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+<div class="title">Geometry.cpp</div> </div>
+</div><!--header-->
+<div class="contents">
+<a href="_geometry_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span>&#160;<span class="comment">/* Project nGenEx</span></div>
+<div class="line"><a name="l00002"></a><span class="lineno"> 2</span>&#160;<span class="comment"> Destroyer Studios LLC</span></div>
+<div class="line"><a name="l00003"></a><span class="lineno"> 3</span>&#160;<span class="comment"> Copyright © 1997-2004. All Rights Reserved.</span></div>
+<div class="line"><a name="l00004"></a><span class="lineno"> 4</span>&#160;<span class="comment"></span></div>
+<div class="line"><a name="l00005"></a><span class="lineno"> 5</span>&#160;<span class="comment"> SUBSYSTEM: nGenEx.lib</span></div>
+<div class="line"><a name="l00006"></a><span class="lineno"> 6</span>&#160;<span class="comment"> FILE: Geometry.cpp</span></div>
+<div class="line"><a name="l00007"></a><span class="lineno"> 7</span>&#160;<span class="comment"> AUTHOR: John DiCamillo</span></div>
+<div class="line"><a name="l00008"></a><span class="lineno"> 8</span>&#160;<span class="comment"></span></div>
+<div class="line"><a name="l00009"></a><span class="lineno"> 9</span>&#160;<span class="comment"></span></div>
+<div class="line"><a name="l00010"></a><span class="lineno"> 10</span>&#160;<span class="comment"> OVERVIEW</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"> Geometric Utilities</span></div>
+<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>&#160;<span class="comment">*/</span></div>
+<div class="line"><a name="l00014"></a><span class="lineno"> 14</span>&#160;</div>
+<div class="line"><a name="l00015"></a><span class="lineno"> 15</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="_mem_debug_8h.html">MemDebug.h</a>&quot;</span></div>
+<div class="line"><a name="l00016"></a><span class="lineno"> 16</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="_geometry_8h.html">Geometry.h</a>&quot;</span></div>
+<div class="line"><a name="l00017"></a><span class="lineno"> 17</span>&#160;</div>
+<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</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="code" href="struct_rect.html#aaf7b062bbef6819c1104f6de549c58c7"> 20</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="struct_rect.html#aaf7b062bbef6819c1104f6de549c58c7">Rect::Inflate</a>(<span class="keywordtype">int</span> dx, <span class="keywordtype">int</span> dy)</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; <a class="code" href="struct_rect.html#a64d1ef14e429e1816539de4c54361e55">x</a> -= dx;</div>
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+<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160; <a class="code" href="struct_rect.html#a1e37b6f8a4fb0d68ba22c8fffffab0a4">y</a> -= dy;</div>
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+<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160;}</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"><a class="code" href="struct_rect.html#a1508d1d285a77918f29b9632327c31c7"> 28</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="struct_rect.html#a1508d1d285a77918f29b9632327c31c7">Rect::Deflate</a>(<span class="keywordtype">int</span> dx, <span class="keywordtype">int</span> dy)</div>
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+<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160;}</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"><a class="code" href="struct_rect.html#a9763b4eb1b7944b98f1e52636fe58423"> 36</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="struct_rect.html#a9763b4eb1b7944b98f1e52636fe58423">Rect::Inset</a>(<span class="keywordtype">int</span> l, <span class="keywordtype">int</span> r, <span class="keywordtype">int</span> t, <span class="keywordtype">int</span> b)</div>
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+<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160;<span class="keyword"></span>{</div>
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+<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160;</div>
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+<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
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+<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160;}</div>
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+<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160;</div>
+<div class="line"><a name="l00101"></a><span class="lineno"><a class="code" href="_geometry_8h.html#ad3944c476d46188249376f290a934d21"> 101</a></span>&#160;<span class="keywordtype">double</span> <a class="code" href="_geometry_8cpp.html#ad3944c476d46188249376f290a934d21">ClosestApproachTime</a>(<span class="keyword">const</span> <a class="code" href="struct_point.html">Point</a>&amp; loc1, <span class="keyword">const</span> <a class="code" href="struct_point.html">Point</a>&amp; vel1,</div>
+<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160;<span class="keyword">const</span> <a class="code" href="struct_point.html">Point</a>&amp; loc2, <span class="keyword">const</span> <a class="code" href="struct_point.html">Point</a>&amp; vel2)</div>
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+<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; <a class="code" href="struct_point.html">Point</a> Dv = vel1-vel2;</div>
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+<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; <span class="keywordflow">if</span> (Dv.<a class="code" href="struct_point.html#ab99c56589bc8ad5fa5071387110a5bc7">x</a> || Dv.<a class="code" href="struct_point.html#afa38be143ae800e6ad69ce8ed4df62d8">y</a> || Dv.<a class="code" href="struct_point.html#a05ba3b1dfcb19430582ae953cbbfbded">z</a>)</div>
+<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; t = -1 * (Dv*D) / (Dv*Dv);</div>
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+<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160;</div>
+<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160;</div>
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+<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160;</div>
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+<div class="line"><a name="l00135"></a><span class="lineno"><a class="code" href="struct_vec3.html#a269d13893a87a616b6709e5fc3d34d4f"> 135</a></span>&#160;<a class="code" href="struct_vec3.html#a269d13893a87a616b6709e5fc3d34d4f">Vec3::Normalize</a>()</div>
+<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>&#160;{</div>
+<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>&#160; <span class="keywordtype">float</span> scale = 1.0f;</div>
