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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_QUATERNION_INC_)</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span>&#160;<span class="preprocessor">#define ON_QUATERNION_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"><a class="line" href="../../d9/d33/class_o_n___quaternion.html"> 20</a></span>&#160;<span class="keyword">class </span>ON_CLASS <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a></div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160;{</div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160;<span class="keyword">public</span>:</div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160; <span class="comment">// quaternion = a + bi + cj + dk</span></div><div class="line"><a name="l00024"></a><span class="lineno"><a class="line" href="../../d9/d33/class_o_n___quaternion.html#a9d929b768ea432cb9e2f4d2c45431c05"> 24</a></span>&#160; <span class="keywordtype">double</span> a,b,c,<a class="code" href="../../d9/d33/class_o_n___quaternion.html#a9d929b768ea432cb9e2f4d2c45431c05">d</a>;</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"><a class="line" href="../../d9/d33/class_o_n___quaternion.html#ac5b5284547fce4d835db622a13952c93"> 26</a></span>&#160; <span class="keyword">static</span> <span class="keyword">const</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> <a class="code" href="../../d9/d33/class_o_n___quaternion.html#ac5b5284547fce4d835db622a13952c93">Zero</a>; <span class="comment">// 0 = (0,0,0,0</span></div><div class="line"><a name="l00027"></a><span class="lineno"><a class="line" href="../../d9/d33/class_o_n___quaternion.html#a70fe3af1b1d8598e85e2649029d3f554"> 27</a></span>&#160; <span class="keyword">static</span> <span class="keyword">const</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> <a class="code" href="../../d9/d33/class_o_n___quaternion.html#a70fe3af1b1d8598e85e2649029d3f554">Identity</a>; <span class="comment">// 1 = (1,0,0,0)</span></div><div class="line"><a name="l00028"></a><span class="lineno"><a class="line" href="../../d9/d33/class_o_n___quaternion.html#a0d34db53e780c5081c90180ba59ebd92"> 28</a></span>&#160; <span class="keyword">static</span> <span class="keyword">const</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> <a class="code" href="../../d9/d33/class_o_n___quaternion.html#a0d34db53e780c5081c90180ba59ebd92">I</a>; <span class="comment">// &quot;i&quot; = (0,1,0,0)</span></div><div class="line"><a name="l00029"></a><span class="lineno"><a class="line" href="../../d9/d33/class_o_n___quaternion.html#a68ec3851e8d2ee8774e541eea06a69cb"> 29</a></span>&#160; <span class="keyword">static</span> <span class="keyword">const</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> <a class="code" href="../../d9/d33/class_o_n___quaternion.html#a68ec3851e8d2ee8774e541eea06a69cb">J</a>; <span class="comment">// &quot;j&quot; = (0,0,1,0)</span></div><div class="line"><a name="l00030"></a><span class="lineno"><a class="line" href="../../d9/d33/class_o_n___quaternion.html#a9dc264f67e8bdb22726d79d078d3dc7f"> 30</a></span>&#160; <span class="keyword">static</span> <span class="keyword">const</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> <a class="code" href="../../d9/d33/class_o_n___quaternion.html#a9dc264f67e8bdb22726d79d078d3dc7f">K</a>; <span class="comment">// &quot;k&quot; = (0,0,0,1)</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"><a class="line" href="../../d9/d33/class_o_n___quaternion.html#a6049aaea1fef16350e0a4bb31a594e17"> 32</a></span>&#160; <a class="code" href="../../d9/d33/class_o_n___quaternion.html#a6049aaea1fef16350e0a4bb31a594e17">ON_Quaternion</a>() {}</div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160;</div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a>(<span class="keywordtype">double</span> qa, <span class="keywordtype">double</span> qb, <span class="keywordtype">double</span> qc, <span class="keywordtype">double</span> qd);</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; <span class="comment">// (a,b,c,d) = (0,v.x,v.y,v.z)</span></div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a>(<span class="keyword">const</span> <a class="code" href="../../d5/dae/class_o_n__3d_vector.html">ON_3dVector</a>&amp; v);</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; <span class="comment">// (a,b,c,d) = (0,v.x,v.y,v.z)</span></div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a>&amp; operator=(<span class="keyword">const</span> <a class="code" href="../../d5/dae/class_o_n__3d_vector.html">ON_3dVector</a>&amp; v);</div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160;</div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <span class="keywordtype">void</span> Set(<span class="keywordtype">double</span> qa, <span class="keywordtype">double</span> qb, <span class="keywordtype">double</span> qc, <span class="keywordtype">double</span> qd);</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; <span class="comment">// arithmetic operators</span></div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> operator*(<span class="keywordtype">int</span>) <span class="keyword">const</span>;</div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> operator/(<span class="keywordtype">int</span>) <span class="keyword">const</span>;</div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> operator*(<span class="keywordtype">float</span>) <span