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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span>&#160;<span class="comment">/* $NoKeywords: $ */</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span>&#160;<span class="comment">//</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span>&#160;<span class="comment">// Copyright (c) 1993-2012 Robert McNeel &amp; Associates. All rights reserved.</span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span>&#160;<span class="comment">// OpenNURBS, Rhinoceros, and Rhino3D are registered trademarks of Robert</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span>&#160;<span class="comment">// McNeel &amp; Associates.</span></div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span>&#160;<span class="comment">//</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span>&#160;<span class="comment">// THIS SOFTWARE IS PROVIDED &quot;AS IS&quot; WITHOUT EXPRESS OR IMPLIED WARRANTY.</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span>&#160;<span class="comment">// ALL IMPLIED WARRANTIES OF FITNESS FOR ANY PARTICULAR PURPOSE AND OF</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span>&#160;<span class="comment">// MERCHANTABILITY ARE HEREBY DISCLAIMED.</span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span>&#160;<span class="comment">// </span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span>&#160;<span class="comment">// For complete openNURBS copyright information see &lt;http://www.opennurbs.org&gt;.</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span>&#160;<span class="comment">//</span><span class="comment"></span></div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span>&#160;<span class="comment">////////////////////////////////////////////////////////////////</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span>&#160;<span class="comment"></span>*/</div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span>&#160;</div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span>&#160;<span class="preprocessor">#if !defined(OPENNURBS_ELLIPSE_INC_)</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span>&#160;<span class="preprocessor">#define OPENNURBS_ELLIPSE_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="keyword">class </span><a class="code" href="../../d6/dd8/class_o_n___ellipse.html">ON_Ellipse</a>;</div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160;<span class="keyword">class </span><a class="code" href="../../d4/d48/class_o_n___plane.html">ON_Plane</a>;</div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160;</div><div class="line"><a name="l00023"></a><span class="lineno"><a class="line" href="../../d6/dd8/class_o_n___ellipse.html"> 23</a></span>&#160;<span class="keyword">class </span>ON_CLASS <a class="code" href="../../d6/dd8/class_o_n___ellipse.html">ON_Ellipse</a></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;<span class="keyword">public</span>:</div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160; <a class="code" href="../../d6/dd8/class_o_n___ellipse.html">ON_Ellipse</a>(); <span class="comment">// zeros all fields - plane is invalid</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; <a class="code" href="../../d6/dd8/class_o_n___ellipse.html">ON_Ellipse</a>(</div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d4/d48/class_o_n___plane.html">ON_Plane</a>&amp;,</div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; <span class="keywordtype">double</span>, <span class="keywordtype">double</span> <span class="comment">// radii for x and y vectors</span></div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; );</div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160;</div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; <a class="code" href="../../d6/dd8/class_o_n___ellipse.html">ON_Ellipse</a>(</div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d1/d1b/class_o_n___circle.html">ON_Circle</a>&amp;</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; ~<a class="code" href="../../d6/dd8/class_o_n___ellipse.html">ON_Ellipse</a>();</div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160;</div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <a class="code" href="../../d6/dd8/class_o_n___ellipse.html">ON_Ellipse</a>&amp; operator=(<span class="keyword">const</span> <a class="code" href="../../d1/d1b/class_o_n___circle.html">ON_Circle</a>&amp;);</div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160;</div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <span class="keywordtype">bool</span> Create(</div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d4/d48/class_o_n___plane.html">ON_Plane</a>&amp;, <span class="comment">// point on the plane</span></div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <span class="keywordtype">double</span>, <span class="keywordtype">double</span> <span class="comment">// radii for x and y vectors</span></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;</div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="keywordtype">bool</span> Create(</div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d1/d1b/class_o_n___circle.html">ON_Circle</a>&amp;</div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; );</div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160;</div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; <span class="keywordtype">bool</span> IsValid() <span class="keyword">const</span>; <span class="comment">// returns true if all fields contain reasonable</span></div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; <span class="comment">// information and equation jibes with point and Z.