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 <span id="projectnumber">2.3.0</span>
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<div id="projectbrief">A 2D Physics Engine for Games</div>
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<li class="navelem"><a class="el" href="dir_a7f953fea4e008d17e00594b3bbaff29.html">Box2D</a></li><li class="navelem"><a class="el" href="dir_2bb440aa7e31c6a1fa7299279b8cd0fb.html">Common</a></li> </ul>
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<div class="title">b2Math.h</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/*</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">* Copyright (c) 2006-2009 Erin Catto http://www.box2d.org</span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">*</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">* This software is provided 'as-is', without any express or implied</span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">* warranty. In no event will the authors be held liable for any damages</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">* arising from the use of this software.</span></div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">* Permission is granted to anyone to use this software for any purpose,</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">* including commercial applications, and to alter it and redistribute it</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">* freely, subject to the following restrictions:</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">* 1. The origin of this software must not be misrepresented; you must not</span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">* claim that you wrote the original software. If you use this software</span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">* in a product, an acknowledgment in the product documentation would be</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment">* appreciated but is not required.</span></div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">* 2. Altered source versions must be plainly marked as such, and must not be</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">* misrepresented as being the original software.</span></div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">* 3. This notice may not be removed or altered from any source distribution.</span></div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment">*/</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> </div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor">#ifndef B2_MATH_H</span></div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor">#define B2_MATH_H</span></div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> </div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#include <<a class="code" href="b2_settings_8h.html">Box2D/Common/b2Settings.h</a>></span></div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="preprocessor">#include <math.h></span></div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> </div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> b2IsValid(float32 x)</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>  int32 ix = *<span class="keyword">reinterpret_cast<</span>int32*<span class="keyword">></span>(&x);</div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  <span class="keywordflow">return</span> (ix & 0x7f800000) != 0x7f800000;</div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span> }</div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span> </div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="keyword">inline</span> float32 b2InvSqrt(float32 x)</div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span> {</div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keyword">union</span></div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  {</div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  float32 x;</div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  int32 i;</div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  } convert;</div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span> </div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  convert.x = x;</div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  float32 xhalf = 0.5f * x;</div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  convert.i = 0x5f3759df - (convert.i >> 1);</div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  x = convert.x;</div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  x = x * (1.5f - xhalf * x * x);</div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="keywordflow">return</span> x;</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> </div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="preprocessor">#define b2Sqrt(x) sqrtf(x)</span></div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="preprocessor">#define b2Atan2(y, x) atan2f(y, x)</span></div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span> </div><div class="line"><a name="l00053"></a><span class="lineno"><a class="line" href="structb2_vec2.html"> 53</a></span> <span class="keyword">struct </span><a class="code" href="structb2_vec2.html">b2Vec2</a></div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span> {</div><div class="line"><a name="l00056"></a><span class="lineno"><a class="line" href="structb2_vec2.html#a9171b31deb83af96872f99689939a12f"> 56</a></span>  <a class="code" href="structb2_vec2.html#a9171b31deb83af96872f99689939a12f">b2Vec2</a>() {}</div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span> </div><div class="line"><a name="l00059"></a><span class="lineno"><a class="line" href="structb2_vec2.html#aa8a2f026420a84bbbc62f3a3de2041d6"> 59</a></span>  <a class="code" href="structb2_vec2.html#aa8a2f026420a84bbbc62f3a3de2041d6">b2Vec2</a>(float32 x, float32 y) : x(x), y(y) {}</div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span> </div><div class="line"><a name="l00062"></a><span class="lineno"><a class="line" href="structb2_vec2.html#a5c6cbe27cfb29c6dbb29b9a3285b88d0"> 62</a></span>  <span class="keywordtype">void</span> <a class="code" href="structb2_vec2.html#a5c6cbe27cfb29c6dbb29b9a3285b88d0">SetZero</a>() { x = 0.0f; y = 0.0f; }</div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span> </div><div class="line"><a name="l00065"></a><span class="lineno"><a class="line" href="structb2_vec2.html#a4d61640a645e470a50b451307d8e94c3"> 65</a></span>  <span class="keywordtype">void</span> <a class="code" href="structb2_vec2.html#a4d61640a645e470a50b451307d8e94c3">Set</a>(float32 x_, float32 y_) { x = x_; y = y_; }</div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span> </div><div class="line"><a name="l00068"></a><span class="lineno"><a class="line" href="structb2_vec2.html#a6cb15514ea571b4ddf73b6829551a127"> 68</a></span>  <a class="code" href="structb2_vec2.html">b2Vec2</a> <a class="code" href="structb2_vec2.html#a6cb15514ea571b4ddf73b6829551a127">operator -</a>()<span class="keyword"> const </span>{ <a class="code" href="structb2_vec2.html">b2Vec2</a> v; v.<a class="code" href="structb2_vec2.html#a4d61640a645e470a50b451307d8e94c3">Set</a>(-x, -y); <span class="keywordflow">return</span> v; }</div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  </div><div class="line"><a name="l00071"></a><span class="lineno"><a class="line" href="structb2_vec2.html#a543b5264d17df35448632071f8ae7e4d"> 71</a></span>  float32 <a class="code" href="structb2_vec2.html#a543b5264d17df35448632071f8ae7e4d">operator () </a>(int32 i)<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> (&x)[i];</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="l00077"></a><span class="lineno"><a class="line" href="structb2_vec2.html#a50b39580d9f479e17b23ce3cb8efbac6"> 77</a></span>  float32& <a class="code" href="structb2_vec2.html#a543b5264d17df35448632071f8ae7e4d">operator () </a>(int32 i)</div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  {</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keywordflow">return</span> (&x)[i];</div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  }</div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span> </div><div class="line"><a name="l00083"></a><span class="lineno"><a class="line" href="structb2_vec2.html#a590789342e22ac1e7f9c1a63a2778b6d"> 83</a></span>  <span class="keywordtype">void</span> <a class="code" href="structb2_vec2.html#a590789342e22ac1e7f9c1a63a2778b6d">operator += </a>(<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& v)</div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  {</div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  x += v.x; y += v.y;</div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  }</div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  </div><div class="line"><a name="l00089"></a><span class="lineno"><a class="line" href="structb2_vec2.html#a6b48cab4695a979ae40b7613aedc8b17"> 89</a></span>  <span class="keywordtype">void</span> <a class="code" href="structb2_vec2.html#a6b48cab4695a979ae40b7613aedc8b17">operator -= </a>(<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& v)</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>  x -= v.x; y -= v.y;</div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  }</div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span> </div><div class="line"><a name="l00095"></a><span class="lineno"><a class="line" href="structb2_vec2.html#a7097696dce578322928f4535b34f1c6b"> 95</a></span>  <span class="keywordtype">void</span> <a class="code" href="structb2_vec2.html#a7097696dce578322928f4535b34f1c6b">operator *= </a>(float32 a)</div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  {</div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  x *= a; y *= a;</div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  }</div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span> </div><div class="line"><a name="l00101"></a><span class="lineno"><a class="line" href="structb2_vec2.html#a04cb9ac9e845a59f4212b2d7149fa3d9"> 101</a></span>  float32 <a class="code" href="structb2_vec2.html#a04cb9ac9e845a59f4212b2d7149fa3d9">Length</a>()<span class="keyword"> const</span></div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="keyword"> </span>{</div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keywordflow">return</span> b2Sqrt(x * x + y * y);</div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  }</div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span> </div><div class="line"><a name="l00108"></a><span class="lineno"><a class="line" href="structb2_vec2.html#af8a081dac7eea7800fdbfbf95ac9e395"> 108</a></span>  float32 <a class="code" href="structb2_vec2.html#af8a081dac7eea7800fdbfbf95ac9e395">LengthSquared</a>()<span class="keyword"> const</span></div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="keyword"> </span>{</div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keywordflow">return</span> x * x + y * y;</div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  }</div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span> </div><div class="line"><a name="l00114"></a><span class="lineno"><a class="line" href="structb2_vec2.html#adda78c92f318fe53d8a53f9b5cfd8e41"> 114</a></span>  float32 <a class="code" href="structb2_vec2.html#adda78c92f318fe53d8a53f9b5cfd8e41">Normalize</a>()</div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  {</div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  float32 length = <a class="code" href="structb2_vec2.html#a04cb9ac9e845a59f4212b2d7149fa3d9">Length</a>();</div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keywordflow">if</span> (length < b2_epsilon)</div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  {</div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keywordflow">return</span> 0.0f;</div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  }</div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  float32 invLength = 1.0f / length;</div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  x *= invLength;</div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  y *= invLength;</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="keywordflow">return</span> length;</div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  }</div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span> </div><div class="line"><a name="l00129"></a><span class="lineno"><a class="line" href="structb2_vec2.html#abad59bf9a0269f02cda9dc919592c0ee"> 129</a></span>  <span class="keywordtype">bool</span> <a class="code" href="structb2_vec2.html#abad59bf9a0269f02cda9dc919592c0ee">IsValid</a>()<span class="keyword"> const</span></div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="keyword"> </span>{</div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keywordflow">return</span> b2IsValid(x) && b2IsValid(y);</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  }</div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span> </div><div class="line"><a name="l00135"></a><span class="lineno"><a class="line" href="structb2_vec2.html#aaf36e082a20368b24edb635511872a74"> 135</a></span>  <a class="code" href="structb2_vec2.html">b2Vec2</a> <a class="code" href="structb2_vec2.html#aaf36e082a20368b24edb635511872a74">Skew</a>()<span class="keyword"> const</span></div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="keyword"> </span>{</div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec2.html#a9171b31deb83af96872f99689939a12f">b2Vec2</a>(-y, x);</div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  }</div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span> </div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  float32 x, y;</div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span> };</div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span> </div><div class="line"><a name="l00144"></a><span class="lineno"><a class="line" href="structb2_vec3.html"> 144</a></span> <span class="keyword">struct </span><a class="code" href="structb2_vec3.html">b2Vec3</a></div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span> {</div><div class="line"><a name="l00147"></a><span class="lineno"><a class="line" href="structb2_vec3.html#a837423f66d6fb72d815e7390c09938b9"> 147</a></span>  <a class="code" href="structb2_vec3.html#a837423f66d6fb72d815e7390c09938b9">b2Vec3</a>() {}</div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span> </div><div class="line"><a name="l00150"></a><span class="lineno"><a class="line" href="structb2_vec3.html#a47df55b26ab254dcf42a16638c7feeeb"> 150</a></span>  <a class="code" href="structb2_vec3.html#a47df55b26ab254dcf42a16638c7feeeb">b2Vec3</a>(float32 x, float32 y, float32 z) : x(x), y(y), z(z) {}</div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span> </div><div class="line"><a name="l00153"></a><span class="lineno"><a class="line" href="structb2_vec3.html#a5a459ed49f1910a347ca247f848a2dd8"> 153</a></span>  <span class="keywordtype">void</span> <a class="code" href="structb2_vec3.html#a5a459ed49f1910a347ca247f848a2dd8">SetZero</a>() { x = 0.0f; y = 0.0f; z = 0.0f; }</div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span> </div><div class="line"><a name="l00156"></a><span class="lineno"><a class="line" href="structb2_vec3.html#a12a1bc14bbe722dfb175a492d2d00a79"> 156</a></span>  <span class="keywordtype">void</span> <a class="code" href="structb2_vec3.html#a12a1bc14bbe722dfb175a492d2d00a79">Set</a>(float32 x_, float32 y_, float32 z_) { x = x_; y = y_; z = z_; }</div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span> </div><div class="line"><a name="l00159"></a><span class="lineno"><a class="line" href="structb2_vec3.html#a396e2b5b3c53a502859ff80544c27db8"> 159</a></span>  <a class="code" href="structb2_vec3.html">b2Vec3</a> <a class="code" href="structb2_vec3.html#a396e2b5b3c53a502859ff80544c27db8">operator -</a>()<span class="keyword"> const </span>{ <a class="code" href="structb2_vec3.html">b2Vec3</a> v; v.<a class="code" href="structb2_vec3.html#a12a1bc14bbe722dfb175a492d2d00a79">Set</a>(-x, -y, -z); <span class="keywordflow">return</span> v; }</div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span> </div><div class="line"><a name="l00162"></a><span class="lineno"><a class="line" href="structb2_vec3.html#a2aaeed3f5308aad85d19c5f0efc72641"> 162</a></span>  <span class="keywordtype">void</span> <a class="code" href="structb2_vec3.html#a2aaeed3f5308aad85d19c5f0efc72641">operator += </a>(<span class="keyword">const</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>& v)</div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  {</div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  x += v.x; y += v.y; z += v.z;</div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  }</div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span> </div><div class="line"><a name="l00168"></a><span class="lineno"><a class="line" href="structb2_vec3.html#a9e5b535548e1c5dfc0dc258d08f5ca32"> 168</a></span>  <span class="keywordtype">void</span> <a class="code" href="structb2_vec3.html#a9e5b535548e1c5dfc0dc258d08f5ca32">operator -= </a>(<span class="keyword">const</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>& v)</div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  {</div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  x -= v.x; y -= v.y; z -= v.z;</div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  }</div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span> </div><div class="line"><a name="l00174"></a><span class="lineno"><a class="line" href="structb2_vec3.html#aaa9aa20195cd0ee53c7176a9a9b02389"> 174</a></span>  <span class="keywordtype">void</span> <a class="code" href="structb2_vec3.html#aaa9aa20195cd0ee53c7176a9a9b02389">operator *= </a>(float32 s)</div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  {</div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  x *= s; y *= s; z *= s;</div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  }</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>  float32 x, y, z;</div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span> };</div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span> </div><div class="line"><a name="l00183"></a><span class="lineno"><a class="line" href="structb2_mat22.html"> 183</a></span> <span class="keyword">struct </span><a class="code" href="structb2_mat22.html">b2Mat22</a></div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span> {</div><div class="line"><a name="l00186"></a><span class="lineno"><a class="line" href="structb2_mat22.html#ac3e10f6d457c8dab9062ba378f66bc4d"> 186</a></span>  <a class="code" href="structb2_mat22.html#ac3e10f6d457c8dab9062ba378f66bc4d">b2Mat22</a>() {}</div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span> </div><div class="line"><a name="l00189"></a><span class="lineno"><a class="line" href="structb2_mat22.html#abd674c6d92e26962977f34bcd92ff24d"> 189</a></span>  <a class="code" href="structb2_mat22.html#abd674c6d92e26962977f34bcd92ff24d">b2Mat22</a>(<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& c1, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& c2)</div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  {</div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  ex = c1;</div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  ey = c2;</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> </div><div class="line"><a name="l00196"></a><span class="lineno"><a class="line" href="structb2_mat22.html#a41d5d8743bda32cb8c6e212528934810"> 196</a></span>  <a class="code" href="structb2_mat22.html#a41d5d8743bda32cb8c6e212528934810">b2Mat22</a>(float32 a11, float32 a12, float32 a21, float32 a22)</div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  {</div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  ex.x = a11; ex.y = a21;</div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  ey.x = a12; ey.y = a22;</div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  }</div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span> </div><div class="line"><a name="l00203"></a><span class="lineno"><a class="line" href="structb2_mat22.html#aed3bee1de38a0b3f36e21c90faa24112"> 203</a></span>  <span class="keywordtype">void</span> <a class="code" href="structb2_mat22.html#aed3bee1de38a0b3f36e21c90faa24112">Set</a>(<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& c1, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& c2)</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>  ex = c1;</div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  ey = c2;</div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  }</div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span> </div><div class="line"><a name="l00210"></a><span class="lineno"><a class="line" href="structb2_mat22.html#a7192f063b771ac9ded060e41df890509"> 210</a></span>  <span class="keywordtype">void</span> <a class="code" href="structb2_mat22.html#a7192f063b771ac9ded060e41df890509">SetIdentity</a>()</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>  ex.x = 1.0f; ey.x = 0.0f;</div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  ex.y = 0.0f; ey.y = 1.0f;</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="l00217"></a><span class="lineno"><a class="line" href="structb2_mat22.html#aaeae95f61cf3171ffb94703980e3594b"> 217</a></span>  <span class="keywordtype">void</span> <a class="code" href="structb2_mat22.html#aaeae95f61cf3171ffb94703980e3594b">SetZero</a>()</div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  {</div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  ex.x = 0.0f; ey.x = 0.0f;</div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  ex.y = 0.0f; ey.y = 0.0f;</div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  }</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>  <a class="code" href="structb2_mat22.html">b2Mat22</a> GetInverse()<span class="keyword"> const</span></div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span> <span class="keyword"> </span>{</div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  float32 a = ex.x, b = ey.x, c = ex.y, d = ey.y;</div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <a class="code" href="structb2_mat22.html">b2Mat22</a> B;</div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  float32 det = a * d - b * c;</div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <span class="keywordflow">if</span> (det != 0.0f)</div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  {</div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  det = 1.0f / det;</div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  }</div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  B.ex.x = det * d; B.ey.x = -det * b;</div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  B.ex.y = -det * c; B.ey.y = det * a;</div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keywordflow">return</span> B;</div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  }</div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span> </div><div class="line"><a name="l00239"></a><span class="lineno"><a class="line" href="structb2_mat22.html#a3313c8d135c01fbf74e7fea31f1ea4c1"> 239</a></span>  <a class="code" href="structb2_vec2.html">b2Vec2</a> <a class="code" href="structb2_mat22.html#a3313c8d135c01fbf74e7fea31f1ea4c1">Solve</a>(<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& b)<span class="keyword"> const</span></div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="keyword"> </span>{</div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  float32 a11 = ex.x, a12 = ey.x, a21 = ex.y, a22 = ey.y;</div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  float32 det = a11 * a22 - a12 * a21;</div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="keywordflow">if</span> (det != 0.0f)</div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  {</div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  det = 1.0f / det;</div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  }</div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <a class="code" href="structb2_vec2.html">b2Vec2</a> x;</div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  x.x = det * (a22 * b.x - a12 * b.y);</div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  x.y = det * (a11 * b.y - a21 * b.x);</div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <span class="keywordflow">return</span> x;</div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  }</div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span> </div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <a class="code" href="structb2_vec2.html">b2Vec2</a> ex, ey;</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="l00257"></a><span class="lineno"><a class="line" href="structb2_mat33.html"> 257</a></span> <span class="keyword">struct </span><a class="code" href="structb2_mat33.html">b2Mat33</a></div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span> {</div><div class="line"><a name="l00260"></a><span class="lineno"><a class="line" href="structb2_mat33.html#a1f4d7ddf1c8a202fc08ec64dfe191463"> 260</a></span>  <a class="code" href="structb2_mat33.html#a1f4d7ddf1c8a202fc08ec64dfe191463">b2Mat33</a>() {}</div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span> </div><div class="line"><a name="l00263"></a><span class="lineno"><a class="line" href="structb2_mat33.html#a36d99a037008776c8d09fe0aeb5c759c"> 263</a></span>  <a class="code" href="structb2_mat33.html#a36d99a037008776c8d09fe0aeb5c759c">b2Mat33</a>(<span class="keyword">const</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>& c1, <span class="keyword">const</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>& c2, <span class="keyword">const</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>& c3)</div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  {</div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  ex = c1;</div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  ey = c2;</div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  ez = c3;</div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  }</div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span> </div><div class="line"><a name="l00271"></a><span class="lineno"><a class="line" href="structb2_mat33.html#a42fc6953b025e1c8b59717d0ee7accde"> 271</a></span>  <span class="keywordtype">void</span> <a class="code" href="structb2_mat33.html#a42fc6953b025e1c8b59717d0ee7accde">SetZero</a>()</div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  {</div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  ex.<a class="code" href="structb2_vec3.html#a5a459ed49f1910a347ca247f848a2dd8">SetZero</a>();</div><div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  ey.<a class="code" href="structb2_vec3.html#a5a459ed49f1910a347ca247f848a2dd8">SetZero</a>();</div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  ez.<a class="code" href="structb2_vec3.html#a5a459ed49f1910a347ca247f848a2dd8">SetZero</a>();</div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  }</div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span> </div><div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <a class="code" href="structb2_vec3.html">b2Vec3</a> <a class="code" href="structb2_mat33.html#a2ce48f409ba5951a04da821dada9e285">Solve33</a>(<span class="keyword">const</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>& b) <span class="keyword">const</span>;</div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span> </div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <a class="code" href="structb2_vec2.html">b2Vec2</a> <a class="code" href="structb2_mat33.html#acdf892aab7e26283f8aa600ade91dcef">Solve22</a>(<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& b) <span class="keyword">const</span>;</div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span> </div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="keywordtype">void</span> <a class="code" href="structb2_mat33.html#aa020bfd08e28c4cecda303ba335fe517">GetInverse22</a>(<a class="code" href="structb2_mat33.html">b2Mat33</a>* M) <span class="keyword">const</span>;</div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span> </div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="keywordtype">void</span> <a class="code" href="structb2_mat33.html#a2620944663233096d3b82bc4b1a991e9">GetSymInverse33</a>(<a class="code" href="structb2_mat33.html">b2Mat33</a>* M) <span class="keyword">const</span>;</div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span> </div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <a class="code" href="structb2_vec3.html">b2Vec3</a> ex, ey, ez;</div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span> };</div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span> </div><div class="line"><a name="l00299"></a><span class="lineno"><a class="line" href="structb2_rot.html"> 299</a></span> <span class="keyword">struct </span><a class="code" href="structb2_rot.html">b2Rot</a></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>  <a class="code" href="structb2_rot.html">b2Rot</a>() {}</div><div class="line"><a name="l00302"></a><span class="lineno"> 302</span> </div><div class="line"><a name="l00304"></a><span class="lineno"><a class="line" href="structb2_rot.html#aa40dda6d390a2f54c793c63027a9b46e"> 304</a></span>  <span class="keyword">explicit</span> <a class="code" href="structb2_rot.html#aa40dda6d390a2f54c793c63027a9b46e">b2Rot</a>(float32 angle)</div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  {</div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a> = sinf(angle);</div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  c = cosf(angle);</div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  }</div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span> </div><div class="line"><a name="l00312"></a><span class="lineno"><a class="line" href="structb2_rot.html#acde9186de0a4a7397bf8ef714408ad60"> 312</a></span>  <span class="keywordtype">void</span> <a class="code" href="structb2_rot.html#acde9186de0a4a7397bf8ef714408ad60">Set</a>(float32 angle)</div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  {</div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a> = sinf(angle);</div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  c = cosf(angle);</div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  }</div><div class="line"><a name="l00318"></a><span class="lineno"> 318</span> </div><div class="line"><a name="l00320"></a><span class="lineno"><a class="line" href="structb2_rot.html#a7f534cb7ece8d325662d7d0e27d4f617"> 320</a></span>  <span class="keywordtype">void</span> <a class="code" href="structb2_rot.html#a7f534cb7ece8d325662d7d0e27d4f617">SetIdentity</a>()</div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  {</div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a> = 0.0f;</div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  c = 1.0f;</div><div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  }</div><div class="line"><a name="l00325"></a><span class="lineno"> 325</span> </div><div class="line"><a name="l00327"></a><span class="lineno"><a class="line" href="structb2_rot.html#a45031fccfa11d3b3a09154008ce28b39"> 327</a></span>  float32 <a class="code" href="structb2_rot.html#a45031fccfa11d3b3a09154008ce28b39">GetAngle</a>()<span class="keyword"> const</span></div><div class="line"><a name="l00328"></a><span class="lineno"> 328</span> <span class="keyword"> </span>{</div><div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <span class="keywordflow">return</span> b2Atan2(<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a>, c);</div><div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  }</div><div class="line"><a name="l00331"></a><span class="lineno"> 331</span> </div><div class="line"><a name="l00333"></a><span class="lineno"><a class="line" href="structb2_rot.html#a952a5555c1f68ce3e39ac992fcf4eba9"> 333</a></span>  <a class="code" href="structb2_vec2.html">b2Vec2</a> <a class="code" href="structb2_rot.html#a952a5555c1f68ce3e39ac992fcf4eba9">GetXAxis</a>()<span class="keyword"> const</span></div><div class="line"><a name="l00334"></a><span class="lineno"> 334</span> <span class="keyword"> </span>{</div><div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>(c, <a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a>);</div><div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  }</div><div class="line"><a name="l00337"></a><span class="lineno"> 337</span> </div><div class="line"><a name="l00339"></a><span class="lineno"><a class="line" href="structb2_rot.html#ab057c4e9dc821099949391a6ded36dd6"> 339</a></span>  <a class="code" href="structb2_vec2.html">b2Vec2</a> <a class="code" href="structb2_rot.html#ab057c4e9dc821099949391a6ded36dd6">GetYAxis</a>()<span class="keyword"> const</span></div><div class="line"><a name="l00340"></a><span class="lineno"> 340</span> <span class="keyword"> </span>{</div><div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>(-<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a>, c);</div><div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  }</div><div class="line"><a name="l00343"></a><span class="lineno"> 343</span> </div><div class="line"><a name="l00345"></a><span class="lineno"><a class="line" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce"> 345</a></span>  float32 <a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a>, c;</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="l00350"></a><span class="lineno"><a class="line" href="structb2_transform.html"> 350</a></span> <span class="keyword">struct </span><a class="code" href="structb2_transform.html">b2Transform</a></div><div class="line"><a name="l00351"></a><span class="lineno"> 351</span> {</div><div class="line"><a name="l00353"></a><span class="lineno"><a class="line" href="structb2_transform.html#a765a2e5c692a2e1d05c7a5441019373d"> 353</a></span>  <a class="code" href="structb2_transform.html#a765a2e5c692a2e1d05c7a5441019373d">b2Transform</a>() {}</div><div class="line"><a name="l00354"></a><span class="lineno"> 354</span> </div><div class="line"><a name="l00356"></a><span class="lineno"><a class="line" href="structb2_transform.html#a823e190e4810e35e8100f4414d0bef62"> 356</a></span>  <a class="code" href="structb2_transform.html#a823e190e4810e35e8100f4414d0bef62">b2Transform</a>(<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& position, <span class="keyword">const</span> <a class="code" href="structb2_rot.html">b2Rot</a>& rotation) : p(position), q(rotation) {}</div><div class="line"><a name="l00357"></a><span class="lineno"> 357</span> </div><div class="line"><a name="l00359"></a><span class="lineno"><a class="line" href="structb2_transform.html#af92af4ec6833552b1b22a6ca6d4f5644"> 359</a></span>  <span class="keywordtype">void</span> <a class="code" href="structb2_transform.html#af92af4ec6833552b1b22a6ca6d4f5644">SetIdentity</a>()</div><div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  {</div><div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  p.<a class="code" href="structb2_vec2.html#a5c6cbe27cfb29c6dbb29b9a3285b88d0">SetZero</a>();</div><div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  q.<a class="code" href="structb2_rot.html#a7f534cb7ece8d325662d7d0e27d4f617">SetIdentity</a>();</div><div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  }</div><div class="line"><a name="l00364"></a><span class="lineno"> 364</span> </div><div class="line"><a name="l00366"></a><span class="lineno"><a class="line" href="structb2_transform.html#a4db696a0b3fada95f95cde3e7e85ced9"> 366</a></span>  <span class="keywordtype">void</span> <a class="code" href="structb2_transform.html#a4db696a0b3fada95f95cde3e7e85ced9">Set</a>(<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& position, float32 angle)</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>  p = position;</div><div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  q.