class="keyword">const</span>;</div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> operator/(<span class="keywordtype">float</span>) <span class="keyword">const</span>;</div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> operator*(<span class="keywordtype">double</span>) <span class="keyword">const</span>;</div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> operator/(<span class="keywordtype">double</span>) <span class="keyword">const</span>;</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; <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> operator+(<span class="keyword">const</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a>&amp;) <span class="keyword">const</span>;</div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> operator-(<span class="keyword">const</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a>&amp;) <span class="keyword">const</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="comment">// quaternion multiplication is not commutative</span></div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> operator*(<span class="keyword">const</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a>&amp;) <span class="keyword">const</span>;</div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160;</div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160;<span class="comment"> True if a, b, c, and d are valid finite IEEE doubles.</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="keywordtype">bool</span> IsValid() <span class="keyword">const</span>;</div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160;</div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160;<span class="comment"> Description:</span></div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160;<span class="comment"> Returns the conjugate of the quaternion = (a,-b,-c,-d).</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; <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> Conjugate() <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">/*</span></div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160;<span class="comment"> Description:</span></div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160;<span class="comment"> Sets the quaternion to a/L2, -b/L2, -c/L2, -d/L2,</span></div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160;<span class="comment"> where L2 = length squared = (a*a + b*b + c*c + d*d).</span></div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160;<span class="comment"> This is the multiplicative inverse, i.e.,</span></div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160;<span class="comment"> (a,b,c,d)*(a/L2, -b/L2, -c/L2, -d/L2) = (1,0,0,0).</span></div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160;<span class="comment"> True if successful. False if the quaternion is zero</span></div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160;<span class="comment"> and cannot be inverted.</span></div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="keywordtype">bool</span> Invert();</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">/*</span></div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160;<span class="comment"> Sets the quaternion to a/L2, -b/L2, -c/L2, -d/L2,</span></div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160;<span class="comment"> where L2 = length squared = (a*a + b*b + c*c + d*d).</span></div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160;<span class="comment"> This is the multiplicative inverse, i.e.,</span></div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160;<span class="comment"> (a,b,c,d)*(a/L2, -b/L2, -c/L2, -d/L2) = (1,0,0,0).</span></div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160;<span class="comment"> If &quot;this&quot; is the zero quaternion, then the zero quaternion</span></div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160;<span class="comment"> is returned.</span></div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> Inverse() <span class="keyword">const</span>;</div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160;</div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160;<span class="comment"> Returns the length or norm of the quaternion</span></div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160;<span class="comment"> sqrt(a*a + b*b + c*c + d*d).</span></div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; <span class="keywordtype">double</span> Length() <span class="keyword">const</span>;</div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160;</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160;<span class="comment"> Returns a*a + b*b + c*c + d*d.</span></div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; <span class="keywordtype">double</span> LengthSquared() <span class="keyword">const</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; <span class="comment">/*</span></div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160;<span class="comment"> The distance or norm of the difference between the two quaternions.</span></div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160;<span class="comment"> = (&quot;this&quot; - q).Length().</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; <span class="keywordtype">double</span> DistanceTo(<span class="keyword">const</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a>&amp; q) <span class="keyword">const</span>;</div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160;</div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160;<span class="comment"> The distance or norm of the difference between the two quaternions.