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+<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>&#160;</div>
+<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>&#160;<a class="code" href="struct_vec3.html">Vec3</a></div>
+<div class="line"><a name="l00153"></a><span class="lineno"><a class="code" href="struct_vec3.html#a494390c0d3295ed2f48f9441dfcf4b62"> 153</a></span>&#160;<a class="code" href="struct_vec3.html#aebd448cbed356f0915c8217fa25f2ca7">Vec3::operator*</a>(<span class="keyword">const</span> <a class="code" href="struct_matrix.html">Matrix</a>&amp; m)<span class="keyword"> const</span></div>
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+<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[1][0] = vup.<a class="code" href="struct_point.html#ab99c56589bc8ad5fa5071387110a5bc7">x</a>;</div>
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+<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[2][1] = vpn.<a class="code" href="struct_point.html#afa38be143ae800e6ad69ce8ed4df62d8">y</a>;</div>
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+<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>&#160;}</div>
+<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>&#160;</div>
+<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>&#160;</div>
+<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>&#160;<a class="code" href="struct_matrix.html">Matrix</a>&amp;</div>
+<div class="line"><a name="l00229"></a><span class="lineno"><a class="code" href="struct_matrix.html#aea5a06385f646eb4a63929fae6fa3e14"> 229</a></span>&#160;<a class="code" href="struct_matrix.html#aea5a06385f646eb4a63929fae6fa3e14">Matrix::operator =</a>(<span class="keyword">const</span> <a class="code" href="struct_matrix.html">Matrix</a>&amp; m)</div>
+<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>&#160;{</div>
+<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>&#160; CopyMemory(<a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>, m.<a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>, <span class="keyword">sizeof</span>(<a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>));</div>
+<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>&#160;</div>
+<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>&#160; <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
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+<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;</div>
+<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>&#160;<a class="code" href="struct_matrix.html">Matrix</a>&amp;</div>
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+<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>&#160;</div>
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+<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>&#160;}</div>
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+<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>&#160;</div>
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+<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>&#160;</div>
+<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>&#160;</div>
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+<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>&#160; <span class="keywordtype">double</span> sp = sin(pitch);</div>
+<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>&#160; <span class="keywordtype">double</span> cp = cos(pitch);</div>
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+<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>&#160; <span class="keywordtype">double</span> e10 = <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[1][0];</div>
+<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>&#160; <span class="keywordtype">double</span> e11 = <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[1][1];</div>
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+<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>&#160;</div>
+<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[0][0] = c*e00 + s*e10;</div>
+<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[0][1] = c*e01 + s*e11;</div>
+<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[0][2] = c*e02 + s*e12;</div>
+<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>&#160;</div>
+<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[1][0] = -s*e00 + c*e10;</div>
+<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[1][1] = -s*e01 + c*e11;</div>
+<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[1][2] = -s*e02 + c*e12;</div>
+<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>&#160;}</div>
+<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>&#160;</div>
+<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>&#160;</div>
+<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>&#160;<span class="keywordtype">void</span></div>
+<div class="line"><a name="l00343"></a><span class="lineno"><a class="code" href="struct_matrix.html#a3e2bffe4b3d999875653a0ffeb9970b5"> 343</a></span>&#160;<a class="code" href="struct_matrix.html#a3e2bffe4b3d999875653a0ffeb9970b5">Matrix::Pitch</a>(<span class="keywordtype">double</span> pitch)</div>
+<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>&#160;{</div>
+<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>&#160; <span class="keywordtype">double</span> s = sin(pitch);</div>
+<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>&#160; <span class="keywordtype">double</span> c = cos(pitch);</div>
+<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>&#160;</div>
+<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>&#160; <span class="keywordtype">double</span> e10 = <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[1][0];</div>
+<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>&#160; <span class="keywordtype">double</span> e11 = <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[1][1];</div>
+<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>&#160; <span class="keywordtype">double</span> e12 = <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[1][2];</div>
+<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>&#160; <span class="keywordtype">double</span> e20 = <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[2][0];</div>
+<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>&#160; <span class="keywordtype">double</span> e21 = <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[2][1];</div>
+<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>&#160; <span class="keywordtype">double</span> e22 = <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[2][2];</div>
+<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>&#160;</div>