<a class="code" href="structb2_rot.html#acde9186de0a4a7397bf8ef714408ad60">Set</a>(angle);</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="l00372"></a><span class="lineno"> 372</span>  <a class="code" href="structb2_vec2.html">b2Vec2</a> p;</div><div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  <a class="code" href="structb2_rot.html">b2Rot</a> q;</div><div class="line"><a name="l00374"></a><span class="lineno"> 374</span> };</div><div class="line"><a name="l00375"></a><span class="lineno"> 375</span> </div><div class="line"><a name="l00380"></a><span class="lineno"><a class="line" href="structb2_sweep.html"> 380</a></span> <span class="keyword">struct </span><a class="code" href="structb2_sweep.html">b2Sweep</a></div><div class="line"><a name="l00381"></a><span class="lineno"> 381</span> {</div><div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  <span class="keywordtype">void</span> <a class="code" href="structb2_sweep.html#a22ae50509de51876aefc48cd76248c61">GetTransform</a>(<a class="code" href="structb2_transform.html">b2Transform</a>* xfb, float32 beta) <span class="keyword">const</span>;</div><div class="line"><a name="l00385"></a><span class="lineno"> 385</span> </div><div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  <span class="keywordtype">void</span> <a class="code" href="structb2_sweep.html#a35eb9b976ca87c9b8d758bec070c6c06">Advance</a>(float32 alpha);</div><div class="line"><a name="l00389"></a><span class="lineno"> 389</span> </div><div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  <span class="keywordtype">void</span> <a class="code" href="structb2_sweep.html#ad66a3086bc7656df9cf7454013a2f61b">Normalize</a>();</div><div class="line"><a name="l00392"></a><span class="lineno"> 392</span> </div><div class="line"><a name="l00393"></a><span class="lineno"><a class="line" href="structb2_sweep.html#a4bcc302cf78771896d6256fc53f2f8be"> 393</a></span>  <a class="code" href="structb2_vec2.html">b2Vec2</a> <a class="code" href="structb2_sweep.html#a4bcc302cf78771896d6256fc53f2f8be">localCenter</a>; </div><div class="line"><a name="l00394"></a><span class="lineno"><a class="line" href="structb2_sweep.html#a1b5402e01b92cc82473389fc6f0375c3"> 394</a></span>  <a class="code" href="structb2_vec2.html">b2Vec2</a> c0, <a class="code" href="structb2_sweep.html#a1b5402e01b92cc82473389fc6f0375c3">c</a>; </div><div class="line"><a name="l00395"></a><span class="lineno"><a class="line" href="structb2_sweep.html#afa96bacc91dd3c92ae716a45512332d6"> 395</a></span>  float32 a0, <a class="code" href="structb2_sweep.html#afa96bacc91dd3c92ae716a45512332d6">a</a>; </div><div class="line"><a name="l00396"></a><span class="lineno"> 396</span> </div><div class="line"><a name="l00399"></a><span class="lineno"><a class="line" href="structb2_sweep.html#aa5f8ab90178b58bc0777096cbc6b91cf"> 399</a></span>  float32 <a class="code" href="structb2_sweep.html#aa5f8ab90178b58bc0777096cbc6b91cf">alpha0</a>;</div><div class="line"><a name="l00400"></a><span class="lineno"> 400</span> };</div><div class="line"><a name="l00401"></a><span class="lineno"> 401</span> </div><div class="line"><a name="l00403"></a><span class="lineno"> 403</span> <span class="keyword">extern</span> <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a> b2Vec2_zero;</div><div class="line"><a name="l00404"></a><span class="lineno"> 404</span> </div><div class="line"><a name="l00406"></a><span class="lineno"> 406</span> <span class="keyword">inline</span> float32 b2Dot(<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& a, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& b)</div><div class="line"><a name="l00407"></a><span class="lineno"> 407</span> {</div><div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  <span class="keywordflow">return</span> a.x * b.x + a.y * b.y;</div><div class="line"><a name="l00409"></a><span class="lineno"> 409</span> }</div><div class="line"><a name="l00410"></a><span class="lineno"> 410</span> </div><div class="line"><a name="l00412"></a><span class="lineno"> 412</span> <span class="keyword">inline</span> float32 b2Cross(<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& a, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& b)</div><div class="line"><a name="l00413"></a><span class="lineno"> 413</span> {</div><div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  <span class="keywordflow">return</span> a.x * b.y - a.y * b.x;</div><div class="line"><a name="l00415"></a><span class="lineno"> 415</span> }</div><div class="line"><a name="l00416"></a><span class="lineno"> 416</span> </div><div class="line"><a name="l00419"></a><span class="lineno"> 419</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec2.html">b2Vec2</a> b2Cross(<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& a, float32 s)</div><div class="line"><a name="l00420"></a><span class="lineno"> 420</span> {</div><div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>(s * a.y, -s * a.x);</div><div class="line"><a name="l00422"></a><span class="lineno"> 422</span> }</div><div class="line"><a name="l00423"></a><span class="lineno"> 423</span> </div><div class="line"><a name="l00426"></a><span class="lineno"> 426</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec2.html">b2Vec2</a> b2Cross(float32 s, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& a)</div><div class="line"><a name="l00427"></a><span class="lineno"> 427</span> {</div><div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>(-s * a.y, s * a.x);</div><div class="line"><a name="l00429"></a><span class="lineno"> 429</span> }</div><div class="line"><a name="l00430"></a><span class="lineno"> 430</span> </div><div class="line"><a name="l00433"></a><span class="lineno"> 433</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec2.html">b2Vec2</a> b2Mul(<span class="keyword">const</span> <a class="code" href="structb2_mat22.html">b2Mat22</a>& A, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& v)</div><div class="line"><a name="l00434"></a><span class="lineno"> 434</span> {</div><div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>(A.ex.x * v.x + A.ey.x * v.y, A.ex.y * v.x + A.ey.y * v.y);</div><div class="line"><a name="l00436"></a><span class="lineno"> 436</span> }</div><div class="line"><a name="l00437"></a><span class="lineno"> 437</span> </div><div class="line"><a name="l00440"></a><span class="lineno"> 440</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec2.html">b2Vec2</a> b2MulT(<span class="keyword">const</span> <a class="code" href="structb2_mat22.html">b2Mat22</a>& A, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& v)</div><div class="line"><a name="l00441"></a><span class="lineno"> 441</span> {</div><div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>(b2Dot(v, A.ex), b2Dot(v, A.ey));</div><div class="line"><a name="l00443"></a><span class="lineno"> 443</span> }</div><div class="line"><a name="l00444"></a><span class="lineno"> 444</span> </div><div class="line"><a name="l00446"></a><span class="lineno"> 446</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec2.html">b2Vec2</a> operator + (<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& a, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& b)</div><div class="line"><a name="l00447"></a><span class="lineno"> 447</span> {</div><div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>(a.x + b.x, a.y + b.y);</div><div class="line"><a name="l00449"></a><span class="lineno"> 449</span> }</div><div class="line"><a name="l00450"></a><span class="lineno"> 450</span> </div><div class="line"><a name="l00452"></a><span class="lineno"> 452</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec2.html">b2Vec2</a> operator - (<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& a, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& b)</div><div class="line"><a name="l00453"></a><span class="lineno"> 453</span> {</div><div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>(a.x - b.x, a.y - b.y);</div><div class="line"><a name="l00455"></a><span class="lineno"> 455</span> }</div><div class="line"><a name="l00456"></a><span class="lineno"> 456</span> </div><div class="line"><a name="l00457"></a><span class="lineno"> 457</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec2.html">b2Vec2</a> operator * (float32 s, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& a)</div><div class="line"><a name="l00458"></a><span class="lineno"> 458</span> {</div><div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>(s * a.x, s * a.y);</div><div class="line"><a name="l00460"></a><span class="lineno"> 460</span> }</div><div class="line"><a name="l00461"></a><span class="lineno"> 461</span> </div><div class="line"><a name="l00462"></a><span class="lineno"> 462</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator == (<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& a, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& b)</div><div class="line"><a name="l00463"></a><span class="lineno"> 463</span> {</div><div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  <span class="keywordflow">return</span> a.x == b.x && a.y == b.y;</div><div class="line"><a name="l00465"></a><span class="lineno"> 465</span> }</div><div class="line"><a name="l00466"></a><span class="lineno"> 466</span> </div><div class="line"><a name="l00467"></a><span class="lineno"> 467</span> <span class="keyword">inline</span> float32 b2Distance(<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& a, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& b)</div><div class="line"><a name="l00468"></a><span class="lineno"> 468</span> {</div><div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  <a class="code" href="structb2_vec2.html">b2Vec2</a> c = a - b;</div><div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  <span class="keywordflow">return</span> c.<a class="code" href="structb2_vec2.html#a04cb9ac9e845a59f4212b2d7149fa3d9">Length</a>();</div><div class="line"><a name="l00471"></a><span class="lineno"> 471</span> }</div><div class="line"><a name="l00472"></a><span class="lineno"> 472</span> </div><div class="line"><a name="l00473"></a><span class="lineno"> 473</span> <span class="keyword">inline</span> float32 b2DistanceSquared(<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& a, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& b)</div><div class="line"><a name="l00474"></a><span class="lineno"> 474</span> {</div><div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  <a class="code" href="structb2_vec2.html">b2Vec2</a> c = a - b;</div><div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  <span class="keywordflow">return</span> b2Dot(c, c);</div><div class="line"><a name="l00477"></a><span class="lineno"> 477</span> }</div><div class="line"><a name="l00478"></a><span class="lineno"> 478</span> </div><div class="line"><a name="l00479"></a><span class="lineno"> 479</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec3.html">b2Vec3</a> operator * (float32 s, <span class="keyword">const</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>& a)</div><div class="line"><a name="l00480"></a><span class="lineno"> 480</span> {</div><div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>(s * a.x, s * a.y, s * a.z);</div><div class="line"><a name="l00482"></a><span class="lineno"> 482</span> }</div><div class="line"><a name="l00483"></a><span class="lineno"> 483</span> </div><div class="line"><a name="l00485"></a><span class="lineno"> 485</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec3.html">b2Vec3</a> operator + (<span class="keyword">const</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>& a, <span class="keyword">const</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>& b)</div><div class="line"><a name="l00486"></a><span class="lineno"> 486</span> {</div><div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>(a.x + b.x, a.y + b.y, a.z + b.z);</div><div class="line"><a name="l00488"></a><span class="lineno"> 488</span> }</div><div class="line"><a name="l00489"></a><span class="lineno"> 489</span> </div><div class="line"><a name="l00491"></a><span class="lineno"> 491</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec3.html">b2Vec3</a> operator - (<span class="keyword">const</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>& a, <span class="keyword">const</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>& b)</div><div class="line"><a name="l00492"></a><span class="lineno"> 492</span> {</div><div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>(a.x - b.x, a.y - b.y, a.z - b.z);</div><div class="line"><a name="l00494"></a><span class="lineno"> 494</span> }</div><div class="line"><a name="l00495"></a><span class="lineno"> 495</span> </div><div class="line"><a name="l00497"></a><span class="lineno"> 497</span> <span class="keyword">inline</span> float32 b2Dot(<span class="keyword">const</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>& a, <span class="keyword">const</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>& b)</div><div