</span></div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160;<span class="comment"> = (p - q).Length().</span></div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160; <span class="keyword">static</span> <span class="keywordtype">double</span> Distance(<span class="keyword">const</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a>&amp; p, <span class="keyword">const</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a>&amp; q);</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="comment">/*</span></div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160;<span class="comment"> 4x4 real valued matrix form of the quaternion</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"> a b c d</span></div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160;<span class="comment"> -b a -d c</span></div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160;<span class="comment"> -c d a -b</span></div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160;<span class="comment"> -d -c b a</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"> which has the same arithmetic properties in as the</span></div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160;<span class="comment"> quaternion. </span></div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span>&#160;<span class="comment"> Remarks:</span></div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160;<span class="comment"> Do not confuse this with the rotation defined</span></div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160;<span class="comment"> by the quaternion. This function will only be interesting</span></div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160;<span class="comment"> to math nerds and is not useful in rendering or animation</span></div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160;<span class="comment"> applications.</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; <a class="code" href="../../d3/d13/class_o_n___xform.html">ON_Xform</a> MatrixForm() <span class="keyword">const</span>;</div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span>&#160;</div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>&#160;<span class="comment"> Description:</span></div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span>&#160;<span class="comment"> Scales the quaternion&#39;s coordinates so that</span></div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span>&#160;<span class="comment"> a*a + b*b + c*c + d*d = 1.</span></div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span>&#160;<span class="comment"> True if successful. False if the quaternion is zero</span></div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span>&#160;<span class="comment"> and cannot be unitized.</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="keywordtype">bool</span> Unitize();</div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>&#160;</div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>&#160;<span class="comment"> Description:</span></div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span>&#160;<span class="comment"> Sets the quaternion to </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"> cos(angle/2), sin(angle/2)*x, sin(angle/2)*y, sin(angle/2)*z</span></div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span>&#160;<span class="comment"> where (x,y,z) is the unit vector parallel to axis. This is</span></div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span>&#160;<span class="comment"> the unit quaternion that represents the rotation of angle</span></div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span>&#160;<span class="comment"> about axis.</span></div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span>&#160;<span class="comment"> Parameters:</span></div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span>&#160;<span class="comment"> angle - [in] in radians</span></div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span>&#160;<span class="comment"> axis - [in] axis of rotation</span></div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span>&#160;<span class="comment"> Returns:</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="keywordtype">void</span> SetRotation(<span class="keywordtype">double</span> angle, <span class="keyword">const</span> <a class="code" href="../../d5/dae/class_o_n__3d_vector.html">ON_3dVector</a>&amp; axis);</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"> Parameters:</span></div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span>&#160;<span class="comment"> angle - [in] in radians</span></div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span>&#160;<span class="comment"> axis - [in] axis of rotation</span></div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span>&#160;<span class="comment"> The unit quaternion </span></div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span>&#160;<span class="comment"> cos(angle/2), sin(angle/2)*x, sin(angle/2)*y, sin(angle/2)*z</span></div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span>&#160;<span class="comment"> where (x,y,z) is the unit vector parallel to axis. This is the</span></div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span>&#160;<span class="comment"> unit quaternion that represents the rotation of angle about axis.