</span></div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160;</div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <span class="keywordtype">bool</span> IsCircle() <span class="keyword">const</span>; <span class="comment">// returns true is ellipse is a circle</span></div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160;</div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; <span class="keywordtype">double</span> Radius( </div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="keywordtype">int</span> <span class="comment">// 0 = x axis radius, 1 = y axis radius</span></div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; ) <span class="keyword">const</span>; </div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d2/d35/class_o_n__3d_point.html">ON_3dPoint</a>&amp; Center() <span class="keyword">const</span>;</div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d5/dae/class_o_n__3d_vector.html">ON_3dVector</a>&amp; Normal() <span class="keyword">const</span>;</div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d4/d48/class_o_n___plane.html">ON_Plane</a>&amp; Plane() <span class="keyword">const</span>; <span class="comment">// plane containing ellipse</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; <span class="comment">/*</span></div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160;<span class="comment"> Distance from the center to a focus, commonly called &quot;c&quot;.</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="keywordtype">double</span> FocalDistance() <span class="keyword">const</span>;</div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160;</div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="keywordtype">bool</span> GetFoci( <a class="code" href="../../d2/d35/class_o_n__3d_point.html">ON_3dPoint</a>&amp; F1, <a class="code" href="../../d2/d35/class_o_n__3d_point.html">ON_3dPoint</a>&amp; F2 ) <span class="keyword">const</span>;</div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160;</div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; <span class="comment">// Evaluation uses the trigonometrix parameterization</span></div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <span class="comment">// t -&gt; plane.origin + cos(t)*radius[0]*plane.xaxis + sin(t)*radius[1]*plane.yaxis</span></div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <span class="comment">// evaluate parameters and return point</span></div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <a class="code" href="../../d2/d35/class_o_n__3d_point.html">ON_3dPoint</a> PointAt( <span class="keywordtype">double</span> ) <span class="keyword">const</span>;</div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; <a class="code" href="../../d5/dae/class_o_n__3d_vector.html">ON_3dVector</a> DerivativeAt( </div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <span class="keywordtype">int</span>, <span class="comment">// desired derivative ( &gt;= 0 )</span></div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <span class="keywordtype">double</span> <span class="comment">// parameter</span></div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; ) <span class="keyword">const</span>;</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; <a class="code" href="../../d5/dae/class_o_n__3d_vector.html">ON_3dVector</a> TangentAt( <span class="keywordtype">double</span> ) <span class="keyword">const</span>; <span class="comment">// returns unit tangent</span></div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <a class="code" href="../../d5/dae/class_o_n__3d_vector.html">ON_3dVector</a> CurvatureAt( <span class="keywordtype">double</span> ) <span class="keyword">const</span>; <span class="comment">// returns curvature vector</span></div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160;</div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <span class="comment">// returns parameters of point on ellipse that is closest to given point</span></div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; <span class="keywordtype">bool</span> ClosestPointTo( </div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d2/d35/class_o_n__3d_point.html">ON_3dPoint</a>&amp;, </div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; <span class="keywordtype">double</span>*</div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; ) <span class="keyword">const</span>;</div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; <span class="comment">// returns point on ellipse that is closest to given point</span></div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; <a class="code" href="../../d2/d35/class_o_n__3d_point.html">ON_3dPoint</a> ClosestPointTo( </div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d2/d35/class_o_n__3d_point.html">ON_3dPoint</a>&amp; </div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; ) <span class="keyword">const</span>;</div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160;</div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; <span class="comment">// evaluate ellipse&#39;s implicit equation in plane</span></div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; <span class="keywordtype">double</span> EquationAt( <span class="keyword">const</span> <a class="code" href="../../dd/dd9/class_o_n__2d_point.html">ON_2dPoint</a>&amp; ) <span class="keyword">const</span>;</div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <a class="code" href="../../da/d08/class_o_n__2d_vector.html">ON_2dVector</a> GradientAt( <span class="keyword">const</span> <a class="code" href="../../dd/dd9/class_o_n__2d_point.html">ON_2dPoint</a>&amp; ) <span class="keyword">const</span>;</div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160;</div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; <span class="comment">// rotate ellipse about its center</span></div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; <span class="keywordtype">bool</span> Rotate(</div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; <span class="keywordtype">double</span>, <span class="comment">// sin(angle)</span></div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; <span class="keywordtype">double</span>, <span class="comment">// cos(angle)</span></div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d5/dae/class_o_n__3d_vector.html">ON_3dVector</a>&amp; <span class="comment">// axis of rotation</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="keywordtype">bool</span> Rotate(</div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; <span