class="line"><a name="l00498"></a><span class="lineno"> 498</span> {</div><div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  <span class="keywordflow">return</span> a.x * b.x + a.y * b.y + a.z * b.z;</div><div class="line"><a name="l00500"></a><span class="lineno"> 500</span> }</div><div class="line"><a name="l00501"></a><span class="lineno"> 501</span> </div><div class="line"><a name="l00503"></a><span class="lineno"> 503</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec3.html">b2Vec3</a> b2Cross(<span class="keyword">const</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>& a, <span class="keyword">const</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>& b)</div><div class="line"><a name="l00504"></a><span class="lineno"> 504</span> {</div><div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>(a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x);</div><div class="line"><a name="l00506"></a><span class="lineno"> 506</span> }</div><div class="line"><a name="l00507"></a><span class="lineno"> 507</span> </div><div class="line"><a name="l00508"></a><span class="lineno"> 508</span> <span class="keyword">inline</span> <a class="code" href="structb2_mat22.html">b2Mat22</a> operator + (<span class="keyword">const</span> <a class="code" href="structb2_mat22.html">b2Mat22</a>& A, <span class="keyword">const</span> <a class="code" href="structb2_mat22.html">b2Mat22</a>& B)</div><div class="line"><a name="l00509"></a><span class="lineno"> 509</span> {</div><div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_mat22.html">b2Mat22</a>(A.ex + B.ex, A.ey + B.ey);</div><div class="line"><a name="l00511"></a><span class="lineno"> 511</span> }</div><div class="line"><a name="l00512"></a><span class="lineno"> 512</span> </div><div class="line"><a name="l00513"></a><span class="lineno"> 513</span> <span class="comment">// A * B</span></div><div class="line"><a name="l00514"></a><span class="lineno"> 514</span> <span class="keyword">inline</span> <a class="code" href="structb2_mat22.html">b2Mat22</a> b2Mul(<span class="keyword">const</span> <a class="code" href="structb2_mat22.html">b2Mat22</a>& A, <span class="keyword">const</span> <a class="code" href="structb2_mat22.html">b2Mat22</a>& B)</div><div class="line"><a name="l00515"></a><span class="lineno"> 515</span> {</div><div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_mat22.html">b2Mat22</a>(b2Mul(A, B.ex), b2Mul(A, B.ey));</div><div class="line"><a name="l00517"></a><span class="lineno"> 517</span> }</div><div class="line"><a name="l00518"></a><span class="lineno"> 518</span> </div><div class="line"><a name="l00519"></a><span class="lineno"> 519</span> <span class="comment">// A^T * B</span></div><div class="line"><a name="l00520"></a><span class="lineno"> 520</span> <span class="keyword">inline</span> <a class="code" href="structb2_mat22.html">b2Mat22</a> b2MulT(<span class="keyword">const</span> <a class="code" href="structb2_mat22.html">b2Mat22</a>& A, <span class="keyword">const</span> <a class="code" href="structb2_mat22.html">b2Mat22</a>& B)</div><div class="line"><a name="l00521"></a><span class="lineno"> 521</span> {</div><div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  <a class="code" href="structb2_vec2.html">b2Vec2</a> c1(b2Dot(A.ex, B.ex), b2Dot(A.ey, B.ex));</div><div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  <a class="code" href="structb2_vec2.html">b2Vec2</a> c2(b2Dot(A.ex, B.ey), b2Dot(A.ey, B.ey));</div><div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_mat22.html">b2Mat22</a>(c1, c2);</div><div class="line"><a name="l00525"></a><span class="lineno"> 525</span> }</div><div class="line"><a name="l00526"></a><span class="lineno"> 526</span> </div><div class="line"><a name="l00528"></a><span class="lineno"> 528</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec3.html">b2Vec3</a> b2Mul(<span class="keyword">const</span> <a class="code" href="structb2_mat33.html">b2Mat33</a>& A, <span class="keyword">const</span> <a class="code" href="structb2_vec3.html">b2Vec3</a>& v)</div><div class="line"><a name="l00529"></a><span class="lineno"> 529</span> {</div><div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  <span class="keywordflow">return</span> v.x * A.ex + v.y * A.ey + v.z * A.ez;</div><div class="line"><a name="l00531"></a><span class="lineno"> 531</span> }</div><div class="line"><a name="l00532"></a><span class="lineno"> 532</span> </div><div class="line"><a name="l00534"></a><span class="lineno"> 534</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec2.html">b2Vec2</a> b2Mul22(<span class="keyword">const</span> <a class="code" href="structb2_mat33.html">b2Mat33</a>& A, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& v)</div><div class="line"><a name="l00535"></a><span class="lineno"> 535</span> {</div><div class="line"><a name="l00536"></a><span class="lineno"> 536</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>(A.ex.x * v.x + A.ey.x * v.y, A.ex.y * v.x + A.ey.y * v.y);</div><div class="line"><a name="l00537"></a><span class="lineno"> 537</span> }</div><div class="line"><a name="l00538"></a><span class="lineno"> 538</span> </div><div class="line"><a name="l00540"></a><span class="lineno"> 540</span> <span class="keyword">inline</span> <a class="code" href="structb2_rot.html">b2Rot</a> b2Mul(<span class="keyword">const</span> <a class="code" href="structb2_rot.html">b2Rot</a>& q, <span class="keyword">const</span> <a class="code" href="structb2_rot.html">b2Rot</a>& r)</div><div class="line"><a name="l00541"></a><span class="lineno"> 541</span> {</div><div class="line"><a name="l00542"></a><span class="lineno"> 542</span>  <span class="comment">// [qc -qs] * [rc -rs] = [qc*rc-qs*rs -qc*rs-qs*rc]</span></div><div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  <span class="comment">// [qs qc] [rs rc] [qs*rc+qc*rs -qs*rs+qc*rc]</span></div><div class="line"><a name="l00544"></a><span class="lineno"> 544</span>  <span class="comment">// s = qs * rc + qc * rs</span></div><div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  <span class="comment">// c = qc * rc - qs * rs</span></div><div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  <a class="code" href="structb2_rot.html">b2Rot</a> qr;</div><div class="line"><a name="l00547"></a><span class="lineno"> 547</span>  qr.<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a> = q.<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a> * r.c + q.c * r.<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a>;</div><div class="line"><a name="l00548"></a><span class="lineno"> 548</span>  qr.c = q.c * r.c - q.<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a> * r.<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a>;</div><div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  <span class="keywordflow">return</span> qr;</div><div class="line"><a name="l00550"></a><span class="lineno"> 550</span> }</div><div class="line"><a name="l00551"></a><span class="lineno"> 551</span> </div><div class="line"><a name="l00553"></a><span class="lineno"> 553</span> <span class="keyword">inline</span> <a class="code" href="structb2_rot.html">b2Rot</a> b2MulT(<span class="keyword">const</span> <a class="code" href="structb2_rot.html">b2Rot</a>& q, <span class="keyword">const</span> <a class="code" href="structb2_rot.html">b2Rot</a>& r)</div><div class="line"><a name="l00554"></a><span class="lineno"> 554</span> {</div><div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  <span class="comment">// [ qc qs] * [rc -rs] = [qc*rc+qs*rs -qc*rs+qs*rc]</span></div><div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  <span class="comment">// [-qs qc] [rs rc] [-qs*rc+qc*rs qs*rs+qc*rc]</span></div><div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  <span class="comment">// s = qc * rs - qs * rc</span></div><div class="line"><a name="l00558"></a><span class="lineno"> 558</span>  <span class="comment">// c = qc * rc + qs * rs</span></div><div class="line"><a name="l00559"></a><span class="lineno"> 559</span>  <a class="code" href="structb2_rot.html">b2Rot</a> qr;</div><div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  qr.<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a> = q.c * r.<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a> - q.<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a> * r.c;</div><div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  qr.c = q.c * r.c + q.<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a> * r.<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a>;</div><div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  <span class="keywordflow">return</span> qr;</div><div class="line"><a name="l00563"></a><span class="lineno"> 563</span> }</div><div class="line"><a name="l00564"></a><span class="lineno"> 564</span> </div><div class="line"><a name="l00566"></a><span class="lineno"> 566</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec2.html">b2Vec2</a> b2Mul(<span class="keyword">const</span> <a class="code" href="structb2_rot.html">b2Rot</a>& q, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& v)</div><div class="line"><a name="l00567"></a><span class="lineno"> 567</span> {</div><div class="line"><a name="l00568"></a><span class="lineno"> 568</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>(q.c * v.x - q.<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a> * v.y, q.<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a> * v.x + q.c * v.y);</div><div class="line"><a name="l00569"></a><span class="lineno"> 569</span> }</div><div class="line"><a name="l00570"></a><span class="lineno"> 570</span> </div><div class="line"><a name="l00572"></a><span class="lineno"> 572</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec2.html">b2Vec2</a> b2MulT(<span class="keyword">const</span> <a class="code" href="structb2_rot.html">b2Rot</a>& q, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& v)</div><div class="line"><a name="l00573"></a><span class="lineno"> 573</span> {</div><div class="line"><a name="l00574"></a><span class="lineno"> 574</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>(q.c * v.x + q.<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a> * v.y, -q.<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a> * v.x + q.c * v.y);</div><div class="line"><a name="l00575"></a><span class="lineno"> 575</span> }</div><div class="line"><a name="l00576"></a><span class="lineno"> 576</span> </div><div class="line"><a name="l00577"></a><span class="lineno"> 577</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec2.html">b2Vec2</a> b2Mul(<span class="keyword">const</span> <a class="code" href="structb2_transform.html">b2Transform</a>& T, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& v)</div><div class="line"><a name="l00578"></a><span class="lineno"> 578</span> {</div><div class="line"><a name="l00579"></a><span class="lineno"> 579</span>  float32 x = (T.q.c * v.x - T.q.<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a> * v.y) + T.p.x;</div><div class="line"><a name="l00580"></a><span class="lineno"> 580</span>  float32 y = (T.q.<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a> * v.x + T.q.c * v.y) + T.p.y;</div><div class="line"><a name="l00581"></a><span class="lineno"> 581</span> </div><div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>(x, y);</div><div class="line"><a name="l00583"></a><span class="lineno"> 583</span> }</div><div class="line"><a name="l00584"></a><span class="lineno"> 584</span> </div><div class="line"><a name="l00585"></a><span class="lineno"> 585</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec2.html">b2Vec2</a> b2MulT(<span class="keyword">const</span> <a class="code" href="structb2_transform.html">b2Transform</a>& T, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& v)</div><div class="line"><a name="l00586"></a><span class="lineno"> 586</span> {</div><div class="line"><a name="l00587"></a><span class="lineno"> 587</span>  float32 px = v.x - T.p.x;</div><div class="line"><a name="l00588"></a><span class="lineno"> 588</span>  float32 py = v.y - T.p.y;</div><div class="line"><a name="l00589"></a><span class="lineno"> 589</span>  float32 x = (T.q.c * px + T.q.