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<div id="projectname">CMU462 Library
 <span id="projectnumber">1.0</span>
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<div id="projectbrief">15-462/15-662: Computer Graphics (Fall 2015)</div>
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<li class="navelem"><a class="el" href="dir_d44c64559bbebec7f509842c48db8b23.html">include</a></li><li class="navelem"><a class="el" href="dir_93cde9e1f49b119e2b24d2ae2dcc682a.html">CMU462</a></li> </ul>
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<div class="title">quaternion.h</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="preprocessor">#ifndef CMU462_QUATERNION_H</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="preprocessor">#define CMU462_QUATERNION_H</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> </div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="preprocessor">#include "CMU462.h"</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="preprocessor">#include "matrix3x3.h"</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="preprocessor">#include "matrix4x4.h"</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> </div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="preprocessor">#include <iosfwd></span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> </div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="keyword">namespace </span><a class="code" href="namespace_c_m_u462.html">CMU462</a> {</div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> </div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="keyword">class </span>Quaternion : <span class="keyword">public</span> Vector4D {</div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> </div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  Quaternion( ) : <a class="code" href="class_c_m_u462_1_1_vector4_d.html#a1e930c168b0e56b6ee1b14937644a318">Vector4D</a>( 0.0, 0.0, 0.0, 1.0 ) { }</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> </div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  Quaternion(<span class="keyword">const</span> Vector3D& v, <span class="keywordtype">double</span> w) : <a class="code" href="class_c_m_u462_1_1_vector4_d.html#a1e930c168b0e56b6ee1b14937644a318">Vector4D</a>(v.x, v.y, v.z, w) { }</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> </div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  Quaternion(<span class="keyword">const</span> Vector4D& v) : <a class="code" href="class_c_m_u462_1_1_vector4_d.html#a1e930c168b0e56b6ee1b14937644a318">Vector4D</a>(v.x, v.y, v.z, v.w) { }</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> </div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  Quaternion(<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y, <span class="keywordtype">double</span> z, <span class="keywordtype">double</span> w) : <a class="code" href="class_c_m_u462_1_1_vector4_d.html#a1e930c168b0e56b6ee1b14937644a318">Vector4D</a>(x, y, z, w) { }</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> </div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keywordtype">void</span> from_axis_angle(<span class="keyword">const</span> Vector3D& axis, <span class="keywordtype">double</span> radians) {</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  radians /= 2;</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keyword">const</span> Vector3D& nAxis = axis.unit();</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keywordtype">double</span> sinTheta = sin(radians);</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  x = sinTheta * nAxis.x;</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  y = sinTheta * nAxis.y;</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  z = sinTheta * nAxis.z;</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  w = cos(radians);</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  this-><a class="code" href="class_c_m_u462_1_1_vector4_d.html#aa473c7f0bc98a04c9894dd4f920b8a56">normalize</a>();</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  }</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> </div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  Vector3D complex()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> Vector3D(x, y, z); }</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="keywordtype">void</span> setComplex(<span class="keyword">const</span> Vector3D& c)</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  {</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  x = c.x;</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  y = c.y;</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  z = c.z;</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  }</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> </div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keywordtype">double</span> real()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> w; }</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keywordtype">void</span> setReal(<span class="keywordtype">double</span> r) { w = r; }</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> </div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  Quaternion conjugate(<span class="keywordtype">void</span>)<span class="keyword"> const</span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keywordflow">return</span> Quaternion(-complex(), real());</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  }</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> </div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  Quaternion inverse(<span class="keywordtype">void</span>)<span class="keyword"> const</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="keywordflow">return</span> conjugate() / <a class="code" href="class_c_m_u462_1_1_vector4_d.html#abec701db9f3125be7c2c7569d9c82e51">norm</a>();</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  }</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> </div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span> </div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  Quaternion product(<span class="keyword">const</span> Quaternion& rhs)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordflow">return</span> Quaternion(y*rhs.z - z*rhs.y + x*rhs.w + w*rhs.x,</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  z*rhs.x - x*rhs.z + y*rhs.w + w*rhs.y,</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  x*rhs.y - y*rhs.x + z*rhs.w + w*rhs.z,</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  w*rhs.w - x*rhs.x - y*rhs.y - z*rhs.z);</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  }</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span> </div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  Quaternion operator*(<span class="keyword">const</span> Quaternion& rhs)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keywordflow">return</span> product(rhs);</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  }</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span> </div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  Matrix4x4 matrix()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span> </div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keywordtype">double</span> m[16] = {</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  w, -z, y, x,</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  z, w, -x, y,</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  -y, x, w, z,</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  -x, -y, -z, w</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  };</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> </div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keywordflow">return</span> Matrix4x4(m);</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  }</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span> </div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  Matrix4x4 rightMatrix()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="keywordtype">double</span> m[16] = {</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  +w, -z, y, -x,</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  +z, w, -x, -y,</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  -y, x, w, -z,</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  +x, y, z, w</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  };</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span> </div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="keywordflow">return</span> Matrix4x4(m);</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  }</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> </div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <a class="code" href="class_c_m_u462_1_1_vector4_d.html#a1e930c168b0e56b6ee1b14937644a318">Vector4D</a> vector()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="class_c_m_u462_1_1_vector4_d.html#a1e930c168b0e56b6ee1b14937644a318">Vector4D</a>(x, y, z, w); }</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span> </div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  Matrix3x3 rotationMatrix()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="keywordtype">double</span> m[9] = {</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  1-2*y*y-2*z*z, 2*x*y - 2*z*w, 2*x*z + 2*y*w,</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  2*x*y + 2*z*w, 1-2*x*x-2*z*z, 2*y*z - 2*x*w,</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  2*x*z - 2*y*w, 2*y*z + 2*x*w, 1-2*x*x-2*y*y</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  };</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span> </div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="keywordflow">return</span> Matrix3x3(m);</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  }</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span> </div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span> </div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  Vector3D scaledAxis(<span class="keywordtype">void</span>)<span class="keyword"> const</span>{</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span> </div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  Quaternion q1 = (Quaternion)<a class="code" href="class_c_m_u462_1_1_vector4_d.html#ae374d31af8bc0300a884f04a62cdb890">unit</a>();</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span> </div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="comment">// Algorithm from http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToAngle/</span></div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span> </div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="keywordtype">double</span> angle = 2 * acos(q1.w);</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span> </div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="comment">// s must be positive, because q1 <= 1, due to normalization.</span></div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="keywordtype">double</span> s = sqrt(1-q1.w*q1.w);</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span> </div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="comment">// Avoid dividing by 0.</span></div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="keywordflow">if</span> (s < 0.001)</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  {</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="comment">// if s close to zero then direction of axis not important</span></div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="comment">// if it is important that axis is normalised then replace with x=1; y=z=0;</span></div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span> </div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <span class="keywordflow">return</span> Vector3D(q1.x, q1.y, q1.z);</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  }</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  {</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  <span class="comment">// normalise axis</span></div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="keywordflow">return</span> Vector3D(q1.x / s, q1.y / s, q1.z / s);</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  }</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span> </div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="comment">// NEVER getsgg HERE.</span></div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span> </div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  }</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> </div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="keywordtype">void</span> scaledAxis(<span class="keyword">const</span> Vector3D& vec_in)</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  {</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keywordtype">double</span> theta = vec_in.norm();</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span> </div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <span class="comment">// Small magnitudes are handled via the default vector.</span></div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="keywordflow">if</span> (theta > 0.0001)</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  {</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <span class="keywordtype">double</span> s = sin(theta / 2.0);</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  Vector3D W(vec_in / theta * s);</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  x = W.x;</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  y = W.y;</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  z = W.z;</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  w = cos(theta / 2.0);</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  }</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  {</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  x = y = z = 0;</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  w = 1.0;</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  }</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  }</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span> </div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  Vector3D rotatedVector(<span class="keyword">const</span> Vector3D& v)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  <span class="keywordflow">return</span> (((*<span class="keyword">this</span>) * Quaternion(v, 0)) * conjugate()).complex();</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  }</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span> </div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span> </div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span> </div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <span class="keywordtype">void</span> euler(<span class="keyword">const</span> Vector3D& euler) {</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="keywordtype">double</span> c1 = cos(euler[2] * 0.5);</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  <span class="keywordtype">double</span> c2 = cos(euler[1] * 0.5);</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <span class="keywordtype">double</span> c3 = cos(euler[0] * 0.5);</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="keywordtype">double</span> s1 = sin(euler[2] * 0.5);</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="keywordtype">double</span> s2 = sin(euler[1] * 0.5);</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="keywordtype">double</span> s3 = sin(euler[0] * 0.5);</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span> </div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  x = c1*c2*s3 - s1*s2*c3;</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  y = c1*s2*c3 + s1*c2*s3;</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  z = s1*c2*c3 - c1*s2*s3;</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  w = c1*c2*c3 + s1*s2*s3;</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  }</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span> </div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  Vector3D euler(<span class="keywordtype">void</span>)<span class="keyword"> const</span></div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  Vector3D euler;</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  <span class="keyword">const</span> <span class="keyword">static</span> <span class="keywordtype">double</span> PI_OVER_2 = M_PI * 0.5;</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <span class="keywordtype">double</span> sqw, sqx, sqy, sqz;</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span> </div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="comment">// quick conversion to Euler angles to give tilt to user</span></div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  sqw = w*w;</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  sqx = x*x;</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  sqy = y*y;</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  sqz = z*z;</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span> </div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  euler[1] = asin(2.0 * (w*y - x*z));</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="keywordflow">if</span> (PI_OVER_2 - fabs(euler[1]) > EPS_D) {</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  euler[2] = atan2(2.0 * (x*y + w*z),</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  sqx - sqy - sqz + sqw);</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  euler[0] = atan2(2.0 * (w*x + y*z),</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  sqw - sqx - sqy + sqz);</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  }</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  {</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <span class="comment">// compute heading from local 'down' vector</span></div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  euler[2] = atan2(2*y*z - 2*x*w,</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  2*x*z + 2*y*w);</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  euler[0] = 0.0;</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span> </div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  <span class="comment">// If facing down, reverse yaw</span></div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <span class="keywordflow">if</span> (euler[1] < 0)</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  {</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  euler[2] = M_PI - euler[2];</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  }</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  }</div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span> </div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <span class="keywordflow">return</span> euler;</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  }</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span> </div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  <span class="keywordtype">void</span> decoupleZ(Quaternion* Qxy, Quaternion* Qz)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  Vector3D ztt(0,0,1);</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  Vector3D zbt = this->rotatedVector(ztt);</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  Vector3D axis_xy = cross(ztt, zbt);</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <span class="keywordtype">double</span> axis_norm = axis_xy.norm();</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span> </div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <span class="keywordtype">double</span> axis_theta = acos(clamp(zbt.z, -1.0, 1.0));</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  <span class="keywordflow">if</span> (axis_norm > 0.00001)</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  {</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  axis_xy = axis_xy * (axis_theta/axis_norm); <span class="comment">// limit is *1</span></div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  }</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span> </div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  Qxy->scaledAxis(axis_xy);</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  *Qz = (Qxy->conjugate() * (*this));</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  }</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span> </div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  Quaternion slerp(<span class="keyword">const</span> Quaternion& q1, <span class="keywordtype">double</span> t)</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  {</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  <span class="keywordflow">return</span> slerp(*<span class="keyword">this</span>, q1, t);</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  }</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span> </div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="keyword">static</span> Quaternion slerp(<span class="keyword">const</span> Quaternion& q0, <span class="keyword">const</span> Quaternion& q1, <span class="keywordtype">double</span> t) {</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span> </div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  <span class="keywordtype">double</span> omega = acos(clamp(q0.x*q1.x +</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  q0.y*q1.y +</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  q0.z*q1.z +</div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  q0.w*q1.w, -1.0, 1.0));</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  <span class="keywordflow">if</span> (fabs(omega) < 1e-10)</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  {</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  omega = 1e-10;</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  }</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  <span class="keywordtype">double</span> som = sin(omega);</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  <span class="keywordtype">double</span> st0 = sin((1-t) * omega) / som;</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  <span class="keywordtype">double</span> st1 = sin(t * omega) / som;</div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span> </div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  <span class="keywordflow">return</span> Quaternion(q0.x*st0 + q1.x*st1,</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  q0.y*st0 + q1.y*st1,</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  q0.z*st0 + q1.z*st1,</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  q0.w*st0 + q1.w*st1);</div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  }</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span> </div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span> </div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span> };</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span> </div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span> Quaternion operator*(<span class="keywordtype">double</span> s, <span class="keyword">const</span> Quaternion& q);</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span> </div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span> } <span class="comment">// namespace CMU462</span></div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span> </div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span> <span class="preprocessor">#endif </span><span class="comment">/* CMU462_QUATERNION_H */</span><span class="preprocessor"></span></div>
<div class="ttc" id="class_c_m_u462_1_1_vector4_d_html_ae374d31af8bc0300a884f04a62cdb890"><div class="ttname"><a href="class_c_m_u462_1_1_vector4_d.html#ae374d31af8bc0300a884f04a62cdb890">CMU462::Vector4D::unit</a></div><div class="ttdeci">Vector4D unit(void) const </div><div class="ttdoc">Returns unit vector. </div><div class="ttdef"><b>Definition:</b> vector4D.h:137</div></div>
<div class="ttc" id="namespace_c_m_u462_html"><div class="ttname"><a href="namespace_c_m_u462.html">CMU462</a></div><div class="ttdef"><b>Definition:</b> CMU462.h:8</div></div>
<div class="ttc" id="class_c_m_u462_1_1_vector4_d_html_abec701db9f3125be7c2c7569d9c82e51"><div class="ttname"><a href="class_c_m_u462_1_1_vector4_d.html#abec701db9f3125be7c2c7569d9c82e51">CMU462::Vector4D::norm</a></div><div class="ttdeci">double norm(void) const </div><div class="ttdoc">Returns Euclidean distance metric extended to 4 dimensions. </div><div class="ttdef"><b>Definition:</b> vector4D.h:123</div></div>
<div class="ttc" id="class_c_m_u462_1_1_vector4_d_html_a1e930c168b0e56b6ee1b14937644a318"><div class="ttname"><a href="class_c_m_u462_1_1_vector4_d.html#a1e930c168b0e56b6ee1b14937644a318">CMU462::Vector4D::Vector4D</a></div><div class="ttdeci">Vector4D()</div><div class="ttdoc">Constructor. </div><div class="ttdef"><b>Definition:</b> vector4D.h:25</div></div>
<div class="ttc" id="class_c_m_u462_1_1_vector4_d_html_aa473c7f0bc98a04c9894dd4f920b8a56"><div class="ttname"><a href="class_c_m_u462_1_1_vector4_d.html#aa473c7f0bc98a04c9894dd4f920b8a56">CMU462::Vector4D::normalize</a></div><div class="ttdeci">void normalize(void)</div><div class="ttdoc">Divides by Euclidean length. </div><div class="ttdef"><b>Definition:</b> vector4D.h:146</div></div>
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