class="keywordtype">double</span>, <span class="comment">// angle in radians</span></div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d5/dae/class_o_n__3d_vector.html">ON_3dVector</a>&amp; <span class="comment">// axis of rotation</span></div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; );</div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160;</div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; <span class="comment">// rotate ellipse about a point and axis</span></div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; <span class="keywordtype">bool</span> Rotate(</div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; <span class="keywordtype">double</span>, <span class="comment">// sin(angle)</span></div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; <span class="keywordtype">double</span>, <span class="comment">// cos(angle)</span></div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d5/dae/class_o_n__3d_vector.html">ON_3dVector</a>&amp;, <span class="comment">// axis of rotation</span></div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d2/d35/class_o_n__3d_point.html">ON_3dPoint</a>&amp; <span class="comment">// center of rotation</span></div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160; );</div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160; <span class="keywordtype">bool</span> Rotate(</div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160; <span class="keywordtype">double</span>, <span class="comment">// angle in radians</span></div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d5/dae/class_o_n__3d_vector.html">ON_3dVector</a>&amp;, <span class="comment">// axis of rotation</span></div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d2/d35/class_o_n__3d_point.html">ON_3dPoint</a>&amp; <span class="comment">// center of rotation</span></div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160; );</div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>&#160;</div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160; <span class="keywordtype">bool</span> Translate(</div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160; <span class="keyword">const</span> <a class="code" href="../../d5/dae/class_o_n__3d_vector.html">ON_3dVector</a>&amp;</div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160; );</div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160;</div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>&#160; <span class="comment">// parameterization of NURBS curve does not match ellipse&#39;s transcendental paramaterization</span></div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160; <span class="keywordtype">int</span> GetNurbForm( <a class="code" href="../../d3/d6a/class_o_n___nurbs_curve.html">ON_NurbsCurve</a>&amp; ) <span class="keyword">const</span>; <span class="comment">// returns 0=failure, 2=success</span></div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160;</div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160;<span class="keyword">public</span>: <span class="comment">// members left public</span></div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; <span class="comment">// The center of the ellipse is at the plane&#39;s origin. The axes of the</span></div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160; <span class="comment">// ellipse are the plane&#39;s x and y axes. The equation of the ellipse </span></div><div class="line"><a name="l00130"></a><span class="lineno"><a class="line" href="../../d6/dd8/class_o_n___ellipse.html#a9e944840b14eb40d1315d1f9c0ff589c"> 130</a></span>&#160; <span class="comment">// with respect to the plane is (x/m_r[0])^2 + (y/m_r[1])^2 = 1;</span></div><div class="line"><a name="l00131"></a><span class="lineno"><a class="line" href="../../d6/dd8/class_o_n___ellipse.html#a2f4b5c8f7c69ed65602e7f35022989ae"> 131</a></span>&#160; <a class="code" href="../../d4/d48/class_o_n___plane.html">ON_Plane</a> plane;</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160; <span class="keywordtype">double</span> radius[2]; <span class="comment">// radii for x and y axes (both must be &gt; 0)</span></div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160;};</div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160;</div><div class="line"><a name="l00135"></a><span class="lineno"> 135</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="ttdoc">ON_Circle is a circle in 3d. The cirle is represented by a radius and an orthonormal frame of the pla...</div><div class="ttdef"><b>Definition:</b> opennurbs_circle.h:32</div></div>
<div class="ttc" id="class_o_n__2d_point_html"><div class="ttname"><a href="../../dd/dd9/class_o_n__2d_point.html">ON_2dPoint</a></div><div class="ttdef"><b>Definition:</b> opennurbs_point.h:277</div></div>
<div class="ttc" id="class_o_n___ellipse_html"><div class="ttname"><a href="../../d6/dd8/class_o_n___ellipse.html">ON_Ellipse</a></div><div class="ttdef"><b>Definition:</b> opennurbs_ellipse.h:23</div></div>
<div class="ttc" id="class_o_n___nurbs_curve_html"><div class="ttname"><a href="../../d3/d6a/class_o_n___nurbs_curve.html">ON_NurbsCurve</a></div><div class="ttdef"><b>Definition:</b> opennurbs_nurbscurve.h:26</div></div>
<div class="ttc" id="class_o_n__3d_point_html"><div class="ttname"><a href="../../d2/d35/class_o_n__3d_point.html">ON_3dPoint</a></div><div class="ttdef"><b>Definition:</b> opennurbs_point.h:460</div></div>
<div class="ttc" id="class_o_n___plane_html"><div class="ttname"><a href="../../d4/d48/class_o_n___plane.html">ON_Plane</a></div><div class="ttdef"><b>Definition:</b> opennurbs_plane.h:20</div></div>
<div class="ttc" id="class_o_n__2d_vector_html"><div class="ttname"><a href="../../da/d08/class_o_n__2d_vector.html">ON_2dVector</a></div><div class="ttdef"><b>Definition:</b> opennurbs_point.h:839</div></div>
<div class="ttc" id="class_o_n__3d_vector_html"><div class="ttname"><a href="../../d5/dae/class_o_n__3d_vector.html">ON_3dVector</a></div><div class="ttdef"><b>Definition:</b> opennurbs_point.h:1152</div></div>
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