div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160;<span class="comment"> true if the interesection is a singe point.</span></div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160;<span class="comment"> and false otherwise.</span></div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span>&#160;<span class="comment"> If returned parameter is &lt; 0 or &gt; 1, then the line</span></div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span>&#160;<span class="comment"> segment between line.m_point[0] and line.m_point[1]</span></div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span>&#160;<span class="comment"> does not intersect the plane</span></div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span>&#160;<span class="comment">*/</span></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_Intersect(</div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d4/d6f/class_o_n___line.html">ON_Line</a>&amp; line, </div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span>&#160; <span class="keyword">const</span> <a class="code" href="../../dd/d89/class_o_n___plane_equation.html">ON_PlaneEquation</a>&amp; plane_equation, </div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span>&#160; <span class="keywordtype">double</span>* line_parameter</div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span>&#160; );</div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span>&#160;<span class="comment">/* 15 Sept 2016 - Already in opennurbs_math.h</span></div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>&#160;<span class="comment">ON_DECL</span></div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>&#160;<span class="comment">bool ON_Intersect( const ON_Plane&amp;, </span></div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>&#160;<span class="comment"> const ON_Plane&amp;, </span></div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span>&#160;<span class="comment"> ON_Line&amp; // intersection line is returned here</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;<span class="comment">*/</span></div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span>&#160;</div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span>&#160;<span class="comment">/* 15 Sept 2016 - Already in opennurbs_math.h</span></div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span>&#160;<span class="comment">ON_DECL</span></div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span>&#160;<span class="comment">bool ON_Intersect( const ON_Plane&amp;, </span></div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span>&#160;<span class="comment"> const ON_Plane&amp;, </span></div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span>&#160;<span class="comment"> const ON_Plane&amp;,</span></div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span>&#160;<span class="comment"> ON_3dPoint&amp; // intersection point is returned here</span></div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span>&#160;<span class="comment"> );</span></div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span>&#160;<span class="comment"> */</span></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;<span class="comment">/*</span></div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span>&#160;<span class="comment">Description:</span></div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span>&#160;<span class="comment"> Intersect a plane and a sphere.</span></div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span>&#160;<span class="comment">Parameters:</span></div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span>&#160;<span class="comment"> plane - [in]</span></div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span>&#160;<span class="comment"> sphere - [in]</span></div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span>&#160;<span class="comment"> circle - [out]</span></div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span>&#160;<span class="comment"> 0: no intersection</span></div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span>&#160;<span class="comment"> circle radius = 0 and circle origin = point on the plane</span></div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span>&#160;<span class="comment"> closest to the sphere.</span></div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span>&#160;<span class="comment"> 1: intersection is a single point</span></div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span>&#160;<span class="comment"> circle radius = 0;</span></div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span>&#160;<span class="comment"> 2: intersection is a circle</span></div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span>&#160;<span class="comment"> circle radius &gt; 0.</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">/* 15 Sept 2016 - Already in opennurbs_math.h</span></div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span>&#160;<span class="comment">ON_DECL</span></div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span>&#160;<span class="comment">int ON_Intersect(</span></div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span>&#160;<span class="comment"> const ON_Plane&amp; plane, </span></div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span>&#160;<span class="comment"> const ON_Sphere&amp; sphere,</span></div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>&#160;<span class="comment"> ON_Circle&amp; circle</span></div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>&#160;<span class="comment"> );</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;</div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span>&#160;<span class="comment">/* 15 Sept 2016 - Already in opennurbs_math.h</span></div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span>&#160;<span class="comment">ON_DECL</span></div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span>&#160;<span class="comment">int ON_Intersect( // returns 0 = no intersections, </span></div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span>&#160;<span class="comment"> // 1 = one intersection, </span></div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span>&#160;<span class="comment"> // 2 = 2 intersections</span></div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span>&#160;<span class="comment"> // If 0 is returned, first point is point </span></div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>&#160;<span class="comment"> // on line closest to sphere and 2nd point is the point</span></div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>&#160;<span class="comment"> // on the sphere closest to the line.</span></div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span>&#160;<span class="comment"> // If 1 is returned, first point is obtained by evaluating</span></div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span>&#160;<span class="comment"> // the line and the second point is obtained by evaluating</span></div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span>&#160;<span class="comment"> // the sphere.</span></div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span>&#160;<span class="comment"> const ON_Line&amp;, const ON_Sphere&amp;,</span></div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span>&#160;<span class="comment"> ON_3dPoint&amp;, ON_3dPoint&amp; // intersection point(s) returned here</span></div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span>&#160;<span class="comment"> );</span></div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span>&#160;</div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span>&#160;<span class="comment">/* 15 Sept 2016 - Already in opennurbs_math.h</span></div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>&#160;<span class="comment">ON_DECL</span></div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span>&#160;<span class="comment">int ON_Intersect( // returns 0 = no intersections, </span></div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span>&#160;<span class="comment"> // 1 = one intersection, </span></div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span>&#160;<span class="comment"> // 2 = 2 intersections</span></div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span>&#160;<span class="comment"> // 3 = line lies on cylinder</span></div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span>&#160;<span class="comment"> // If 0 is returned, first point is point </span></div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span>&#160;<span class="comment"> // on line closest to cylinder and 2nd point is the point</span></div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span>&#160;<span class="comment"> // on the sphere closest to the line.