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    111. 

  111. <a href="_spring_part_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">// Jolt Physics Library (https://github.com/jrouwe/JoltPhysics)</span></div>
    112. 

  112. <div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment">// SPDX-FileCopyrightText: 2021 Jorrit Rouwe</span></div>
    113. 

  113. <div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment">// SPDX-License-Identifier: MIT</span></div>
    114. 

  114. <div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span> </div>
    115. 

  115. <div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="preprocessor">#pragma once</span></div>
    116. 

  116. <div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span> </div>
    117. 

  117. <div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><a class="code hl_define" href="_core_8h.html#ad14098b68b8c44ea6112601031268405">JPH_NAMESPACE_BEGIN</a></div>
    118. 

  118. <div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="preprocessor">#ifndef JPH_PLATFORM_DOXYGEN </span><span class="comment">// Somehow Doxygen gets confused and thinks the parameters to CalculateSpringProperties belong to this macro</span></div>
    119. 

  119. <div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><a class="code hl_define" href="_core_8h.html#a7e50ac7352b8f5948a91b543756c84a8">JPH_MSVC_SUPPRESS_WARNING</a>(4723) <span class="comment">// potential divide by 0 - caused by line: outEffectiveMass = 1.0f / inInvEffectiveMass, note that JPH_NAMESPACE_BEGIN already pushes the warning state</span></div>
    120. 

  120. <div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="preprocessor">#endif </span><span class="comment">// !JPH_PLATFORM_DOXYGEN</span></div>
    121. 

  121. <div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span> </div>
    122. 

  122. <div class="foldopen" id="foldopen00013" data-start="{" data-end="};">
    123. 

  123. <div class="line"><a id="l00013" name="l00013"></a><span class="lineno"><a class="line" href="class_spring_part.html">   13</a></span><span class="keyword">class </span><a class="code hl_class" href="class_spring_part.html">SpringPart</a></div>
    124. 

  124. <div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span>{</div>
    125. 

  125. <div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="keyword">private</span>:</div>
    126. 

  126. <div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span>    JPH_INLINE <span class="keywordtype">void</span>             CalculateSpringPropertiesHelper(<span class="keywordtype">float</span> inDeltaTime, <span class="keywordtype">float</span> inInvEffectiveMass, <span class="keywordtype">float</span> inBias, <span class="keywordtype">float</span> inC, <span class="keywordtype">float</span> inStiffness, <span class="keywordtype">float</span> inDamping, <span class="keywordtype">float</span> &amp;outEffectiveMass)</div>
    127. 

  127. <div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span>    {</div>
    128. 

  128. <div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span>        <span class="comment">// Soft constraints as per: Soft Constraints: Reinventing The Spring - Erin Catto - GDC 2011</span></div>
    129. 

  129. <div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span> </div>
    130. 

  130. <div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span>        <span class="comment">// Note that the calculation of beta and gamma below are based on the solution of an implicit Euler integration scheme</span></div>
    131. 

  131. <div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>        <span class="comment">// This scheme is unconditionally stable but has built in damping, so even when you set the damping ratio to 0 there will still</span></div>
    132. 

  132. <div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>        <span class="comment">// be damping. See page 16 and 32.</span></div>
    133. 

  133. <div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span> </div>
    134. 

  134. <div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span>        <span class="comment">// Calculate softness (gamma in the slides)</span></div>
    135. 

  135. <div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span>        <span class="comment">// See page 34 and note that the gamma needs to be divided by delta time since we&#39;re working with impulses rather than forces:</span></div>
    136. 

  136. <div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>        <span class="comment">// softness = 1 / (dt * (c + dt * k))</span></div>
    137. 

  137. <div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>        <span class="comment">// Note that the spring stiffness is k and the spring damping is c</span></div>
    138. 

  138. <div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>        mSoftness = 1.0f / (inDeltaTime * (inDamping + inDeltaTime * inStiffness));</div>
    139. 

  139. <div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span> </div>
    140. 

  140. <div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>        <span class="comment">// Calculate bias factor (baumgarte stabilization):</span></div>
    141. 

  141. <div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>        <span class="comment">// beta = dt * k / (c + dt * k) = dt * k^2 * softness</span></div>
    142. 

  142. <div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>        <span class="comment">// b = beta / dt * C = dt * k * softness * C</span></div>
    143. 

  143. <div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>        mBias = inBias + inDeltaTime * inStiffness * mSoftness * inC;</div>
    144. 