</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="keyword">static</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> Rotation(<span class="keywordtype">double</span> angle, <span class="keyword">const</span> <a class="code" href="../../d5/dae/class_o_n__3d_vector.html">ON_3dVector</a>&amp; axis);</div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span>&#160;</div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span>&#160;<span class="comment"> Descriptin:</span></div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span>&#160;<span class="comment"> Sets the quaternion to the unit quaternion which rotates</span></div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160;<span class="comment"> plane0.xaxis to plane1.xaxis,</span></div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span>&#160;<span class="comment"> plane0.yaxis to plane1.yaxis, and </span></div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span>&#160;<span class="comment"> plane0.zaxis to plane1.zaxis.</span></div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span>&#160;<span class="comment"> Parameters:</span></div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span>&#160;<span class="comment"> plane0 - [in]</span></div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>&#160;<span class="comment"> plane1 - [in]</span></div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>&#160;<span class="comment"> Remarks:</span></div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span>&#160;<span class="comment"> The plane origins are ignored.</span></div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span>&#160; <span class="keywordtype">void</span> SetRotation(<span class="keyword">const</span> <a class="code" href="../../d4/d48/class_o_n___plane.html">ON_Plane</a>&amp; plane0, <span class="keyword">const</span> <a class="code" href="../../d4/d48/class_o_n___plane.html">ON_Plane</a>&amp; plane1);</div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span>&#160;</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;<span class="comment"> Parameters:</span></div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span>&#160;<span class="comment"> plane0 - [in]</span></div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span>&#160;<span class="comment"> plane1 - [in]</span></div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>&#160;<span class="comment"> The unit quaternion that represents the the rotation that maps</span></div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>&#160;<span class="comment"> plane0.xaxis to plane1.xaxis,</span></div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span>&#160;<span class="comment"> plane0.yaxis to plane1.yaxis, and </span></div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span>&#160;<span class="comment"> plane0.zaxis to plane1.zaxis.</span></div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span>&#160;<span class="comment"> Remarks:</span></div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span>&#160;<span class="comment"> The plane origins are ignored.</span></div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span>&#160; <span class="keyword">static</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> Rotation(<span class="keyword">const</span> <a class="code" href="../../d4/d48/class_o_n___plane.html">ON_Plane</a>&amp; plane0, <span class="keyword">const</span> <a class="code" href="../../d4/d48/class_o_n___plane.html">ON_Plane</a>&amp; plane1);</div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span>&#160;</div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span>&#160;<span class="comment"> Parameters:</span></div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span>&#160;<span class="comment"> angle - [out]</span></div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>&#160;<span class="comment"> in radians</span></div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span>&#160;<span class="comment"> axis - [out]</span></div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span>&#160;<span class="comment"> unit axis of rotation of 0 if (b,c,d) is the zero vector.</span></div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span>&#160;<span class="comment"> The rotation defined by the quaternion.</span></div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span>&#160;<span class="comment"> Remarks:</span></div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span>&#160;<span class="comment"> If the quaternion is not unitized, the rotation of its</span></div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span>&#160;<span class="comment"> unitized form is returned.</span></div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span>&#160; <span class="keywordtype">bool</span> GetRotation(<span class="keywordtype">double</span>&amp; angle, <a class="code" href="../../d5/dae/class_o_n__3d_vector.html">ON_3dVector</a>&amp; axis) <span class="keyword">const</span>;</div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span>&#160;</div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span>&#160;<span class="comment"> Description:</span></div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span>&#160;<span class="comment"> The transformation returned by this function has the property</span></div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span>&#160;<span class="comment"> that xform*V = q.Rotate(V).