+<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[1][0] = c*e10 + s*e20;</div>
+<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[1][1] = c*e11 + s*e21;</div>
+<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[1][2] = c*e12 + s*e22;</div>
+<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>&#160;</div>
+<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[2][0] = -s*e10 + c*e20;</div>
+<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[2][1] = -s*e11 + c*e21;</div>
+<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[2][2] = -s*e12 + c*e22;</div>
+<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>&#160;}</div>
+<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>&#160;</div>
+<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>&#160;</div>
+<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>&#160;<span class="keywordtype">void</span></div>
+<div class="line"><a name="l00367"></a><span class="lineno"><a class="code" href="struct_matrix.html#ab46d7353f782f0a9a93d16ace7095145"> 367</a></span>&#160;<a class="code" href="struct_matrix.html#ab46d7353f782f0a9a93d16ace7095145">Matrix::Yaw</a>(<span class="keywordtype">double</span> yaw)</div>
+<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>&#160;{</div>
+<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>&#160; <span class="keywordtype">double</span> s = sin(yaw);</div>
+<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>&#160; <span class="keywordtype">double</span> c = cos(yaw);</div>
+<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>&#160;</div>
+<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>&#160; <span class="keywordtype">double</span> e00 = <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[0][0];</div>
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+<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>&#160; <span class="keywordtype">double</span> e02 = <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[0][2];</div>
+<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>&#160; <span class="keywordtype">double</span> e20 = <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[2][0];</div>
+<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>&#160; <span class="keywordtype">double</span> e21 = <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[2][1];</div>
+<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>&#160; <span class="keywordtype">double</span> e22 = <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[2][2];</div>
+<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>&#160;</div>
+<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[0][0] = c*e00 - s*e20;</div>
+<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[0][1] = c*e01 - s*e21;</div>
+<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[0][2] = c*e02 - s*e22;</div>
+<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>&#160;</div>
+<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[2][0] = s*e00 + c*e20;</div>
+<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[2][1] = s*e01 + c*e21;</div>
+<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[2][2] = s*e02 + c*e22;</div>
+<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>&#160;}</div>
+<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>&#160;</div>
+<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>&#160;</div>
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+<div class="line"><a name="l00393"></a><span class="lineno"><a class="code" href="struct_matrix.html#abac777e8af319d45d091a5c187dba26f"> 393</a></span>&#160;<a class="code" href="struct_matrix.html#abac777e8af319d45d091a5c187dba26f">Matrix::ComputeEulerAngles</a>(<span class="keywordtype">double</span>&amp; roll, <span class="keywordtype">double</span>&amp; pitch, <span class="keywordtype">double</span>&amp; yaw)<span class="keyword"> const</span></div>
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+<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>&#160;</div>
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+<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>&#160; cy = cos(yaw);</div>
+<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>&#160; roll = asin(<a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[0][1] / cy);</div>
+<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>&#160; pitch = asin(<a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[1][2] / cy);</div>
+<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>&#160;</div>
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+<div class="line"><a name="l00407"></a><span class="lineno"> 407</span>&#160;}</div>
+<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>&#160;</div>
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+<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>&#160;</div>
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+<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>&#160;}</div>
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+<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>&#160;</div>
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+<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>&#160;</div>
+<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>&#160; <span class="keywordflow">return</span> result;</div>
+<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>&#160;}</div>
+<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>&#160;</div>
+<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>&#160;</div>
+<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>&#160;<a class="code" href="struct_vec3.html">Vec3</a></div>
+<div class="line"><a name="l00448"></a><span class="lineno"><a class="code" href="struct_matrix.html#a590573aa1238be4afa7e55e8f764b83b"> 448</a></span>&#160;<a class="code" href="struct_matrix.html#a435aaecd9331c9ee02bdb5bba59b20a7">Matrix::operator*</a>(<span class="keyword">const</span> <a class="code" href="struct_vec3.html">Vec3</a>&amp; v)<span class="keyword"> const</span></div>
+<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>&#160;<span class="keyword"></span>{</div>
+<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>&#160; <a class="code" href="struct_vec3.html">Vec3</a> result;</div>
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+<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>&#160; result.<a class="code" href="struct_vec3.html#a2814580e9b9372738c0a61197ea46b51">x</a> = (float) ((<a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[0][0] * v.<a class="code" href="struct_vec3.html#a2814580e9b9372738c0a61197ea46b51">x</a>) + (<a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[0][1] * v.<a class="code" href="struct_vec3.html#abc1d241232cb04aa98217a942402ae68">y</a>) + (<a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[0][2] * v.<a class="code" href="struct_vec3.html#a64f3f00cd2dd9076999eeb2f05210388">z</a>));</div>