<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a> * py);</div><div class="line"><a name="l00590"></a><span class="lineno"> 590</span>  float32 y = (-T.q.<a class="code" href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">s</a> * px + T.q.c * py);</div><div class="line"><a name="l00591"></a><span class="lineno"> 591</span> </div><div class="line"><a name="l00592"></a><span class="lineno"> 592</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>(x, y);</div><div class="line"><a name="l00593"></a><span class="lineno"> 593</span> }</div><div class="line"><a name="l00594"></a><span class="lineno"> 594</span> </div><div class="line"><a name="l00595"></a><span class="lineno"> 595</span> <span class="comment">// v2 = A.q.Rot(B.q.Rot(v1) + B.p) + A.p</span></div><div class="line"><a name="l00596"></a><span class="lineno"> 596</span> <span class="comment">// = (A.q * B.q).Rot(v1) + A.q.Rot(B.p) + A.p</span></div><div class="line"><a name="l00597"></a><span class="lineno"> 597</span> <span class="keyword">inline</span> <a class="code" href="structb2_transform.html">b2Transform</a> b2Mul(<span class="keyword">const</span> <a class="code" href="structb2_transform.html">b2Transform</a>& A, <span class="keyword">const</span> <a class="code" href="structb2_transform.html">b2Transform</a>& B)</div><div class="line"><a name="l00598"></a><span class="lineno"> 598</span> {</div><div class="line"><a name="l00599"></a><span class="lineno"> 599</span>  <a class="code" href="structb2_transform.html">b2Transform</a> C;</div><div class="line"><a name="l00600"></a><span class="lineno"> 600</span>  C.q = b2Mul(A.q, B.q);</div><div class="line"><a name="l00601"></a><span class="lineno"> 601</span>  C.p = b2Mul(A.q, B.p) + A.p;</div><div class="line"><a name="l00602"></a><span class="lineno"> 602</span>  <span class="keywordflow">return</span> C;</div><div class="line"><a name="l00603"></a><span class="lineno"> 603</span> }</div><div class="line"><a name="l00604"></a><span class="lineno"> 604</span> </div><div class="line"><a name="l00605"></a><span class="lineno"> 605</span> <span class="comment">// v2 = A.q' * (B.q * v1 + B.p - A.p)</span></div><div class="line"><a name="l00606"></a><span class="lineno"> 606</span> <span class="comment">// = A.q' * B.q * v1 + A.q' * (B.p - A.p)</span></div><div class="line"><a name="l00607"></a><span class="lineno"> 607</span> <span class="keyword">inline</span> <a class="code" href="structb2_transform.html">b2Transform</a> b2MulT(<span class="keyword">const</span> <a class="code" href="structb2_transform.html">b2Transform</a>& A, <span class="keyword">const</span> <a class="code" href="structb2_transform.html">b2Transform</a>& B)</div><div class="line"><a name="l00608"></a><span class="lineno"> 608</span> {</div><div class="line"><a name="l00609"></a><span class="lineno"> 609</span>  <a class="code" href="structb2_transform.html">b2Transform</a> C;</div><div class="line"><a name="l00610"></a><span class="lineno"> 610</span>  C.q = b2MulT(A.q, B.q);</div><div class="line"><a name="l00611"></a><span class="lineno"> 611</span>  C.p = b2MulT(A.q, B.p - A.p);</div><div class="line"><a name="l00612"></a><span class="lineno"> 612</span>  <span class="keywordflow">return</span> C;</div><div class="line"><a name="l00613"></a><span class="lineno"> 613</span> }</div><div class="line"><a name="l00614"></a><span class="lineno"> 614</span> </div><div class="line"><a name="l00615"></a><span class="lineno"> 615</span> <span class="keyword">template</span> <<span class="keyword">typename</span> T></div><div class="line"><a name="l00616"></a><span class="lineno"> 616</span> <span class="keyword">inline</span> T b2Abs(T a)</div><div class="line"><a name="l00617"></a><span class="lineno"> 617</span> {</div><div class="line"><a name="l00618"></a><span class="lineno"> 618</span>  <span class="keywordflow">return</span> a > T(0) ? a : -a;</div><div class="line"><a name="l00619"></a><span class="lineno"> 619</span> }</div><div class="line"><a name="l00620"></a><span class="lineno"> 620</span> </div><div class="line"><a name="l00621"></a><span class="lineno"> 621</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec2.html">b2Vec2</a> b2Abs(<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& a)</div><div class="line"><a name="l00622"></a><span class="lineno"> 622</span> {</div><div class="line"><a name="l00623"></a><span class="lineno"> 623</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>(b2Abs(a.x), b2Abs(a.y));</div><div class="line"><a name="l00624"></a><span class="lineno"> 624</span> }</div><div class="line"><a name="l00625"></a><span class="lineno"> 625</span> </div><div class="line"><a name="l00626"></a><span class="lineno"> 626</span> <span class="keyword">inline</span> <a class="code" href="structb2_mat22.html">b2Mat22</a> b2Abs(<span class="keyword">const</span> <a class="code" href="structb2_mat22.html">b2Mat22</a>& A)</div><div class="line"><a name="l00627"></a><span class="lineno"> 627</span> {</div><div class="line"><a name="l00628"></a><span class="lineno"> 628</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_mat22.html">b2Mat22</a>(b2Abs(A.ex), b2Abs(A.ey));</div><div class="line"><a name="l00629"></a><span class="lineno"> 629</span> }</div><div class="line"><a name="l00630"></a><span class="lineno"> 630</span> </div><div class="line"><a name="l00631"></a><span class="lineno"> 631</span> <span class="keyword">template</span> <<span class="keyword">typename</span> T></div><div class="line"><a name="l00632"></a><span class="lineno"> 632</span> <span class="keyword">inline</span> T b2Min(T a, T b)</div><div class="line"><a name="l00633"></a><span class="lineno"> 633</span> {</div><div class="line"><a name="l00634"></a><span class="lineno"> 634</span>  <span class="keywordflow">return</span> a < b ? a : b;</div><div class="line"><a name="l00635"></a><span class="lineno"> 635</span> }</div><div class="line"><a name="l00636"></a><span class="lineno"> 636</span> </div><div class="line"><a name="l00637"></a><span class="lineno"> 637</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec2.html">b2Vec2</a> b2Min(<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& a, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& b)</div><div class="line"><a name="l00638"></a><span class="lineno"> 638</span> {</div><div class="line"><a name="l00639"></a><span class="lineno"> 639</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>(b2Min(a.x, b.x), b2Min(a.y, b.y));</div><div class="line"><a name="l00640"></a><span class="lineno"> 640</span> }</div><div class="line"><a name="l00641"></a><span class="lineno"> 641</span> </div><div class="line"><a name="l00642"></a><span class="lineno"> 642</span> <span class="keyword">template</span> <<span class="keyword">typename</span> T></div><div class="line"><a name="l00643"></a><span class="lineno"> 643</span> <span class="keyword">inline</span> T b2Max(T a, T b)</div><div class="line"><a name="l00644"></a><span class="lineno"> 644</span> {</div><div class="line"><a name="l00645"></a><span class="lineno"> 645</span>  <span class="keywordflow">return</span> a > b ? a : b;</div><div class="line"><a name="l00646"></a><span class="lineno"> 646</span> }</div><div class="line"><a name="l00647"></a><span class="lineno"> 647</span> </div><div class="line"><a name="l00648"></a><span class="lineno"> 648</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec2.html">b2Vec2</a> b2Max(<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& a, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& b)</div><div class="line"><a name="l00649"></a><span class="lineno"> 649</span> {</div><div class="line"><a name="l00650"></a><span class="lineno"> 650</span>  <span class="keywordflow">return</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>(b2Max(a.x, b.x), b2Max(a.y, b.y));</div><div class="line"><a name="l00651"></a><span class="lineno"> 651</span> }</div><div class="line"><a name="l00652"></a><span class="lineno"> 652</span> </div><div class="line"><a name="l00653"></a><span class="lineno"> 653</span> <span class="keyword">template</span> <<span class="keyword">typename</span> T></div><div class="line"><a name="l00654"></a><span class="lineno"> 654</span> <span class="keyword">inline</span> T b2Clamp(T a, T low, T high)</div><div class="line"><a name="l00655"></a><span class="lineno"> 655</span> {</div><div class="line"><a name="l00656"></a><span class="lineno"> 656</span>  <span class="keywordflow">return</span> b2Max(low, b2Min(a, high));</div><div class="line"><a name="l00657"></a><span class="lineno"> 657</span> }</div><div class="line"><a name="l00658"></a><span class="lineno"> 658</span> </div><div class="line"><a name="l00659"></a><span class="lineno"> 659</span> <span class="keyword">inline</span> <a class="code" href="structb2_vec2.html">b2Vec2</a> b2Clamp(<span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& a, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& low, <span class="keyword">const</span> <a class="code" href="structb2_vec2.html">b2Vec2</a>& high)</div><div class="line"><a name="l00660"></a><span class="lineno"> 660</span> {</div><div class="line"><a name="l00661"></a><span class="lineno"> 661</span>  <span class="keywordflow">return</span> b2Max(low, b2Min(a, high));</div><div class="line"><a name="l00662"></a><span class="lineno"> 662</span> }</div><div class="line"><a name="l00663"></a><span class="lineno"> 663</span> </div><div class="line"><a name="l00664"></a><span class="lineno"> 664</span> <span class="keyword">template</span><<span class="keyword">typename</span> T> <span class="keyword">inline</span> <span class="keywordtype">void</span> b2Swap(T& a, T& b)</div><div class="line"><a name="l00665"></a><span class="lineno"> 665</span> {</div><div class="line"><a name="l00666"></a><span class="lineno"> 666</span>  T tmp = a;</div><div class="line"><a name="l00667"></a><span class="lineno"> 667</span>  a = b;</div><div class="line"><a name="l00668"></a><span class="lineno"> 668</span>  b = tmp;</div><div class="line"><a name="l00669"></a><span class="lineno"> 669</span> }</div><div class="line"><a name="l00670"></a><span class="lineno"> 670</span> </div><div class="line"><a name="l00676"></a><span class="lineno"> 676</span> <span class="keyword">inline</span> uint32 b2NextPowerOfTwo(uint32 x)</div><div class="line"><a name="l00677"></a><span class="lineno"> 677</span> {</div><div class="line"><a name="l00678"></a><span class="lineno"> 678</span>  x |= (x >> 1);</div><div class="line"><a name="l00679"></a><span class="lineno"> 679</span>  x |= (x >> 2);</div><div class="line"><a name="l00680"></a><span class="lineno"> 680</span>  x |= (x >> 4);</div><div class="line"><a name="l00681"></a><span class="lineno"> 681</span>  x |= (x >> 8);</div><div class="line"><a name="l00682"></a><span class="lineno"> 682</span>  x |= (x >> 16);</div><div class="line"><a name="l00683"></a><span class="lineno"> 683</span>  <span class="keywordflow">return</span> x + 1;</div><div class="line"><a name="l00684"></a><span class="lineno"> 684</span> }</div><div class="line"><a name="l00685"></a><span class="lineno"> 685</span> </div><div class="line"><a name="l00686"></a><span class="lineno"> 686</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> b2IsPowerOfTwo(uint32 x)</div><div class="line"><a name="l00687"></a><span class="lineno"> 687</span> {</div><div class="line"><a name="l00688"></a><span class="lineno"> 688</span>  <span class="keywordtype">bool</span> result = x > 0 && (x & (x - 1)) == 0;</div><div class="line"><a name="l00689"></a><span class="lineno"> 689</span>  <span class="keywordflow">return</span> result;</div><div class="line"><a name="l00690"></a><span class="lineno"> 690</span> }</div><div class="line"><a name="l00691"></a><span class="lineno"> 691</span> </div><div class="line"><a name="l00692"></a><span class="lineno"><a class="line" href="structb2_sweep.html#a22ae50509de51876aefc48cd76248c61"> 692</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="structb2_sweep.html#a22ae50509de51876aefc48cd76248c61">b2Sweep::GetTransform</a>(<a class="code" href="structb2_transform.html">b2Transform</a>* xf, float32 beta)<span class="keyword"> const</span></div><div class="line"><a name="l00693"></a><span class="lineno"> 693</span> <span class="keyword"></span>{</div><div class="line"><a name="l00694"></a><span class="lineno"> 694</span>  xf->p = (1.0f - beta) * c0 + beta * <a class="code" href="structb2_sweep.html#a1b5402e01b92cc82473389fc6f0375c3">c</a>;</div><div class="line"><a name="l00695"></a><span class="lineno"> 695</span>  float32 angle = (1.0f - beta) * a0 + beta * <a class="code" href="structb2_sweep.html#afa96bacc91dd3c92ae716a45512332d6">a</a>;</div><div class="line"><a name="l00696"></a><span class="lineno"> 696</span>  xf->q.