  144. <div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span> </div>
    145. 

  145. <div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>        <span class="comment">// Update the effective mass, see post by Erin Catto: http://www.bulletphysics.org/Bullet/phpBB3/viewtopic.php?f=4&amp;t=1354</span></div>
    146. 

  146. <div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>        <span class="comment">//</span></div>
    147. 

  147. <div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>        <span class="comment">// Newton&#39;s Law:</span></div>
    148. 

  148. <div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>        <span class="comment">// M * (v2 - v1) = J^T * lambda</span></div>
    149. 

  149. <div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>        <span class="comment">//</span></div>
    150. 

  150. <div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>        <span class="comment">// Velocity constraint with softness and Baumgarte:</span></div>
    151. 

  151. <div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>        <span class="comment">// J * v2 + softness * lambda + b = 0</span></div>
    152. 

  152. <div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>        <span class="comment">//</span></div>
    153. 

  153. <div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>        <span class="comment">// where b = beta * C / dt</span></div>
    154. 

  154. <div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>        <span class="comment">//</span></div>
    155. 

  155. <div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>        <span class="comment">// We know everything except v2 and lambda.</span></div>
    156. 

  156. <div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>        <span class="comment">//</span></div>
    157. 

  157. <div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>        <span class="comment">// First solve Newton&#39;s law for v2 in terms of lambda:</span></div>
    158. 

  158. <div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>        <span class="comment">//</span></div>
    159. 

  159. <div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>        <span class="comment">// v2 = v1 + M^-1 * J^T * lambda</span></div>
    160. 

  160. <div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>        <span class="comment">//</span></div>
    161. 

  161. <div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>        <span class="comment">// Substitute this expression into the velocity constraint:</span></div>
    162. 

  162. <div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>        <span class="comment">//</span></div>
    163. 

  163. <div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>        <span class="comment">// J * (v1 + M^-1 * J^T * lambda) + softness * lambda + b = 0</span></div>
    164. 

  164. <div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>        <span class="comment">//</span></div>
    165. 

  165. <div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>        <span class="comment">// Now collect coefficients of lambda:</span></div>
    166. 

  166. <div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>        <span class="comment">//</span></div>
    167. 

  167. <div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>        <span class="comment">// (J * M^-1 * J^T + softness) * lambda = - J * v1 - b</span></div>
    168. 

  168. <div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>        <span class="comment">//</span></div>
    169. 

  169. <div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>        <span class="comment">// Now we define:</span></div>
    170. 

  170. <div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>        <span class="comment">//</span></div>
    171. 

  171. <div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        <span class="comment">// K = J * M^-1 * J^T + softness</span></div>
    172. 

  172. <div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        <span class="comment">//</span></div>
    173. 

  173. <div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        <span class="comment">// So our new effective mass is K^-1</span></div>
    174. 

  174. <div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        outEffectiveMass = 1.0f / (inInvEffectiveMass + mSoftness);</div>
    175. 

  175. <div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    }</div>
    176. 

  176. <div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span> </div>
    177. 

  177. <div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span><span class="keyword">public</span>:</div>
    178. 

  178. <div class="foldopen" id="foldopen00071" data-start="{" data-end="}">
    179. 

  179. <div class="line"><a id="l00071" name="l00071"></a><span class="lineno"><a class="line" href="class_spring_part.html#a75d1d4a45e975a5b9b0ad99525c9f52f">   71</a></span>    <span class="keyword">inline</span> <span class="keywordtype">void</span>                 <a class="code hl_function" href="class_spring_part.html#a75d1d4a45e975a5b9b0ad99525c9f52f">CalculateSpringPropertiesWithBias</a>(<span class="keywordtype">float</span> inBias)</div>
    180. 

  180. <div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    {</div>
    181. 

  181. <div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>        mSoftness = 0.0f;</div>
    182. 

  182. <div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>        mBias = inBias;</div>
    183. 

  183. <div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    }</div>
    184. 

  184. </div>
    185. 

  185. <div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span> </div>
    186. 

  186. <div class="foldopen" id="foldopen00086" data-start="{" data-end="}">
    187. 