+<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>&#160; result.<a class="code" href="struct_vec3.html#abc1d241232cb04aa98217a942402ae68">y</a> = (float) ((<a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[1][0] * v.<a class="code" href="struct_vec3.html#a2814580e9b9372738c0a61197ea46b51">x</a>) + (<a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[1][1] * v.<a class="code" href="struct_vec3.html#abc1d241232cb04aa98217a942402ae68">y</a>) + (<a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[1][2] * v.<a class="code" href="struct_vec3.html#a64f3f00cd2dd9076999eeb2f05210388">z</a>));</div>
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+<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>&#160;</div>
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+<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>&#160;}</div>
+<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>&#160;</div>
+<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>&#160;</div>
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+<div class="line"><a name="l00462"></a><span class="lineno"><a class="code" href="struct_matrix.html#aabd1efff70d937f836b4ed57ca59caef"> 462</a></span>&#160;<a class="code" href="struct_matrix.html#aabd1efff70d937f836b4ed57ca59caef">Matrix::Cofactor</a>(<span class="keywordtype">int</span> i, <span class="keywordtype">int</span> j)<span class="keyword"> const</span></div>
+<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>&#160;<span class="keyword"></span>{</div>
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+<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>&#160; <span class="keywordtype">int</span> j2=2;</div>
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+<div class="line"><a name="l00478"></a><span class="lineno"> 478</span>&#160;}</div>
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+<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>&#160;</div>
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+<div class="line"><a name="l00489"></a><span class="lineno"> 489</span>&#160; <span class="keywordflow">for</span> (j = 0; j &lt; 3; j++)</div>
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+<div class="line"><a name="l00498"></a><span class="lineno"> 498</span>&#160;</div>
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+<div class="line"><a name="l00501"></a><span class="lineno"> 501</span>&#160; <a class="code" href="struct_matrix.html#a5cab8c696d9347b3884df0661ffde8d2">elem</a>[i][j] = f[i][j] * inv;</div>
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+<div class="line"><a name="l00503"></a><span class="lineno"> 503</span>&#160;}</div>
+<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>&#160;</div>
+<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00506"></a><span class="lineno"> 506</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00508"></a><span class="lineno"> 508</span>&#160;</div>
+<div class="line"><a name="l00509"></a><span class="lineno"><a class="code" href="struct_plane.html#acac0d9c003e0ab10d07b146c3566a0c7"> 509</a></span>&#160;<a class="code" href="struct_plane.html#acac0d9c003e0ab10d07b146c3566a0c7">Plane::Plane</a>()</div>
+<div class="line"><a name="l00510"></a><span class="lineno"> 510</span>&#160;: distance(0.0f)</div>
+<div class="line"><a name="l00511"></a><span class="lineno"> 511</span>&#160;{ }</div>
+<div class="line"><a name="l00512"></a><span class="lineno"> 512</span>&#160;</div>
+<div class="line"><a name="l00513"></a><span class="lineno"><a class="code" href="struct_plane.html#a21dfd453dc60e14dc38a015457046dcd"> 513</a></span>&#160;<a class="code" href="struct_plane.html#acac0d9c003e0ab10d07b146c3566a0c7">Plane::Plane</a>(<span class="keyword">const</span> <a class="code" href="struct_point.html">Point</a>&amp; p0, <span class="keyword">const</span> <a class="code" href="struct_point.html">Point</a>&amp; p1, <span class="keyword">const</span> <a class="code" href="struct_point.html">Point</a>&amp; p2)</div>
+<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>&#160;{</div>
+<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>&#160; <a class="code" href="struct_point.html">Point</a> d1 = p1 - p0;</div>
+<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>&#160; <a class="code" href="struct_point.html">Point</a> d2 = p2 - p0;</div>
+<div class="line"><a name="l00517"></a><span class="lineno"> 517</span>&#160;</div>
+<div class="line"><a name="l00518"></a><span class="lineno"> 518</span>&#160; <a class="code" href="struct_plane.html#a4fca1d30bfad2542c8e38aa32ff13655">normal</a> = (<a class="code" href="struct_vec3.html">Vec3</a>) d1.<a class="code" href="struct_point.html#ae600bcc9fe480e782a05fade3b78f8c0">cross</a>(d2);</div>
+<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>&#160; <a class="code" href="struct_plane.html#a4fca1d30bfad2542c8e38aa32ff13655">normal</a>.<a class="code" href="struct_vec3.html#a269d13893a87a616b6709e5fc3d34d4f">Normalize</a>();</div>
+<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>&#160;</div>
+<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>&#160; <a class="code" href="struct_plane.html#a6ad7fdbb1461aa0527eb1f6745e10962">distance</a> = (float) (<a class="code" href="struct_plane.html#a4fca1d30bfad2542c8e38aa32ff13655">normal</a> * p0);</div>
+<div class="line"><a name="l00522"></a><span class="lineno"> 522</span>&#160;}</div>
+<div class="line"><a name="l00523"></a><span class="lineno"> 523</span>&#160;</div>
+<div class="line"><a name="l00524"></a><span class="lineno"><a class="code" href="struct_plane.html#aa8e0322387866b021b0a3c5fad2b4290"> 524</a></span>&#160;<a class="code" href="struct_plane.html#acac0d9c003e0ab10d07b146c3566a0c7">Plane::Plane</a>(<span class="keyword">const</span> <a class="code" href="struct_vec3.html">Vec3</a>&amp; v0, <span class="keyword">const</span> <a class="code" href="struct_vec3.html">Vec3</a>&amp; v1, <span class="keyword">const</span> <a class="code" href="struct_vec3.html">Vec3</a>&amp; v2)</div>
+<div class="line"><a name="l00525"></a><span class="lineno"> 525</span>&#160;{</div>
+<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>&#160; <a class="code" href="struct_vec3.html">Vec3</a> d1 = v1 - v0;</div>
+<div class="line"><a name="l00527"></a><span class="lineno"> 527</span>&#160; <a class="code" href="struct_vec3.html">Vec3</a> d2 = v2 - v0;</div>
+<div class="line"><a name="l00528"></a><span class="lineno"> 528</span>&#160;</div>