<a class="code" href="structb2_rot.html#acde9186de0a4a7397bf8ef714408ad60">Set</a>(angle);</div><div class="line"><a name="l00697"></a><span class="lineno"> 697</span> </div><div class="line"><a name="l00698"></a><span class="lineno"> 698</span>  <span class="comment">// Shift to origin</span></div><div class="line"><a name="l00699"></a><span class="lineno"> 699</span>  xf->p -= b2Mul(xf->q, <a class="code" href="structb2_sweep.html#a4bcc302cf78771896d6256fc53f2f8be">localCenter</a>);</div><div class="line"><a name="l00700"></a><span class="lineno"> 700</span> }</div><div class="line"><a name="l00701"></a><span class="lineno"> 701</span> </div><div class="line"><a name="l00702"></a><span class="lineno"><a class="line" href="structb2_sweep.html#a35eb9b976ca87c9b8d758bec070c6c06"> 702</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="structb2_sweep.html#a35eb9b976ca87c9b8d758bec070c6c06">b2Sweep::Advance</a>(float32 alpha)</div><div class="line"><a name="l00703"></a><span class="lineno"> 703</span> {</div><div class="line"><a name="l00704"></a><span class="lineno"> 704</span>  b2Assert(<a class="code" href="structb2_sweep.html#aa5f8ab90178b58bc0777096cbc6b91cf">alpha0</a> < 1.0f);</div><div class="line"><a name="l00705"></a><span class="lineno"> 705</span>  float32 beta = (alpha - <a class="code" href="structb2_sweep.html#aa5f8ab90178b58bc0777096cbc6b91cf">alpha0</a>) / (1.0f - <a class="code" href="structb2_sweep.html#aa5f8ab90178b58bc0777096cbc6b91cf">alpha0</a>);</div><div class="line"><a name="l00706"></a><span class="lineno"> 706</span>  c0 += beta * (<a class="code" href="structb2_sweep.html#a1b5402e01b92cc82473389fc6f0375c3">c</a> - c0);</div><div class="line"><a name="l00707"></a><span class="lineno"> 707</span>  a0 += beta * (<a class="code" href="structb2_sweep.html#afa96bacc91dd3c92ae716a45512332d6">a</a> - a0);</div><div class="line"><a name="l00708"></a><span class="lineno"> 708</span>  <a class="code" href="structb2_sweep.html#aa5f8ab90178b58bc0777096cbc6b91cf">alpha0</a> = alpha;</div><div class="line"><a name="l00709"></a><span class="lineno"> 709</span> }</div><div class="line"><a name="l00710"></a><span class="lineno"> 710</span> </div><div class="line"><a name="l00712"></a><span class="lineno"><a class="line" href="structb2_sweep.html#ad66a3086bc7656df9cf7454013a2f61b"> 712</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="structb2_sweep.html#ad66a3086bc7656df9cf7454013a2f61b">b2Sweep::Normalize</a>()</div><div class="line"><a name="l00713"></a><span class="lineno"> 713</span> {</div><div class="line"><a name="l00714"></a><span class="lineno"> 714</span>  float32 twoPi = 2.0f * b2_pi;</div><div class="line"><a name="l00715"></a><span class="lineno"> 715</span>  float32 d = twoPi * floorf(a0 / twoPi);</div><div class="line"><a name="l00716"></a><span class="lineno"> 716</span>  a0 -= d;</div><div class="line"><a name="l00717"></a><span class="lineno"> 717</span>  <a class="code" href="structb2_sweep.html#afa96bacc91dd3c92ae716a45512332d6">a</a> -= d;</div><div class="line"><a name="l00718"></a><span class="lineno"> 718</span> }</div><div class="line"><a name="l00719"></a><span class="lineno"> 719</span> </div><div class="line"><a name="l00720"></a><span class="lineno"> 720</span> <span class="preprocessor">#endif</span></div><div class="ttc" id="structb2_transform_html"><div class="ttname"><a href="structb2_transform.html">b2Transform</a></div><div class="ttdef"><b>Definition:</b> b2Math.h:350</div></div>
<div class="ttc" id="structb2_transform_html_a765a2e5c692a2e1d05c7a5441019373d"><div class="ttname"><a href="structb2_transform.html#a765a2e5c692a2e1d05c7a5441019373d">b2Transform::b2Transform</a></div><div class="ttdeci">b2Transform()</div><div class="ttdoc">The default constructor does nothing. </div><div class="ttdef"><b>Definition:</b> b2Math.h:353</div></div>
<div class="ttc" id="structb2_vec3_html_a47df55b26ab254dcf42a16638c7feeeb"><div class="ttname"><a href="structb2_vec3.html#a47df55b26ab254dcf42a16638c7feeeb">b2Vec3::b2Vec3</a></div><div class="ttdeci">b2Vec3(float32 x, float32 y, float32 z)</div><div class="ttdoc">Construct using coordinates. </div><div class="ttdef"><b>Definition:</b> b2Math.h:150</div></div>
<div class="ttc" id="structb2_vec3_html"><div class="ttname"><a href="structb2_vec3.html">b2Vec3</a></div><div class="ttdoc">A 2D column vector with 3 elements. </div><div class="ttdef"><b>Definition:</b> b2Math.h:144</div></div>
<div class="ttc" id="structb2_mat22_html_abd674c6d92e26962977f34bcd92ff24d"><div class="ttname"><a href="structb2_mat22.html#abd674c6d92e26962977f34bcd92ff24d">b2Mat22::b2Mat22</a></div><div class="ttdeci">b2Mat22(const b2Vec2 &c1, const b2Vec2 &c2)</div><div class="ttdoc">Construct this matrix using columns. </div><div class="ttdef"><b>Definition:</b> b2Math.h:189</div></div>
<div class="ttc" id="structb2_vec3_html_a837423f66d6fb72d815e7390c09938b9"><div class="ttname"><a href="structb2_vec3.html#a837423f66d6fb72d815e7390c09938b9">b2Vec3::b2Vec3</a></div><div class="ttdeci">b2Vec3()</div><div class="ttdoc">Default constructor does nothing (for performance). </div><div class="ttdef"><b>Definition:</b> b2Math.h:147</div></div>
<div class="ttc" id="structb2_mat33_html"><div class="ttname"><a href="structb2_mat33.html">b2Mat33</a></div><div class="ttdoc">A 3-by-3 matrix. Stored in column-major order. </div><div class="ttdef"><b>Definition:</b> b2Math.h:257</div></div>
<div class="ttc" id="structb2_vec2_html_a9171b31deb83af96872f99689939a12f"><div class="ttname"><a href="structb2_vec2.html#a9171b31deb83af96872f99689939a12f">b2Vec2::b2Vec2</a></div><div class="ttdeci">b2Vec2()</div><div class="ttdoc">Default constructor does nothing (for performance). </div><div class="ttdef"><b>Definition:</b> b2Math.h:56</div></div>
<div class="ttc" id="structb2_vec3_html_a12a1bc14bbe722dfb175a492d2d00a79"><div class="ttname"><a href="structb2_vec3.html#a12a1bc14bbe722dfb175a492d2d00a79">b2Vec3::Set</a></div><div class="ttdeci">void Set(float32 x_, float32 y_, float32 z_)</div><div class="ttdoc">Set this vector to some specified coordinates. </div><div class="ttdef"><b>Definition:</b> b2Math.h:156</div></div>
<div class="ttc" id="structb2_rot_html_a45031fccfa11d3b3a09154008ce28b39"><div class="ttname"><a href="structb2_rot.html#a45031fccfa11d3b3a09154008ce28b39">b2Rot::GetAngle</a></div><div class="ttdeci">float32 GetAngle() const</div><div class="ttdoc">Get the angle in radians. </div><div class="ttdef"><b>Definition:</b> b2Math.h:327</div></div>
<div class="ttc" id="structb2_vec2_html_adda78c92f318fe53d8a53f9b5cfd8e41"><div class="ttname"><a href="structb2_vec2.html#adda78c92f318fe53d8a53f9b5cfd8e41">b2Vec2::Normalize</a></div><div class="ttdeci">float32 Normalize()</div><div class="ttdoc">Convert this vector into a unit vector. Returns the length. </div><div class="ttdef"><b>Definition:</b> b2Math.h:114</div></div>
<div class="ttc" id="structb2_mat33_html_a1f4d7ddf1c8a202fc08ec64dfe191463"><div class="ttname"><a href="structb2_mat33.html#a1f4d7ddf1c8a202fc08ec64dfe191463">b2Mat33::b2Mat33</a></div><div class="ttdeci">b2Mat33()</div><div class="ttdoc">The default constructor does nothing (for performance). </div><div class="ttdef"><b>Definition:</b> b2Math.h:260</div></div>
<div class="ttc" id="structb2_vec2_html_aa8a2f026420a84bbbc62f3a3de2041d6"><div class="ttname"><a href="structb2_vec2.html#aa8a2f026420a84bbbc62f3a3de2041d6">b2Vec2::b2Vec2</a></div><div class="ttdeci">b2Vec2(float32 x, float32 y)</div><div class="ttdoc">Construct using coordinates. </div><div class="ttdef"><b>Definition:</b> b2Math.h:59</div></div>
<div class="ttc" id="structb2_sweep_html"><div class="ttname"><a href="structb2_sweep.html">b2Sweep</a></div><div class="ttdef"><b>Definition:</b> b2Math.h:380</div></div>
<div class="ttc" id="structb2_vec2_html_af8a081dac7eea7800fdbfbf95ac9e395"><div class="ttname"><a href="structb2_vec2.html#af8a081dac7eea7800fdbfbf95ac9e395">b2Vec2::LengthSquared</a></div><div class="ttdeci">float32 LengthSquared() const</div><div class="ttdef"><b>Definition:</b> b2Math.h:108</div></div>
<div class="ttc" id="structb2_mat33_html_a2620944663233096d3b82bc4b1a991e9"><div class="ttname"><a href="structb2_mat33.html#a2620944663233096d3b82bc4b1a991e9">b2Mat33::GetSymInverse33</a></div><div class="ttdeci">void GetSymInverse33(b2Mat33 *M) const</div><div class="ttdoc">Returns the zero matrix if singular. </div><div class="ttdef"><b>Definition:</b> b2Math.cpp:71</div></div>
<div class="ttc" id="structb2_mat33_html_a2ce48f409ba5951a04da821dada9e285"><div class="ttname"><a href="structb2_mat33.html#a2ce48f409ba5951a04da821dada9e285">b2Mat33::Solve33</a></div><div class="ttdeci">b2Vec3 Solve33(const b2Vec3 &b) const</div><div class="ttdef"><b>Definition:</b> b2Math.cpp:25</div></div>
<div class="ttc" id="structb2_mat22_html_ac3e10f6d457c8dab9062ba378f66bc4d"><div class="ttname"><a href="structb2_mat22.html#ac3e10f6d457c8dab9062ba378f66bc4d">b2Mat22::b2Mat22</a></div><div class="ttdeci">b2Mat22()</div><div class="ttdoc">The default constructor does nothing (for performance). </div><div class="ttdef"><b>Definition:</b> b2Math.h:186</div></div>
<div class="ttc" id="structb2_rot_html_a15725ce0a89cc735ad90687b4c0f4dce"><div class="ttname"><a href="structb2_rot.html#a15725ce0a89cc735ad90687b4c0f4dce">b2Rot::s</a></div><div class="ttdeci">float32 s</div><div class="ttdoc">Sine and cosine. </div><div class="ttdef"><b>Definition:</b> b2Math.h:345</div></div>
<div class="ttc" id="structb2_sweep_html_afa96bacc91dd3c92ae716a45512332d6"><div class="ttname"><a href="structb2_sweep.html#afa96bacc91dd3c92ae716a45512332d6">b2Sweep::a</a></div><div class="ttdeci">float32 a</div><div class="ttdoc">world angles </div><div class="ttdef"><b>Definition:</b> b2Math.h:395</div></div>
<div class="ttc" id="structb2_mat33_html_a36d99a037008776c8d09fe0aeb5c759c"><div class="ttname"><a href="structb2_mat33.html#a36d99a037008776c8d09fe0aeb5c759c">b2Mat33::b2Mat33</a></div><div class="ttdeci">b2Mat33(const b2Vec3 &c1, const b2Vec3 &c2, const b2Vec3 &c3)</div><div class="ttdoc">Construct this matrix using columns. </div><div class="ttdef"><b>Definition:</b> b2Math.h:263</div></div>
<div class="ttc" id="structb2_mat33_html_acdf892aab7e26283f8aa600ade91dcef"><div class="ttname"><a href="structb2_mat33.html#acdf892aab7e26283f8aa600ade91dcef">b2Mat33::Solve22</a></div><div class="ttdeci">b2Vec2 Solve22(const b2Vec2 &b) const</div><div class="ttdef"><b>Definition:</b> b2Math.cpp:41</div></div>
<div class="ttc" id="structb2_vec2_html_aaf36e082a20368b24edb635511872a74"><div class="ttname"><a href="structb2_vec2.html#aaf36e082a20368b24edb635511872a74">b2Vec2::Skew</a></div><div class="ttdeci">b2Vec2 Skew() const</div><div class="ttdoc">Get the skew vector such that dot(skew_vec, other) == cross(vec, other) </div><div class="ttdef"><b>Definition:</b> b2Math.h:135</div></div>
<div class="ttc" id="structb2_vec2_html_a4d61640a645e470a50b451307d8e94c3"><div class="ttname"><a href="structb2_vec2.html#a4d61640a645e470a50b451307d8e94c3">b2Vec2::Set</a></div><div class="ttdeci">void Set(float32 x_, float32 y_)</div><div class="ttdoc">Set this vector to some specified coordinates. </div><div class="ttdef"><b>Definition:</b> b2Math.h:65</div></div>
<div class="ttc" id="structb2_transform_html_a4db696a0b3fada95f95cde3e7e85ced9"><div class="ttname"><a href="structb2_transform.html#a4db696a0b3fada95f95cde3e7e85ced9">b2Transform::Set</a></div><div class="ttdeci">void Set(const b2Vec2 &position, float32 angle)</div><div class="ttdoc">Set this based on the position and angle. </div><div class="ttdef"><b>Definition:</b> b2Math.h:366</div></div>