  187. <div class="line"><a id="l00086" name="l00086"></a><span class="lineno"><a class="line" href="class_spring_part.html#a0414048df549022dee152c2b18b31126">   86</a></span>    <span class="keyword">inline</span> <span class="keywordtype">void</span>                 <a class="code hl_function" href="class_spring_part.html#a0414048df549022dee152c2b18b31126">CalculateSpringPropertiesWithFrequencyAndDamping</a>(<span class="keywordtype">float</span> inDeltaTime, <span class="keywordtype">float</span> inInvEffectiveMass, <span class="keywordtype">float</span> inBias, <span class="keywordtype">float</span> inC, <span class="keywordtype">float</span> inFrequency, <span class="keywordtype">float</span> inDamping, <span class="keywordtype">float</span> &amp;outEffectiveMass)</div>
    188. 

  188. <div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>    {</div>
    189. 

  189. <div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        outEffectiveMass = 1.0f / inInvEffectiveMass;</div>
    190. 

  190. <div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span> </div>
    191. 

  191. <div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>        <span class="keywordflow">if</span> (inFrequency &gt; 0.0f)</div>
    192. 

  192. <div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>        {</div>
    193. 

  193. <div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>            <span class="comment">// Calculate angular frequency</span></div>
    194. 

  194. <div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>            <span class="keywordtype">float</span> omega = 2.0f * JPH_PI * inFrequency;</div>
    195. 

  195. <div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span> </div>
    196. 

  196. <div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>            <span class="comment">// Calculate spring stiffness k and damping constant c (page 45)</span></div>
    197. 

  197. <div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>            <span class="keywordtype">float</span> k = outEffectiveMass * <a class="code hl_function" href="_math_8h.html#a61379b8b743a16fe823daeebc1482570">Square</a>(omega);</div>
    198. 

  198. <div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>            <span class="keywordtype">float</span> c = 2.0f * outEffectiveMass * inDamping * omega;</div>
    199. 

  199. <div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span> </div>
    200. 

  200. <div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>            CalculateSpringPropertiesHelper(inDeltaTime, inInvEffectiveMass, inBias, inC, k, c, outEffectiveMass);</div>
    201. 

  201. <div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>        }</div>
    202. 

  202. <div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>        <span class="keywordflow">else</span></div>
    203. 

  203. <div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>        {</div>
    204. 

  204. <div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>            <a class="code hl_function" href="class_spring_part.html#a75d1d4a45e975a5b9b0ad99525c9f52f">CalculateSpringPropertiesWithBias</a>(inBias);</div>
    205. 

  205. <div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>        }</div>
    206. 

  206. <div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    }</div>
    207. 

  207. </div>
    208. 

  208. <div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span> </div>
    209. 

  209. <div class="foldopen" id="foldopen00116" data-start="{" data-end="}">
    210. 

  210. <div class="line"><a id="l00116" name="l00116"></a><span class="lineno"><a class="line" href="class_spring_part.html#a318ab5426c6b10a8ceebd3258144d20a">  116</a></span>    <span class="keyword">inline</span> <span class="keywordtype">void</span>                 <a class="code hl_function" href="class_spring_part.html#a318ab5426c6b10a8ceebd3258144d20a">CalculateSpringPropertiesWithStiffnessAndDamping</a>(<span class="keywordtype">float</span> inDeltaTime, <span class="keywordtype">float</span> inInvEffectiveMass, <span class="keywordtype">float</span> inBias, <span class="keywordtype">float</span> inC, <span class="keywordtype">float</span> inStiffness, <span class="keywordtype">float</span> inDamping, <span class="keywordtype">float</span> &amp;outEffectiveMass)</div>
    211. 

  211. <div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    {</div>
    212. 

  212. <div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>        <span class="keywordflow">if</span> (inStiffness &gt; 0.0f)</div>
    213. 

  213. <div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>        {</div>
    214. 

  214. <div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>            CalculateSpringPropertiesHelper(inDeltaTime, inInvEffectiveMass, inBias, inC, inStiffness, inDamping, outEffectiveMass);</div>
    215. 

  215. <div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>        }</div>
    216. 

  216. <div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>        <span class="keywordflow">else</span></div>
    217. 

  217. <div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>        {</div>
    218. 

  218. <div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>            outEffectiveMass = 1.0f / inInvEffectiveMass;</div>
    219. 

  219. <div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span> </div>
    220. 

  220. <div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>            <a class="code hl_function" href="class_spring_part.html#a75d1d4a45e975a5b9b0ad99525c9f52f">CalculateSpringPropertiesWithBias</a>(inBias);</div>
    221. 

  221. <div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>        }</div>
    222. 

  222. <div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    }</div>
    223. 