+<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>&#160; <a class="code" href="struct_plane.html#a4fca1d30bfad2542c8e38aa32ff13655">normal</a> = d1.<a class="code" href="struct_vec3.html#a85bfd45b956fdd79f7686b9d220576f5">cross</a>(d2);</div>
+<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>&#160; <a class="code" href="struct_plane.html#a4fca1d30bfad2542c8e38aa32ff13655">normal</a>.<a class="code" href="struct_vec3.html#a269d13893a87a616b6709e5fc3d34d4f">Normalize</a>();</div>
+<div class="line"><a name="l00531"></a><span class="lineno"> 531</span>&#160;</div>
+<div class="line"><a name="l00532"></a><span class="lineno"> 532</span>&#160; <a class="code" href="struct_plane.html#a6ad7fdbb1461aa0527eb1f6745e10962">distance</a> = <a class="code" href="struct_plane.html#a4fca1d30bfad2542c8e38aa32ff13655">normal</a> * v0;</div>
+<div class="line"><a name="l00533"></a><span class="lineno"> 533</span>&#160;}</div>
+<div class="line"><a name="l00534"></a><span class="lineno"> 534</span>&#160;</div>
+<div class="line"><a name="l00535"></a><span class="lineno"><a class="code" href="struct_plane.html#abeb77007b8e213e99cd882b4c261dbaf"> 535</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="struct_plane.html#abeb77007b8e213e99cd882b4c261dbaf">Plane::Rotate</a>(<span class="keyword">const</span> <a class="code" href="struct_vec3.html">Vec3</a>&amp; v0, <span class="keyword">const</span> <a class="code" href="struct_matrix.html">Matrix</a>&amp; m)</div>
+<div class="line"><a name="l00536"></a><span class="lineno"> 536</span>&#160;{</div>
+<div class="line"><a name="l00537"></a><span class="lineno"> 537</span>&#160; <a class="code" href="struct_plane.html#a4fca1d30bfad2542c8e38aa32ff13655">normal</a> = <a class="code" href="struct_plane.html#a4fca1d30bfad2542c8e38aa32ff13655">normal</a> * m;</div>
+<div class="line"><a name="l00538"></a><span class="lineno"> 538</span>&#160; <a class="code" href="struct_plane.html#a6ad7fdbb1461aa0527eb1f6745e10962">distance</a> = <a class="code" href="struct_plane.html#a4fca1d30bfad2542c8e38aa32ff13655">normal</a> * v0;</div>
+<div class="line"><a name="l00539"></a><span class="lineno"> 539</span>&#160;}</div>
+<div class="line"><a name="l00540"></a><span class="lineno"> 540</span>&#160;</div>
+<div class="line"><a name="l00541"></a><span class="lineno"><a class="code" href="struct_plane.html#a828846eec3cf928437813a352853c6cd"> 541</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="struct_plane.html#a828846eec3cf928437813a352853c6cd">Plane::Translate</a>(<span class="keyword">const</span> <a class="code" href="struct_vec3.html">Vec3</a>&amp; v0)</div>
+<div class="line"><a name="l00542"></a><span class="lineno"> 542</span>&#160;{</div>
+<div class="line"><a name="l00543"></a><span class="lineno"> 543</span>&#160; <a class="code" href="struct_plane.html#a6ad7fdbb1461aa0527eb1f6745e10962">distance</a> = <a class="code" href="struct_plane.html#a4fca1d30bfad2542c8e38aa32ff13655">normal</a> * v0;</div>
+<div class="line"><a name="l00544"></a><span class="lineno"> 544</span>&#160;}</div>
+<div class="line"><a name="l00545"></a><span class="lineno"> 545</span>&#160;</div>
+<div class="line"><a name="l00546"></a><span class="lineno"> 546</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00547"></a><span class="lineno"> 547</span>&#160;<span class="comment">// 3-D dot product.</span></div>
+<div class="line"><a name="l00548"></a><span class="lineno"> 548</span>&#160;</div>
+<div class="line"><a name="l00549"></a><span class="lineno"><a class="code" href="_geometry_8h.html#af507df72c2927886430fa6c25be87b82"> 549</a></span>&#160;<span class="keywordtype">double</span> <a class="code" href="_geometry_8cpp.html#af507df72c2927886430fa6c25be87b82">DotProduct</a>(<span class="keyword">const</span> <a class="code" href="struct_point.html">Point</a>&amp; a, <span class="keyword">const</span> <a class="code" href="struct_point.html">Point</a>&amp; b)</div>
+<div class="line"><a name="l00550"></a><span class="lineno"> 550</span>&#160;{</div>
+<div class="line"><a name="l00551"></a><span class="lineno"> 551</span>&#160; <span class="keywordflow">return</span> (a.<a class="code" href="struct_point.html#ab99c56589bc8ad5fa5071387110a5bc7">x</a> * b.<a class="code" href="struct_point.html#ab99c56589bc8ad5fa5071387110a5bc7">x</a>) + (a.<a class="code" href="struct_point.html#afa38be143ae800e6ad69ce8ed4df62d8">y</a> * b.<a class="code" href="struct_point.html#afa38be143ae800e6ad69ce8ed4df62d8">y</a>) + (a.<a class="code" href="struct_point.html#a05ba3b1dfcb19430582ae953cbbfbded">z</a> * b.<a class="code" href="struct_point.html#a05ba3b1dfcb19430582ae953cbbfbded">z</a>);</div>
+<div class="line"><a name="l00552"></a><span class="lineno"> 552</span>&#160;}</div>
+<div class="line"><a name="l00553"></a><span class="lineno"> 553</span>&#160;</div>
+<div class="line"><a name="l00554"></a><span class="lineno"> 554</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00555"></a><span class="lineno"> 555</span>&#160;<span class="comment">// 3-D cross product.</span></div>
+<div class="line"><a name="l00556"></a><span class="lineno"> 556</span>&#160;</div>
+<div class="line"><a name="l00557"></a><span class="lineno"><a class="code" href="_geometry_8h.html#a7b32f095e9c893be8afb27d1310bfa1f"> 557</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="l3ds_8cpp.html#a3ac088301f55128c9217bb5a2c4dcc74">CrossProduct</a>(<span class="keyword">const</span> <a class="code" href="struct_point.html">Point</a>&amp; a, <span class="keyword">const</span> <a class="code" href="struct_point.html">Point</a>&amp; b, <a class="code" href="struct_point.html">Point</a>&amp; out)</div>
+<div class="line"><a name="l00558"></a><span class="lineno"> 558</span>&#160;{</div>
+<div class="line"><a name="l00559"></a><span class="lineno"> 559</span>&#160; out.<a class="code" href="struct_point.html#ab99c56589bc8ad5fa5071387110a5bc7">x</a> = (a.<a class="code" href="struct_point.html#afa38be143ae800e6ad69ce8ed4df62d8">y</a> * b.<a class="code" href="struct_point.html#a05ba3b1dfcb19430582ae953cbbfbded">z</a>) - (a.<a class="code" href="struct_point.html#a05ba3b1dfcb19430582ae953cbbfbded">z</a> * b.<a class="code" href="struct_point.html#afa38be143ae800e6ad69ce8ed4df62d8">y</a>);</div>
+<div class="line"><a name="l00560"></a><span class="lineno"> 560</span>&#160; out.<a class="code" href="struct_point.html#afa38be143ae800e6ad69ce8ed4df62d8">y</a> = (a.<a class="code" href="struct_point.html#a05ba3b1dfcb19430582ae953cbbfbded">z</a> * b.<a class="code" href="struct_point.html#ab99c56589bc8ad5fa5071387110a5bc7">x</a>) - (a.<a class="code" href="struct_point.html#ab99c56589bc8ad5fa5071387110a5bc7">x</a> * b.<a class="code" href="struct_point.html#a05ba3b1dfcb19430582ae953cbbfbded">z</a>);</div>