<div class="ttc" id="structb2_vec2_html_a5c6cbe27cfb29c6dbb29b9a3285b88d0"><div class="ttname"><a href="structb2_vec2.html#a5c6cbe27cfb29c6dbb29b9a3285b88d0">b2Vec2::SetZero</a></div><div class="ttdeci">void SetZero()</div><div class="ttdoc">Set this vector to all zeros. </div><div class="ttdef"><b>Definition:</b> b2Math.h:62</div></div>
<div class="ttc" id="structb2_vec2_html_a590789342e22ac1e7f9c1a63a2778b6d"><div class="ttname"><a href="structb2_vec2.html#a590789342e22ac1e7f9c1a63a2778b6d">b2Vec2::operator+=</a></div><div class="ttdeci">void operator+=(const b2Vec2 &v)</div><div class="ttdoc">Add a vector to this vector. </div><div class="ttdef"><b>Definition:</b> b2Math.h:83</div></div>
<div class="ttc" id="structb2_vec3_html_aaa9aa20195cd0ee53c7176a9a9b02389"><div class="ttname"><a href="structb2_vec3.html#aaa9aa20195cd0ee53c7176a9a9b02389">b2Vec3::operator*=</a></div><div class="ttdeci">void operator*=(float32 s)</div><div class="ttdoc">Multiply this vector by a scalar. </div><div class="ttdef"><b>Definition:</b> b2Math.h:174</div></div>
<div class="ttc" id="structb2_transform_html_af92af4ec6833552b1b22a6ca6d4f5644"><div class="ttname"><a href="structb2_transform.html#af92af4ec6833552b1b22a6ca6d4f5644">b2Transform::SetIdentity</a></div><div class="ttdeci">void SetIdentity()</div><div class="ttdoc">Set this to the identity transform. </div><div class="ttdef"><b>Definition:</b> b2Math.h:359</div></div>
<div class="ttc" id="structb2_vec2_html_a6b48cab4695a979ae40b7613aedc8b17"><div class="ttname"><a href="structb2_vec2.html#a6b48cab4695a979ae40b7613aedc8b17">b2Vec2::operator-=</a></div><div class="ttdeci">void operator-=(const b2Vec2 &v)</div><div class="ttdoc">Subtract a vector from this vector. </div><div class="ttdef"><b>Definition:</b> b2Math.h:89</div></div>
<div class="ttc" id="structb2_vec3_html_a5a459ed49f1910a347ca247f848a2dd8"><div class="ttname"><a href="structb2_vec3.html#a5a459ed49f1910a347ca247f848a2dd8">b2Vec3::SetZero</a></div><div class="ttdeci">void SetZero()</div><div class="ttdoc">Set this vector to all zeros. </div><div class="ttdef"><b>Definition:</b> b2Math.h:153</div></div>
<div class="ttc" id="structb2_rot_html_ab057c4e9dc821099949391a6ded36dd6"><div class="ttname"><a href="structb2_rot.html#ab057c4e9dc821099949391a6ded36dd6">b2Rot::GetYAxis</a></div><div class="ttdeci">b2Vec2 GetYAxis() const</div><div class="ttdoc">Get the u-axis. </div><div class="ttdef"><b>Definition:</b> b2Math.h:339</div></div>
<div class="ttc" id="structb2_vec3_html_a9e5b535548e1c5dfc0dc258d08f5ca32"><div class="ttname"><a href="structb2_vec3.html#a9e5b535548e1c5dfc0dc258d08f5ca32">b2Vec3::operator-=</a></div><div class="ttdeci">void operator-=(const b2Vec3 &v)</div><div class="ttdoc">Subtract a vector from this vector. </div><div class="ttdef"><b>Definition:</b> b2Math.h:168</div></div>
<div class="ttc" id="structb2_rot_html_aa40dda6d390a2f54c793c63027a9b46e"><div class="ttname"><a href="structb2_rot.html#aa40dda6d390a2f54c793c63027a9b46e">b2Rot::b2Rot</a></div><div class="ttdeci">b2Rot(float32 angle)</div><div class="ttdoc">Initialize from an angle in radians. </div><div class="ttdef"><b>Definition:</b> b2Math.h:304</div></div>
<div class="ttc" id="structb2_vec3_html_a2aaeed3f5308aad85d19c5f0efc72641"><div class="ttname"><a href="structb2_vec3.html#a2aaeed3f5308aad85d19c5f0efc72641">b2Vec3::operator+=</a></div><div class="ttdeci">void operator+=(const b2Vec3 &v)</div><div class="ttdoc">Add a vector to this vector. </div><div class="ttdef"><b>Definition:</b> b2Math.h:162</div></div>
<div class="ttc" id="structb2_sweep_html_a1b5402e01b92cc82473389fc6f0375c3"><div class="ttname"><a href="structb2_sweep.html#a1b5402e01b92cc82473389fc6f0375c3">b2Sweep::c</a></div><div class="ttdeci">b2Vec2 c</div><div class="ttdoc">center world positions </div><div class="ttdef"><b>Definition:</b> b2Math.h:394</div></div>
<div class="ttc" id="structb2_sweep_html_a4bcc302cf78771896d6256fc53f2f8be"><div class="ttname"><a href="structb2_sweep.html#a4bcc302cf78771896d6256fc53f2f8be">b2Sweep::localCenter</a></div><div class="ttdeci">b2Vec2 localCenter</div><div class="ttdoc">local center of mass position </div><div class="ttdef"><b>Definition:</b> b2Math.h:393</div></div>
<div class="ttc" id="structb2_mat22_html"><div class="ttname"><a href="structb2_mat22.html">b2Mat22</a></div><div class="ttdoc">A 2-by-2 matrix. Stored in column-major order. </div><div class="ttdef"><b>Definition:</b> b2Math.h:183</div></div>
<div class="ttc" id="structb2_vec2_html_a04cb9ac9e845a59f4212b2d7149fa3d9"><div class="ttname"><a href="structb2_vec2.html#a04cb9ac9e845a59f4212b2d7149fa3d9">b2Vec2::Length</a></div><div class="ttdeci">float32 Length() const</div><div class="ttdoc">Get the length of this vector (the norm). </div><div class="ttdef"><b>Definition:</b> b2Math.h:101</div></div>
<div class="ttc" id="structb2_mat22_html_aed3bee1de38a0b3f36e21c90faa24112"><div class="ttname"><a href="structb2_mat22.html#aed3bee1de38a0b3f36e21c90faa24112">b2Mat22::Set</a></div><div class="ttdeci">void Set(const b2Vec2 &c1, const b2Vec2 &c2)</div><div class="ttdoc">Initialize this matrix using columns. </div><div class="ttdef"><b>Definition:</b> b2Math.h:203</div></div>
<div class="ttc" id="structb2_rot_html_a7f534cb7ece8d325662d7d0e27d4f617"><div class="ttname"><a href="structb2_rot.html#a7f534cb7ece8d325662d7d0e27d4f617">b2Rot::SetIdentity</a></div><div class="ttdeci">void SetIdentity()</div><div class="ttdoc">Set to the identity rotation. </div><div class="ttdef"><b>Definition:</b> b2Math.h:320</div></div>
<div class="ttc" id="structb2_sweep_html_aa5f8ab90178b58bc0777096cbc6b91cf"><div class="ttname"><a href="structb2_sweep.html#aa5f8ab90178b58bc0777096cbc6b91cf">b2Sweep::alpha0</a></div><div class="ttdeci">float32 alpha0</div><div class="ttdef"><b>Definition:</b> b2Math.h:399</div></div>
<div class="ttc" id="structb2_mat22_html_a7192f063b771ac9ded060e41df890509"><div class="ttname"><a href="structb2_mat22.html#a7192f063b771ac9ded060e41df890509">b2Mat22::SetIdentity</a></div><div class="ttdeci">void SetIdentity()</div><div class="ttdoc">Set this to the identity matrix. </div><div class="ttdef"><b>Definition:</b> b2Math.h:210</div></div>
<div class="ttc" id="structb2_sweep_html_ad66a3086bc7656df9cf7454013a2f61b"><div class="ttname"><a href="structb2_sweep.html#ad66a3086bc7656df9cf7454013a2f61b">b2Sweep::Normalize</a></div><div class="ttdeci">void Normalize()</div><div class="ttdoc">Normalize the angles. </div><div class="ttdef"><b>Definition:</b> b2Math.h:712</div></div>
<div class="ttc" id="structb2_mat33_html_aa020bfd08e28c4cecda303ba335fe517"><div class="ttname"><a href="structb2_mat33.html#aa020bfd08e28c4cecda303ba335fe517">b2Mat33::GetInverse22</a></div><div class="ttdeci">void GetInverse22(b2Mat33 *M) const</div><div class="ttdef"><b>Definition:</b> b2Math.cpp:56</div></div>
<div class="ttc" id="structb2_sweep_html_a22ae50509de51876aefc48cd76248c61"><div class="ttname"><a href="structb2_sweep.html#a22ae50509de51876aefc48cd76248c61">b2Sweep::GetTransform</a></div><div class="ttdeci">void GetTransform(b2Transform *xfb, float32 beta) const</div><div class="ttdef"><b>Definition:</b> b2Math.h:692</div></div>
<div class="ttc" id="structb2_vec2_html_a543b5264d17df35448632071f8ae7e4d"><div class="ttname"><a href="structb2_vec2.html#a543b5264d17df35448632071f8ae7e4d">b2Vec2::operator()</a></div><div class="ttdeci">float32 operator()(int32 i) const</div><div class="ttdoc">Read from and indexed element. </div><div class="ttdef"><b>Definition:</b> b2Math.h:71</div></div>
<div class="ttc" id="b2_settings_8h_html"><div class="ttname"><a href="b2_settings_8h.html">b2Settings.h</a></div></div>
<div class="ttc" id="structb2_vec2_html_abad59bf9a0269f02cda9dc919592c0ee"><div class="ttname"><a href="structb2_vec2.html#abad59bf9a0269f02cda9dc919592c0ee">b2Vec2::IsValid</a></div><div class="ttdeci">bool IsValid() const</div><div class="ttdoc">Does this vector contain finite coordinates? </div><div class="ttdef"><b>Definition:</b> b2Math.h:129</div></div>
<div class="ttc" id="structb2_mat22_html_aaeae95f61cf3171ffb94703980e3594b"><div class="ttname"><a href="structb2_mat22.html#aaeae95f61cf3171ffb94703980e3594b">b2Mat22::SetZero</a></div><div class="ttdeci">void SetZero()</div><div class="ttdoc">Set this matrix to all zeros. </div><div class="ttdef"><b>Definition:</b> b2Math.h:217</div></div>
<div class="ttc" id="structb2_vec2_html"><div class="ttname"><a href="structb2_vec2.html">b2Vec2</a></div><div class="ttdoc">A 2D column vector. </div><div class="ttdef"><b>Definition:</b> b2Math.h:53</div></div>
<div class="ttc" id="structb2_sweep_html_a35eb9b976ca87c9b8d758bec070c6c06"><div class="ttname"><a href="structb2_sweep.html#a35eb9b976ca87c9b8d758bec070c6c06">b2Sweep::Advance</a></div><div class="ttdeci">void Advance(float32 alpha)</div><div class="ttdef"><b>Definition:</b> b2Math.h:702</div></div>
<div class="ttc" id="structb2_vec2_html_a7097696dce578322928f4535b34f1c6b"><div class="ttname"><a href="structb2_vec2.html#a7097696dce578322928f4535b34f1c6b">b2Vec2::operator*=</a></div><div class="ttdeci">void operator*=(float32 a)</div><div class="ttdoc">Multiply this vector by a scalar. </div><div class="ttdef"><b>Definition:</b> b2Math.h:95</div></div>
<div class="ttc" id="structb2_rot_html_acde9186de0a4a7397bf8ef714408ad60"><div class="ttname"><a href="structb2_rot.html#acde9186de0a4a7397bf8ef714408ad60">b2Rot::Set</a></div><div class="ttdeci">void Set(float32 angle)</div><div class="ttdoc">Set using an angle in radians. </div><div class="ttdef"><b>Definition:</b> b2Math.h:312</div></div>
<div class="ttc" id="structb2_vec2_html_a6cb15514ea571b4ddf73b6829551a127"><div class="ttname"><a href="structb2_vec2.html#a6cb15514ea571b4ddf73b6829551a127">b2Vec2::operator-</a></div><div class="ttdeci">b2Vec2 operator-() const</div><div class="ttdoc">Negate this vector. </div><div class="ttdef"><b>Definition:</b> b2Math.h:68</div></div>
<div class="ttc" id="structb2_transform_html_a823e190e4810e35e8100f4414d0bef62"><div class="ttname"><a href="structb2_transform.html#a823e190e4810e35e8100f4414d0bef62">b2Transform::b2Transform</a></div><div class="ttdeci">b2Transform(const b2Vec2 &position, const b2Rot &rotation)</div><div class="ttdoc">Initialize using a position vector and a rotation. </div><div class="ttdef"><b>Definition:</b> b2Math.h:356</div></div>
<div class="ttc" id="structb2_mat33_html_a42fc6953b025e1c8b59717d0ee7accde"><div class="ttname"><a href="structb2_mat33.html#a42fc6953b025e1c8b59717d0ee7accde">b2Mat33::SetZero</a></div><div class="ttdeci">void SetZero()</div><div class="ttdoc">Set this matrix to all zeros. </div><div class="ttdef"><b>Definition:</b> b2Math.h:271</div></div>
<div class="ttc" id="structb2_mat22_html_a41d5d8743bda32cb8c6e212528934810"><div class="ttname"><a href="structb2_mat22.html#a41d5d8743bda32cb8c6e212528934810">b2Mat22::b2Mat22</a></div><div class="ttdeci">b2Mat22(float32 a11, float32 a12, float32 a21, float32 a22)</div><div class="ttdoc">Construct this matrix using scalars. </div><div class="ttdef"><b>Definition:</b> b2Math.h:196</div></div>
<div class="ttc" id="structb2_mat22_html_a3313c8d135c01fbf74e7fea31f1ea4c1"><div class="ttname"><a href="structb2_mat22.html#a3313c8d135c01fbf74e7fea31f1ea4c1">b2Mat22::Solve</a></div><div class="ttdeci">b2Vec2 Solve(const b2Vec2 &b) const</div><div class="ttdef"><b>Definition:</b> b2Math.h:239</div></div>
<div class="ttc" id="structb2_rot_html_a952a5555c1f68ce3e39ac992fcf4eba9"><div class="ttname"><a href="structb2_rot.html#a952a5555c1f68ce3e39ac992fcf4eba9">b2Rot::GetXAxis</a></div><div class="ttdeci">b2Vec2 GetXAxis() const</div><div class="ttdoc">Get the x-axis. </div><div class="ttdef"><b>Definition:</b> b2Math.h:333</div></div>
<div class="ttc" id="structb2_rot_html"><div class="ttname"><a href="structb2_rot.html">b2Rot</a></div><div class="ttdoc">Rotation. </div><div class="ttdef"><b>Definition:</b> b2Math.h:299</div></div>
<div class="ttc" id="structb2_vec3_html_a396e2b5b3c53a502859ff80544c27db8"><div class="ttname"><a href="structb2_vec3.html#a396e2b5b3c53a502859ff80544c27db8">b2Vec3::operator-</a></div><div class="ttdeci">b2Vec3 operator-() const</div><div class="ttdoc">Negate this vector. </div><div class="ttdef"><b>Definition:</b> b2Math.h:159</div></div>
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