  223. </div>
    224. 

  224. <div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span> </div>
    225. 

  225. <div class="foldopen" id="foldopen00131" data-start="{" data-end="}">
    226. 

  226. <div class="line"><a id="l00131" name="l00131"></a><span class="lineno"><a class="line" href="class_spring_part.html#a9dbe7d09f4a6aaf7f5edd106fb6fe335">  131</a></span>    <span class="keyword">inline</span> <span class="keywordtype">bool</span>                 <a class="code hl_function" href="class_spring_part.html#a9dbe7d09f4a6aaf7f5edd106fb6fe335">IsActive</a>()<span class="keyword"> const</span></div>
    227. 

  227. <div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span><span class="keyword">    </span>{</div>
    228. 

  228. <div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>        <span class="keywordflow">return</span> mSoftness != 0.0f;</div>
    229. 

  229. <div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>    }</div>
    230. 

  230. </div>
    231. 

  231. <div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span> </div>
    232. 

  232. <div class="foldopen" id="foldopen00137" data-start="{" data-end="}">
    233. 

  233. <div class="line"><a id="l00137" name="l00137"></a><span class="lineno"><a class="line" href="class_spring_part.html#a42a39d96e15ae84419256c35067e12ad">  137</a></span>    <span class="keyword">inline</span> <span class="keywordtype">float</span>                <a class="code hl_function" href="class_spring_part.html#a42a39d96e15ae84419256c35067e12ad">GetBias</a>(<span class="keywordtype">float</span> inTotalLambda)<span class="keyword"> const</span></div>
    234. 

  234. <div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span><span class="keyword">    </span>{</div>
    235. 

  235. <div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        <span class="comment">// Remainder of post by Erin Catto: http://www.bulletphysics.org/Bullet/phpBB3/viewtopic.php?f=4&amp;t=1354</span></div>
    236. 

  236. <div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>        <span class="comment">//</span></div>
    237. 

  237. <div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>        <span class="comment">// Each iteration we are not computing the whole impulse, we are computing an increment to the impulse and we are updating the velocity.</span></div>
    238. 

  238. <div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>        <span class="comment">// Also, as we solve each constraint we get a perfect v2, but then some other constraint will come along and mess it up.</span></div>
    239. 

  239. <div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>        <span class="comment">// So we want to patch up the constraint while acknowledging the accumulated impulse and the damaged velocity.</span></div>
    240. 

  240. <div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>        <span class="comment">// To help with that we use P for the accumulated impulse and lambda as the update. Mathematically we have:</span></div>
    241. 

  241. <div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>        <span class="comment">//</span></div>
    242. 

  242. <div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>        <span class="comment">// M * (v2new - v2damaged) = J^T * lambda</span></div>
    243. 

  243. <div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>        <span class="comment">// J * v2new + softness * (total_lambda + lambda) + b = 0</span></div>
    244. 

  244. <div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>        <span class="comment">//</span></div>
    245. 

  245. <div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>        <span class="comment">// If we solve this we get:</span></div>
    246. 

  246. <div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>        <span class="comment">//</span></div>
    247. 

  247. <div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>        <span class="comment">// v2new = v2damaged + M^-1 * J^T * lambda</span></div>
    248. 

  248. <div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>        <span class="comment">// J * (v2damaged + M^-1 * J^T * lambda) + softness * total_lambda + softness * lambda + b = 0</span></div>
    249. 

  249. <div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>        <span class="comment">//</span></div>
    250. 

  250. <div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>        <span class="comment">// (J * M^-1 * J^T + softness) * lambda = -(J * v2damaged + softness * total_lambda + b)</span></div>
    251. 

  251. <div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>        <span class="comment">//</span></div>
    252. 

  252. <div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>        <span class="comment">// So our lagrange multiplier becomes:</span></div>
    253. 

  253. <div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>        <span class="comment">//</span></div>
    254. 

  254. <div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>        <span class="comment">// lambda = -K^-1 (J v + softness * total_lambda + b)</span></div>
    255. 

  255. <div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>        <span class="comment">//</span></div>
    256. 

  256. <div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>        <span class="comment">// So we return the bias: softness * total_lambda + b</span></div>
    257. 

  257. <div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>        <span class="keywordflow">return</span> mSoftness * inTotalLambda + mBias;</div>
    258. 

  258. <div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>    }</div>
    259. 

  259. </div>
    260. 

  260. <div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span> </div>
    261. 