+<div class="line"><a name="l00561"></a><span class="lineno"> 561</span>&#160; out.<a class="code" href="struct_point.html#a05ba3b1dfcb19430582ae953cbbfbded">z</a> = (a.<a class="code" href="struct_point.html#ab99c56589bc8ad5fa5071387110a5bc7">x</a> * b.<a class="code" href="struct_point.html#afa38be143ae800e6ad69ce8ed4df62d8">y</a>) - (a.<a class="code" href="struct_point.html#afa38be143ae800e6ad69ce8ed4df62d8">y</a> * b.<a class="code" href="struct_point.html#ab99c56589bc8ad5fa5071387110a5bc7">x</a>);</div>
+<div class="line"><a name="l00562"></a><span class="lineno"> 562</span>&#160;}</div>
+<div class="line"><a name="l00563"></a><span class="lineno"> 563</span>&#160;</div>
+<div class="line"><a name="l00564"></a><span class="lineno"> 564</span>&#160;<span class="comment">// +--------------------------------------------------------------------+</span></div>
+<div class="line"><a name="l00565"></a><span class="lineno"> 565</span>&#160;<span class="comment">// Concatenate two 3x3 matrices.</span></div>
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+<div class="line"><a name="l00567"></a><span class="lineno"><a class="code" href="_geometry_8h.html#aca1d3b40ee7c81df67a92b3fd102148c"> 567</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="_geometry_8cpp.html#aca1d3b40ee7c81df67a92b3fd102148c">MConcat</a>(<span class="keywordtype">double</span> in1[3][3], <span class="keywordtype">double</span> in2[3][3], <span class="keywordtype">double</span> out[3][3])</div>
+<div class="line"><a name="l00568"></a><span class="lineno"> 568</span>&#160;{</div>
+<div class="line"><a name="l00569"></a><span class="lineno"> 569</span>&#160; <span class="keywordtype">int</span> i, j;</div>
+<div class="line"><a name="l00570"></a><span class="lineno"> 570</span>&#160;</div>
+<div class="line"><a name="l00571"></a><span class="lineno"> 571</span>&#160; <span class="keywordflow">for</span> (i=0 ; i&lt;3 ; i++) {</div>
+<div class="line"><a name="l00572"></a><span class="lineno"> 572</span>&#160; <span class="keywordflow">for</span> (j=0 ; j&lt;3 ; j++) {</div>
+<div class="line"><a name="l00573"></a><span class="lineno"> 573</span>&#160; out[i][j] = in1[i][0] * in2[0][j] +</div>
+<div class="line"><a name="l00574"></a><span class="lineno"> 574</span>&#160; in1[i][1] * in2[1][j] +</div>
+<div class="line"><a name="l00575"></a><span class="lineno"> 575</span>&#160; in1[i][2] * in2[2][j];</div>
+<div class="line"><a name="l00576"></a><span class="lineno"> 576</span>&#160; }</div>
+<div class="line"><a name="l00577"></a><span class="lineno"> 577</span>&#160; }</div>
+<div class="line"><a name="l00578"></a><span class="lineno"> 578</span>&#160;}</div>
+<div class="line"><a name="l00579"></a><span class="lineno"> 579</span>&#160;</div>
+<div class="line"><a name="l00580"></a><span class="lineno"> 580</span>&#160;<span class="comment">/* GRAPHICS GEMS II ----------------------------------------------------</span></div>
+<div class="line"><a name="l00581"></a><span class="lineno"> 581</span>&#160;<span class="comment">*</span></div>
+<div class="line"><a name="l00582"></a><span class="lineno"> 582</span>&#160;<span class="comment">* lines_intersect: AUTHOR: Mukesh Prasad</span></div>
+<div class="line"><a name="l00583"></a><span class="lineno"> 583</span>&#160;<span class="comment">*</span></div>
+<div class="line"><a name="l00584"></a><span class="lineno"> 584</span>&#160;<span class="comment">* This function computes whether two line segments,</span></div>
+<div class="line"><a name="l00585"></a><span class="lineno"> 585</span>&#160;<span class="comment">* respectively joining the input points (x1,y1) -- (x2,y2)</span></div>
+<div class="line"><a name="l00586"></a><span class="lineno"> 586</span>&#160;<span class="comment">* and the input points (x3,y3) -- (x4,y4) intersect.</span></div>
+<div class="line"><a name="l00587"></a><span class="lineno"> 587</span>&#160;<span class="comment">* If the lines intersect, the output variables x, y are</span></div>
+<div class="line"><a name="l00588"></a><span class="lineno"> 588</span>&#160;<span class="comment">* set to coordinates of the point of intersection.</span></div>
+<div class="line"><a name="l00589"></a><span class="lineno"> 589</span>&#160;<span class="comment">*</span></div>
+<div class="line"><a name="l00590"></a><span class="lineno"> 590</span>&#160;<span class="comment">* All values are in integers. The returned value is rounded</span></div>
+<div class="line"><a name="l00591"></a><span class="lineno"> 591</span>&#160;<span class="comment">* to the nearest integer point.</span></div>
+<div class="line"><a name="l00592"></a><span class="lineno"> 592</span>&#160;<span class="comment">*</span></div>
+<div class="line"><a name="l00593"></a><span class="lineno"> 593</span>&#160;<span class="comment">* If non-integral grid points are relevant, the function</span></div>
+<div class="line"><a name="l00594"></a><span class="lineno"> 594</span>&#160;<span class="comment">* can easily be transformed by substituting floating point</span></div>
+<div class="line"><a name="l00595"></a><span class="lineno"> 595</span>&#160;<span class="comment">* calculations instead of integer calculations.</span></div>
+<div class="line"><a name="l00596"></a><span class="lineno"> 596</span>&#160;<span class="comment">*</span></div>
+<div class="line"><a name="l00597"></a><span class="lineno"> 597</span>&#160;<span class="comment">* Entry</span></div>
+<div class="line"><a name="l00598"></a><span class="lineno"> 598</span>&#160;<span class="comment">* x1, y1, x2, y2 Coordinates of endpoints of one segment.</span></div>
+<div class="line"><a name="l00599"></a><span class="lineno"> 599</span>&#160;<span class="comment">* x3, y3, x4, y4 Coordinates of endpoints of other segment.</span></div>
+<div class="line"><a name="l00600"></a><span class="lineno"> 600</span>&#160;<span class="comment">*</span></div>
+<div class="line"><a name="l00601"></a><span class="lineno"> 601</span>&#160;<span class="comment">* Exit</span></div>
+<div class="line"><a name="l00602"></a><span class="lineno"> 602</span>&#160;<span class="comment">* x, y Coordinates of intersection point.</span></div>
+<div class="line"><a name="l00603"></a><span class="lineno"> 603</span>&#160;<span class="comment">*</span></div>
+<div class="line"><a name="l00604"></a><span class="lineno"> 604</span>&#160;<span class="comment">* The value returned by the function is one of:</span></div>
+<div class="line"><a name="l00605"></a><span class="lineno"> 605</span>&#160;<span class="comment">*</span></div>
+<div class="line"><a name="l00606"></a><span class="lineno"> 606</span>&#160;<span class="comment">* DONT_INTERSECT 0</span></div>