</span></div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span>&#160;<span class="comment"> Parameters:</span></div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span>&#160;<span class="comment"> xform - [out]</span></div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span>&#160;<span class="comment"> A transformation matrix that performs the rotation defined </span></div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span>&#160;<span class="comment"> by the quaternion.</span></div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span>&#160;<span class="comment"> Remarks:</span></div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span>&#160;<span class="comment"> If the quaternion is not unitized, the rotation of its</span></div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span>&#160;<span class="comment"> unitized form is returned. Do not confuse the result of this</span></div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span>&#160;<span class="comment"> function the matrix returned by ON_Quaternion::MatrixForm().</span></div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span>&#160;<span class="comment"> The transformation returned by this function has the property</span></div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span>&#160;<span class="comment"> that xform*V = q.Rotate(V).</span></div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span>&#160; <span class="keywordtype">bool</span> GetRotation(<a class="code" href="../../d3/d13/class_o_n___xform.html">ON_Xform</a>&amp; xform) <span class="keyword">const</span>;</div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span>&#160;</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"> Parameters:</span></div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span>&#160;<span class="comment"> plane - [out]</span></div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>&#160;<span class="comment"> The frame created by applying the quaternion&#39;s rotation</span></div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span>&#160;<span class="comment"> to the canonical world frame (1,0,0),(0,1,0),(0,0,1).</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; <span class="keywordtype">bool</span> GetRotation(<a class="code" href="../../d4/d48/class_o_n___plane.html">ON_Plane</a>&amp; plane) <span class="keyword">const</span>;</div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span>&#160;</div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span>&#160;<span class="comment"> Description</span></div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span>&#160;<span class="comment"> Rotate a 3d vector. This operation is also called</span></div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span>&#160;<span class="comment"> conjugation, because the result is the same as</span></div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span>&#160;<span class="comment"> </span></div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span>&#160;<span class="comment"> (q.Conjugate()*(0,x,y,x)*q/q.LengthSquared()).Vector()</span></div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span>&#160;<span class="comment"> Parameters:</span></div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span>&#160;<span class="comment"> v - [in]</span></div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span>&#160;<span class="comment"> R*v, where R is the rotation defined by the unit quaternion.</span></div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span>&#160;<span class="comment"> This is mathematically the same as the values</span></div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span>&#160;<span class="comment"> (Inverse(q)*(0,x,y,z)*q).Vector()</span></div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span>&#160;<span class="comment"> and</span></div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span>&#160;<span class="comment"> (q.Conjugate()*(0,x,y,x)*q/q.LengthSquared()).Vector()</span></div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span>&#160;<span class="comment"> Remarks:</span></div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span>&#160;<span class="comment"> If you need to rotate more than a dozen or so vectors, it will</span></div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span>&#160;<span class="comment"> be more efficient to call GetRotation(ON_Xform&amp; xform)</span></div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span>&#160;<span class="comment"> and multiply the vectors by xform.</span></div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span>&#160; <a class="code" href="../../d5/dae/class_o_n__3d_vector.html">ON_3dVector</a> Rotate(<a class="code" href="../../d5/dae/class_o_n__3d_vector.html">ON_3dVector</a> v) <span class="keyword">const</span>;</div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span>&#160;</div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span>&#160;<span class="comment"> The &quot;vector&quot; or &quot;imaginary&quot; part of the quaternion = (b,c,d)</span></div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00274"></a><span class="lineno"> 274</span>&#160; <a class="code" href="../../d5/dae/class_o_n__3d_vector.html">ON_3dVector</a> Vector() <span class="keyword">const</span>;</div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span>&#160;</div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span>&#160;<span class="comment"> The &quot;real&quot; or &quot;scalar&quot; part of the quaternion = a.