</span></div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span>&#160;<span class="comment"> // If 1 is returned, first point is obtained by evaluating</span></div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span>&#160;<span class="comment"> // the line and the second point is obtained by evaluating</span></div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span>&#160;<span class="comment"> // the sphere.</span></div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>&#160;<span class="comment"> const ON_Line&amp;, const ON_Cylinder&amp;,</span></div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span>&#160;<span class="comment"> ON_3dPoint&amp;, ON_3dPoint&amp; // intersection point(s) returned here</span></div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span>&#160;<span class="comment"> );</span></div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span>&#160;<span class="comment">Description:</span></div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span>&#160;<span class="comment"> Intersect an infinite line and an axis aligned bounding box.</span></div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span>&#160;<span class="comment">Parameters:</span></div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span>&#160;<span class="comment"> bbox - [in]</span></div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span>&#160;<span class="comment"> line - [in]</span></div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span>&#160;<span class="comment"> tolerance - [in] If tolerance &gt; 0.0, then the intersection is</span></div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span>&#160;<span class="comment"> performed against a box that has each side</span></div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span>&#160;<span class="comment"> moved out by tolerance.</span></div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span>&#160;<span class="comment"> line_parameters - [out] </span></div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span>&#160;<span class="comment"> Pass null if you do not need the parameters.</span></div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span>&#160;<span class="comment"> If true is returned and line.from != line.to,</span></div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span>&#160;<span class="comment"> then the chord from line.PointAt(line_parameters[0])</span></div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span>&#160;<span class="comment"> to line.PointAt(line_parameters[1]) is the intersection.</span></div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span>&#160;<span class="comment"> If true is returned and line.from = line.to, then line.from</span></div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span>&#160;<span class="comment"> is in the box and the interval (0.0,0.0) is returned.</span></div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span>&#160;<span class="comment"> If false is returned, the input value of line_parameters</span></div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span>&#160;<span class="comment"> is not changed.</span></div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span>&#160;<span class="comment"> True if the line intersects the box and false otherwise.</span></div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span>&#160;ON_DECL</div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span>&#160;<span class="keywordtype">bool</span> ON_Intersect( <span class="keyword">const</span> <a class="code" href="../../d1/d17/class_o_n___bounding_box.html">ON_BoundingBox</a>&amp; bbox, </div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d4/d6f/class_o_n___line.html">ON_Line</a>&amp; line, </div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span>&#160; <span class="keywordtype">double</span> tolerance,</div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span>&#160; <a class="code" href="../../dc/dc7/class_o_n___interval.html">ON_Interval</a>* line_parameters</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"> Intersect two spheres using exact calculations.</span></div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span>&#160;<span class="comment">Parameters:</span></div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span>&#160;<span class="comment"> sphere0 - [in]</span></div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span>&#160;<span class="comment"> sphere1 - [in]</span></div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span>&#160;<span class="comment"> circle - [out] If intersection is a point, then that point will be the center, radius 0.</span></div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span>&#160;<span class="comment"> 0 if no intersection,</span></div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span>&#160;<span class="comment"> 1 if a single point,</span></div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span>&#160;<span class="comment"> 2 if a circle,</span></div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span>&#160;<span class="comment"> 3 if the spheres are the same.</span></div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span>&#160;ON_DECL</div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span>&#160;<span class="keywordtype">int</span> ON_Intersect( <span class="keyword">const</span> <a class="code" href="../../d7/dd8/class_o_n___sphere.html">ON_Sphere</a>&amp; sphere0, </div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d7/dd8/class_o_n___sphere.html">ON_Sphere</a>&amp; sphere1, </div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span>&#160; <a class="code" href="../../d1/d1b/class_o_n___circle.html">ON_Circle</a>&amp; circle</div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span>&#160; );</div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span>&#160;<span class="preprocessor">#endif</span></div><div class="ttc" id="class_o_n___circle_html"><div class="ttname"><a href="../../d1/d1b/class_o_n___circle.html">ON_Circle</a></div><div class="ttdef"><b>Definition:</b> opennurbs_circle.h:33</div></div>
<div class="ttc" id="class_o_n___bounding_box_html"><div class="ttname"><a href="../../d1/d17/class_o_n___bounding_box.html">ON_BoundingBox</a></div><div class="ttdef"><b>Definition:</b> opennurbs_bounding_box.h:25</div></div>
<div class="ttc" id="class_o_n___line_html"><div class="ttname"><a href="../../d4/d6f/class_o_n___line.html">ON_Line</a></div><div class="ttdef"><b>Definition:</b> opennurbs_line.h:20</div></div>
<div class="ttc" id="class_o_n___plane_equation_html"><div class="ttname"><a href="../../dd/d89/class_o_n___plane_equation.html">ON_PlaneEquation</a></div><div class="ttdef"><b>Definition:</b> opennurbs_point.h:1465</div></div>
<div class="ttc" id="class_o_n___interval_html"><div class="ttname"><a href="../../dc/dc7/class_o_n___interval.html">ON_Interval</a></div><div class="ttdef"><b>Definition:</b> opennurbs_point.h:46</div></div>
<div class="ttc" id="class_o_n___sphere_html"><div class="ttname"><a href="../../d7/dd8/class_o_n___sphere.html">ON_Sphere</a></div><div class="ttdef"><b>Definition:</b> opennurbs_sphere.h:22</div></div>
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