+<div class="line"><a name="l00607"></a><span class="lineno"> 607</span>&#160;<span class="comment">* DO_INTERSECT 1</span></div>
+<div class="line"><a name="l00608"></a><span class="lineno"> 608</span>&#160;<span class="comment">* COLLINEAR 2</span></div>
+<div class="line"><a name="l00609"></a><span class="lineno"> 609</span>&#160;<span class="comment">*</span></div>
+<div class="line"><a name="l00610"></a><span class="lineno"> 610</span>&#160;<span class="comment">* Error conditions:</span></div>
+<div class="line"><a name="l00611"></a><span class="lineno"> 611</span>&#160;<span class="comment">*</span></div>
+<div class="line"><a name="l00612"></a><span class="lineno"> 612</span>&#160;<span class="comment">* Depending upon the possible ranges, and particularly on 16-bit</span></div>
+<div class="line"><a name="l00613"></a><span class="lineno"> 613</span>&#160;<span class="comment">* computers, care should be taken to protect from overflow.</span></div>
+<div class="line"><a name="l00614"></a><span class="lineno"> 614</span>&#160;<span class="comment">*</span></div>
+<div class="line"><a name="l00615"></a><span class="lineno"> 615</span>&#160;<span class="comment">* In the following code, &#39;long&#39; values have been used for this</span></div>
+<div class="line"><a name="l00616"></a><span class="lineno"> 616</span>&#160;<span class="comment">* purpose, instead of &#39;int&#39;.</span></div>
+<div class="line"><a name="l00617"></a><span class="lineno"> 617</span>&#160;<span class="comment">*</span></div>
+<div class="line"><a name="l00618"></a><span class="lineno"> 618</span>&#160;<span class="comment">*/</span></div>
+<div class="line"><a name="l00619"></a><span class="lineno"> 619</span>&#160;</div>
+<div class="line"><a name="l00620"></a><span class="lineno"><a class="code" href="_geometry_8cpp.html#a91433603e317e9be7f539f9757940313"> 620</a></span>&#160;<span class="preprocessor">#define DONT_INTERSECT 0</span></div>
+<div class="line"><a name="l00621"></a><span class="lineno"><a class="code" href="_geometry_8cpp.html#ac8ac7f0cba50c80aac521f0ac022e25d"> 621</a></span>&#160;<span class="preprocessor"></span><span class="preprocessor">#define DO_INTERSECT 1</span></div>
+<div class="line"><a name="l00622"></a><span class="lineno"><a class="code" href="_geometry_8cpp.html#a105caa178db222564f6fab1433ae289b"> 622</a></span>&#160;<span class="preprocessor"></span><span class="preprocessor">#define COLLINEAR 2</span></div>
+<div class="line"><a name="l00623"></a><span class="lineno"> 623</span>&#160;<span class="preprocessor"></span></div>
+<div class="line"><a name="l00624"></a><span class="lineno"><a class="code" href="_geometry_8cpp.html#a1090fdf1744085b0ccd462602b6d5d81"> 624</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">int</span> <a class="code" href="_geometry_8cpp.html#a1090fdf1744085b0ccd462602b6d5d81">SAME_SIGNS</a>(<span class="keywordtype">double</span> a, <span class="keywordtype">double</span> b)</div>
+<div class="line"><a name="l00625"></a><span class="lineno"> 625</span>&#160;{</div>
+<div class="line"><a name="l00626"></a><span class="lineno"> 626</span>&#160; <span class="keywordflow">return</span> ((a&gt;=0 &amp;&amp; b&gt;=0) || (a&lt;0 &amp;&amp; b&lt;0));</div>
+<div class="line"><a name="l00627"></a><span class="lineno"> 627</span>&#160;}</div>
+<div class="line"><a name="l00628"></a><span class="lineno"> 628</span>&#160;</div>
+<div class="line"><a name="l00629"></a><span class="lineno"> 629</span>&#160;<span class="keywordtype">int</span></div>
+<div class="line"><a name="l00630"></a><span class="lineno"><a class="code" href="_geometry_8h.html#abe89a66a9f9ef5d6a7c9feca1cfe13ed"> 630</a></span>&#160;<a class="code" href="_geometry_8cpp.html#a37f9f7b1d82170ce5136881a54b7d7d6">lines_intersect</a>(</div>
+<div class="line"><a name="l00631"></a><span class="lineno"> 631</span>&#160;<span class="comment">/* 1st line segment */</span> <span class="keywordtype">double</span> x1, <span class="keywordtype">double</span> y1, <span class="keywordtype">double</span> x2, <span class="keywordtype">double</span> y2,</div>
+<div class="line"><a name="l00632"></a><span class="lineno"> 632</span>&#160;<span class="comment">/* 2nd line segment */</span> <span class="keywordtype">double</span> x3, <span class="keywordtype">double</span> y3, <span class="keywordtype">double</span> x4, <span class="keywordtype">double</span> y4,</div>
+<div class="line"><a name="l00633"></a><span class="lineno"> 633</span>&#160;<span class="comment">/* pt of intersect */</span> <span class="keywordtype">double</span>&amp; ix, <span class="keywordtype">double</span>&amp; iy)</div>
+<div class="line"><a name="l00634"></a><span class="lineno"> 634</span>&#160;{</div>
+<div class="line"><a name="l00635"></a><span class="lineno"> 635</span>&#160; <span class="keywordtype">double</span> a1, a2, b1, b2, c1, c2; <span class="comment">/* Coefficients of line eqns. */</span></div>
+<div class="line"><a name="l00636"></a><span class="lineno"> 636</span>&#160; <span class="keywordtype">double</span> r1, r2, r3, r4; <span class="comment">/* &#39;Sign&#39; values */</span></div>
+<div class="line"><a name="l00637"></a><span class="lineno"> 637</span>&#160; <span class="keywordtype">double</span> denom, offset, num; <span class="comment">/* Intermediate values */</span></div>
+<div class="line"><a name="l00638"></a><span class="lineno"> 638</span>&#160;</div>
+<div class="line"><a name="l00639"></a><span class="lineno"> 639</span>&#160; <span class="comment">/* Compute a1, b1, c1, where line joining points 1 and 2</span></div>
+<div class="line"><a name="l00640"></a><span class="lineno"> 640</span>&#160;<span class="comment"> * is &quot;a1 x + b1 y + c1 = 0&quot;. */</span></div>
+<div class="line"><a name="l00641"></a><span class="lineno"> 641</span>&#160;</div>
+<div class="line"><a name="l00642"></a><span class="lineno"> 642</span>&#160; a1 = y2 - y1;</div>
+<div class="line"><a name="l00643"></a><span class="lineno"> 643</span>&#160; b1 = x1 - x2;</div>
+<div class="line"><a name="l00644"></a><span class="lineno"> 644</span>&#160; c1 = x2 * y1 - x1 * y2;</div>
+<div class="line"><a name="l00645"></a><span class="lineno"> 645</span>&#160;</div>
+<div class="line"><a name="l00646"></a><span class="lineno"> 646</span>&#160; <span class="comment">/* Compute r3 and r4. */</span></div>
+<div class="line"><a name="l00647"></a><span class="lineno"> 647</span>&#160;</div>
+<div class="line"><a name="l00648"></a><span class="lineno"> 648</span>&#160; r3 = a1 * x3 + b1 * y3 + c1;</div>
+<div class="line"><a name="l00649"></a><span class="lineno"> 649</span>&#160; r4 = a1 * x4 + b1 * y4 + c1;</div>