</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="keywordtype">double</span> Scalar() <span class="keyword">const</span>;</div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span>&#160;</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"> Returns:</span></div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span>&#160;<span class="comment"> True if a, b, c, and d are all zero.</span></div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span>&#160; <span class="keywordtype">bool</span> IsZero() <span class="keyword">const</span>;</div><div class="line"><a name="l00287"></a><span class="lineno"> 287</span>&#160;</div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span>&#160;<span class="comment"> True if a, b, c, and d are all valid, finite and at least one is non-zero.</span></div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span>&#160; <span class="keywordtype">bool</span> IsNotZero() <span class="keyword">const</span>;</div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span>&#160;</div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span>&#160;<span class="comment"> True if b, c, and d are all zero.</span></div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span>&#160; <span class="keywordtype">bool</span> IsScalar() <span class="keyword">const</span>;</div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span>&#160;</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 a = 0 and at least one of b, c, or d is not zero.</span></div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span>&#160; <span class="keywordtype">bool</span> IsVector() <span class="keyword">const</span>; </div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span>&#160;</div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span>&#160;</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;<span class="comment"> Returns:</span></div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span>&#160;<span class="comment"> exp(q) = e^a*( cos(|V|) + V/|V|*sin(|V|) ), where V = b*i + c*j + d*k.</span></div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span>&#160; <span class="keyword">static</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> Exp(<a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> q);</div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span>&#160;</div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00314"></a><span class="lineno"> 314</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span>&#160;<span class="comment"> log(q) = log(|q|) + V/|V|*acos(a/|q|), where V = b*i + c*j + d*k.</span></div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span>&#160; <span class="keyword">static</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> Log(<a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> q);</div><div class="line"><a name="l00318"></a><span class="lineno"> 318</span>&#160;</div><div class="line"><a name="l00319"></a><span class="lineno"> 319</span>&#160; <span class="comment">/*</span></div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span>&#160;<span class="comment"> Returns:</span></div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span>&#160;<span class="comment"> q^t = Exp(t*Log(q))</span></div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span>&#160; <span class="keyword">static</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> Pow(<a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> q, <span class="keywordtype">double</span> t);</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; <span class="keyword">static</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> Slerp(<a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> q0, <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> q1, <span class="keywordtype">double</span> t);</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;};</div><div class="line"><a name="l00329"></a><span class="lineno"> 329</span>&#160;</div><div class="line"><a name="l00330"></a><span class="lineno"> 330</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00331"></a><span class="lineno"> 331</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00332"></a><span class="lineno"> 332</span>&#160;<span class="comment"> The quaternion product of p and q. This is the same value as p*q.</span></div><div class="line"><a name="l00333"></a><span class="lineno"> 333</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00334"></a><span class="lineno"> 334</span>&#160;ON_DECL</div><div class="line"><a name="l00335"></a><span class="lineno"> 335</span>&#160;<a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> ON_QuaternionProduct( <span class="keyword">const</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a>&amp; p, <span class="keyword">const</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a>&amp; q);</div><div class="line"><a name="l00336"></a><span class="lineno"> 336</span>&#160;</div><div class="line"><a name="l00337"></a><span class="lineno"> 337</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00338"></a><span class="lineno"> 338</span>&#160;<span class="comment">Returns:</span></div><div class="line"><a name="l00339"></a><span class="lineno"> 339</span>&#160;<span class="comment"> The vector cross product of p and q = (0,x,y,z) where</span></div><div class="line"><a name="l00340"></a><span class="lineno"> 340</span>&#160;<span class="comment"> (x,y,z) = ON_CrossProduct(p.Vector(),q.Vector())</span></div><div class="line"><a name="l00341"></a><span class="lineno"> 341</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00342"></a><span class="lineno"> 342</span>&#160;<span class="comment"> This is NOT the same as the quaternion product p*q.