+<div class="line"><a name="l00650"></a><span class="lineno"> 650</span>&#160;</div>
+<div class="line"><a name="l00651"></a><span class="lineno"> 651</span>&#160; <span class="comment">/* Check signs of r3 and r4. If both point 3 and point 4 lie on</span></div>
+<div class="line"><a name="l00652"></a><span class="lineno"> 652</span>&#160;<span class="comment"> * same side of line 1, the line segments do not intersect. */</span></div>
+<div class="line"><a name="l00653"></a><span class="lineno"> 653</span>&#160;</div>
+<div class="line"><a name="l00654"></a><span class="lineno"> 654</span>&#160; <span class="keywordflow">if</span> ( r3 != 0 &amp;&amp;</div>
+<div class="line"><a name="l00655"></a><span class="lineno"> 655</span>&#160; r4 != 0 &amp;&amp;</div>
+<div class="line"><a name="l00656"></a><span class="lineno"> 656</span>&#160; <a class="code" href="_geometry_8cpp.html#a1090fdf1744085b0ccd462602b6d5d81">SAME_SIGNS</a>( r3, r4 ))</div>
+<div class="line"><a name="l00657"></a><span class="lineno"> 657</span>&#160; <span class="keywordflow">return</span> ( <a class="code" href="_geometry_8cpp.html#a91433603e317e9be7f539f9757940313">DONT_INTERSECT</a> );</div>
+<div class="line"><a name="l00658"></a><span class="lineno"> 658</span>&#160;</div>
+<div class="line"><a name="l00659"></a><span class="lineno"> 659</span>&#160; <span class="comment">/* Compute a2, b2, c2 */</span></div>
+<div class="line"><a name="l00660"></a><span class="lineno"> 660</span>&#160;</div>
+<div class="line"><a name="l00661"></a><span class="lineno"> 661</span>&#160; a2 = y4 - y3;</div>
+<div class="line"><a name="l00662"></a><span class="lineno"> 662</span>&#160; b2 = x3 - x4;</div>
+<div class="line"><a name="l00663"></a><span class="lineno"> 663</span>&#160; c2 = x4 * y3 - x3 * y4;</div>
+<div class="line"><a name="l00664"></a><span class="lineno"> 664</span>&#160;</div>
+<div class="line"><a name="l00665"></a><span class="lineno"> 665</span>&#160; <span class="comment">/* Compute r1 and r2 */</span></div>
+<div class="line"><a name="l00666"></a><span class="lineno"> 666</span>&#160;</div>
+<div class="line"><a name="l00667"></a><span class="lineno"> 667</span>&#160; r1 = a2 * x1 + b2 * y1 + c2;</div>
+<div class="line"><a name="l00668"></a><span class="lineno"> 668</span>&#160; r2 = a2 * x2 + b2 * y2 + c2;</div>
+<div class="line"><a name="l00669"></a><span class="lineno"> 669</span>&#160;</div>
+<div class="line"><a name="l00670"></a><span class="lineno"> 670</span>&#160; <span class="comment">/* Check signs of r1 and r2. If both point 1 and point 2 lie</span></div>
+<div class="line"><a name="l00671"></a><span class="lineno"> 671</span>&#160;<span class="comment"> * on same side of second line segment, the line segments do</span></div>
+<div class="line"><a name="l00672"></a><span class="lineno"> 672</span>&#160;<span class="comment"> * not intersect. */</span></div>
+<div class="line"><a name="l00673"></a><span class="lineno"> 673</span>&#160;</div>
+<div class="line"><a name="l00674"></a><span class="lineno"> 674</span>&#160; <span class="keywordflow">if</span> ( r1 != 0 &amp;&amp;</div>
+<div class="line"><a name="l00675"></a><span class="lineno"> 675</span>&#160; r2 != 0 &amp;&amp;</div>
+<div class="line"><a name="l00676"></a><span class="lineno"> 676</span>&#160; <a class="code" href="_geometry_8cpp.html#a1090fdf1744085b0ccd462602b6d5d81">SAME_SIGNS</a>( r1, r2 ))</div>
+<div class="line"><a name="l00677"></a><span class="lineno"> 677</span>&#160; <span class="keywordflow">return</span> ( <a class="code" href="_geometry_8cpp.html#a91433603e317e9be7f539f9757940313">DONT_INTERSECT</a> );</div>
+<div class="line"><a name="l00678"></a><span class="lineno"> 678</span>&#160;</div>
+<div class="line"><a name="l00679"></a><span class="lineno"> 679</span>&#160; <span class="comment">/* Line segments intersect: compute intersection point. */</span></div>
+<div class="line"><a name="l00680"></a><span class="lineno"> 680</span>&#160;</div>
+<div class="line"><a name="l00681"></a><span class="lineno"> 681</span>&#160; denom = a1 * b2 - a2 * b1;</div>
+<div class="line"><a name="l00682"></a><span class="lineno"> 682</span>&#160; <span class="keywordflow">if</span> ( denom == 0 )</div>
+<div class="line"><a name="l00683"></a><span class="lineno"> 683</span>&#160; <span class="keywordflow">return</span> ( <a class="code" href="_geometry_8cpp.html#a91433603e317e9be7f539f9757940313">DONT_INTERSECT</a> );</div>
+<div class="line"><a name="l00684"></a><span class="lineno"> 684</span>&#160; offset = denom &lt; 0 ? - denom / 2 : denom / 2;</div>
+<div class="line"><a name="l00685"></a><span class="lineno"> 685</span>&#160;</div>
+<div class="line"><a name="l00686"></a><span class="lineno"> 686</span>&#160; <span class="comment">/* The denom/2 is to get rounding instead of truncating. It</span></div>
+<div class="line"><a name="l00687"></a><span class="lineno"> 687</span>&#160;<span class="comment"> * is added or subtracted to the numerator, depending upon the</span></div>
+<div class="line"><a name="l00688"></a><span class="lineno"> 688</span>&#160;<span class="comment"> * sign of the numerator. */</span></div>
+<div class="line"><a name="l00689"></a><span class="lineno"> 689</span>&#160;</div>
+<div class="line"><a name="l00690"></a><span class="lineno"> 690</span>&#160; num = b1 * c2 - b2 * c1;</div>
+<div class="line"><a name="l00691"></a><span class="lineno"> 691</span>&#160; ix = ( num &lt; 0 ? num - offset : num + offset ) / denom;</div>
+<div class="line"><a name="l00692"></a><span class="lineno"> 692</span>&#160;</div>
+<div class="line"><a name="l00693"></a><span class="lineno"> 693</span>&#160; num = a2 * c1 - a1 * c2;</div>
+<div class="line"><a name="l00694"></a><span class="lineno"> 694</span>&#160; iy = ( num &lt; 0 ? num - offset : num + offset ) / denom;</div>
+<div class="line"><a name="l00695"></a><span class="lineno"> 695</span>&#160;</div>
+<div class="line"><a name="l00696"></a><span class="lineno"> 696</span>&#160; <span class="keywordflow">return</span> ( <a class="code" href="_geometry_8cpp.html#ac8ac7f0cba50c80aac521f0ac022e25d">DO_INTERSECT</a> );</div>
+<div class="line"><a name="l00697"></a><span class="lineno"> 697</span>&#160;}</div>
+<div class="line"><a name="l00698"></a><span class="lineno"> 698</span>&#160;</div>
+</div><!-- fragment --></div><!-- contents -->
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+ <li class="navelem"><a class="el" href="dir_d6625d0f3efd9eb70ff961583505095b.html">nGenEx</a></li><li class="navelem"><a class="el" href="_geometry_8cpp.html">Geometry.cpp</a></li>
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