</span></div><div class="line"><a name="l00343"></a><span class="lineno"> 343</span>&#160;<span class="comment">*/</span></div><div class="line"><a name="l00344"></a><span class="lineno"> 344</span>&#160;ON_DECL</div><div class="line"><a name="l00345"></a><span class="lineno"> 345</span>&#160;<a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> ON_CrossProduct( <span class="keyword">const</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a>&amp; p, <span class="keyword">const</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a>&amp; q);</div><div class="line"><a name="l00346"></a><span class="lineno"> 346</span>&#160;</div><div class="line"><a name="l00347"></a><span class="lineno"> 347</span>&#160;ON_DECL</div><div class="line"><a name="l00348"></a><span class="lineno"> 348</span>&#160;<a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> operator*(<span class="keywordtype">int</span>, <span class="keyword">const</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a>&amp;);</div><div class="line"><a name="l00349"></a><span class="lineno"> 349</span>&#160;</div><div class="line"><a name="l00350"></a><span class="lineno"> 350</span>&#160;ON_DECL</div><div class="line"><a name="l00351"></a><span class="lineno"> 351</span>&#160;<a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> operator*(<span class="keywordtype">float</span>, <span class="keyword">const</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a>&amp;);</div><div class="line"><a name="l00352"></a><span class="lineno"> 352</span>&#160;</div><div class="line"><a name="l00353"></a><span class="lineno"> 353</span>&#160;ON_DECL</div><div class="line"><a name="l00354"></a><span class="lineno"> 354</span>&#160;<a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a> operator*(<span class="keywordtype">double</span>, <span class="keyword">const</span> <a class="code" href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a>&amp;);</div><div class="line"><a name="l00355"></a><span class="lineno"> 355</span>&#160;</div><div class="line"><a name="l00356"></a><span class="lineno"> 356</span>&#160;<span class="preprocessor">#endif</span></div><div class="ttc" id="class_o_n___quaternion_html_a6049aaea1fef16350e0a4bb31a594e17"><div class="ttname"><a href="../../d9/d33/class_o_n___quaternion.html#a6049aaea1fef16350e0a4bb31a594e17">ON_Quaternion::ON_Quaternion</a></div><div class="ttdeci">ON_Quaternion()</div><div class="ttdef"><b>Definition:</b> opennurbs_quaternion.h:32</div></div>
<div class="ttc" id="class_o_n___quaternion_html_a68ec3851e8d2ee8774e541eea06a69cb"><div class="ttname"><a href="../../d9/d33/class_o_n___quaternion.html#a68ec3851e8d2ee8774e541eea06a69cb">ON_Quaternion::J</a></div><div class="ttdeci">static const ON_Quaternion J</div><div class="ttdef"><b>Definition:</b> opennurbs_quaternion.h:29</div></div>
<div class="ttc" id="class_o_n___quaternion_html_a70fe3af1b1d8598e85e2649029d3f554"><div class="ttname"><a href="../../d9/d33/class_o_n___quaternion.html#a70fe3af1b1d8598e85e2649029d3f554">ON_Quaternion::Identity</a></div><div class="ttdeci">static const ON_Quaternion Identity</div><div class="ttdef"><b>Definition:</b> opennurbs_quaternion.h:27</div></div>
<div class="ttc" id="class_o_n___quaternion_html_ac5b5284547fce4d835db622a13952c93"><div class="ttname"><a href="../../d9/d33/class_o_n___quaternion.html#ac5b5284547fce4d835db622a13952c93">ON_Quaternion::Zero</a></div><div class="ttdeci">static const ON_Quaternion Zero</div><div class="ttdef"><b>Definition:</b> opennurbs_quaternion.h:26</div></div>
<div class="ttc" id="class_o_n___quaternion_html"><div class="ttname"><a href="../../d9/d33/class_o_n___quaternion.html">ON_Quaternion</a></div><div class="ttdef"><b>Definition:</b> opennurbs_quaternion.h:20</div></div>
<div class="ttc" id="class_o_n___quaternion_html_a0d34db53e780c5081c90180ba59ebd92"><div class="ttname"><a href="../../d9/d33/class_o_n___quaternion.html#a0d34db53e780c5081c90180ba59ebd92">ON_Quaternion::I</a></div><div class="ttdeci">static const ON_Quaternion I</div><div class="ttdef"><b>Definition:</b> opennurbs_quaternion.h:28</div></div>
<div class="ttc" id="class_o_n___quaternion_html_a9dc264f67e8bdb22726d79d078d3dc7f"><div class="ttname"><a href="../../d9/d33/class_o_n___quaternion.html#a9dc264f67e8bdb22726d79d078d3dc7f">ON_Quaternion::K</a></div><div class="ttdeci">static const ON_Quaternion K</div><div class="ttdef"><b>Definition:</b> opennurbs_quaternion.h:30</div></div>
<div class="ttc" id="class_o_n___xform_html"><div class="ttname"><a href="../../d3/d13/class_o_n___xform.html">ON_Xform</a></div><div class="ttdef"><b>Definition:</b> opennurbs_xform.h:28</div></div>
<div class="ttc" id="class_o_n___quaternion_html_a9d929b768ea432cb9e2f4d2c45431c05"><div class="ttname"><a href="../../d9/d33/class_o_n___quaternion.html#a9d929b768ea432cb9e2f4d2c45431c05">ON_Quaternion::d</a></div><div class="ttdeci">double d</div><div class="ttdef"><b>Definition:</b> opennurbs_quaternion.h:24</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__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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