  261. <div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span><span class="keyword">private</span>:</div>
    262. 

  262. <div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>    <span class="keywordtype">float</span>                       mBias  = 0.0f;</div>
    263. 

  263. <div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>    <span class="keywordtype">float</span>                       mSoftness  = 0.0f;</div>
    264. 

  264. <div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>};</div>
    265. 

  265. </div>
    266. 

  266. <div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span> </div>
    267. 

  267. <div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span><a class="code hl_define" href="_core_8h.html#a73da8725998b00321a9db341202d650d">JPH_NAMESPACE_END</a></div>
    268. 

  268. <div class="ttc" id="a_core_8h_html_a73da8725998b00321a9db341202d650d"><div class="ttname"><a href="_core_8h.html#a73da8725998b00321a9db341202d650d">JPH_NAMESPACE_END</a></div><div class="ttdeci">#define JPH_NAMESPACE_END</div><div class="ttdef"><b>Definition</b> Core.h:425</div></div>
    269. 

  269. <div class="ttc" id="a_core_8h_html_a7e50ac7352b8f5948a91b543756c84a8"><div class="ttname"><a href="_core_8h.html#a7e50ac7352b8f5948a91b543756c84a8">JPH_MSVC_SUPPRESS_WARNING</a></div><div class="ttdeci">#define JPH_MSVC_SUPPRESS_WARNING(w)</div><div class="ttdef"><b>Definition</b> Core.h:330</div></div>
    270. 

  270. <div class="ttc" id="a_core_8h_html_ad14098b68b8c44ea6112601031268405"><div class="ttname"><a href="_core_8h.html#ad14098b68b8c44ea6112601031268405">JPH_NAMESPACE_BEGIN</a></div><div class="ttdeci">#define JPH_NAMESPACE_BEGIN</div><div class="ttdef"><b>Definition</b> Core.h:419</div></div>
    271. 

  271. <div class="ttc" id="a_math_8h_html_a61379b8b743a16fe823daeebc1482570"><div class="ttname"><a href="_math_8h.html#a61379b8b743a16fe823daeebc1482570">Square</a></div><div class="ttdeci">JPH_INLINE constexpr T Square(T inV)</div><div class="ttdoc">Square a value.</div><div class="ttdef"><b>Definition</b> Math.h:55</div></div>
    272. 

  272. <div class="ttc" id="aclass_spring_part_html"><div class="ttname"><a href="class_spring_part.html">SpringPart</a></div><div class="ttdoc">Class used in other constraint parts to calculate the required bias factor in the lagrange multiplier...</div><div class="ttdef"><b>Definition</b> SpringPart.h:14</div></div>
    273. 

  273. <div class="ttc" id="aclass_spring_part_html_a0414048df549022dee152c2b18b31126"><div class="ttname"><a href="class_spring_part.html#a0414048df549022dee152c2b18b31126">SpringPart::CalculateSpringPropertiesWithFrequencyAndDamping</a></div><div class="ttdeci">void CalculateSpringPropertiesWithFrequencyAndDamping(float inDeltaTime, float inInvEffectiveMass, float inBias, float inC, float inFrequency, float inDamping, float &amp;outEffectiveMass)</div><div class="ttdef"><b>Definition</b> SpringPart.h:86</div></div>
    274. 

  274. <div class="ttc" id="aclass_spring_part_html_a318ab5426c6b10a8ceebd3258144d20a"><div class="ttname"><a href="class_spring_part.html#a318ab5426c6b10a8ceebd3258144d20a">SpringPart::CalculateSpringPropertiesWithStiffnessAndDamping</a></div><div class="ttdeci">void CalculateSpringPropertiesWithStiffnessAndDamping(float inDeltaTime, float inInvEffectiveMass, float inBias, float inC, float inStiffness, float inDamping, float &amp;outEffectiveMass)</div><div class="ttdef"><b>Definition</b> SpringPart.h:116</div></div>
    275. 

  275. <div class="ttc" id="aclass_spring_part_html_a42a39d96e15ae84419256c35067e12ad"><div class="ttname"><a href="class_spring_part.html#a42a39d96e15ae84419256c35067e12ad">SpringPart::GetBias</a></div><div class="ttdeci">float GetBias(float inTotalLambda) const</div><div class="ttdoc">Get total bias b, including supplied bias and bias for spring: lambda = J v + b.</div><div class="ttdef"><b>Definition</b> SpringPart.h:137</div></div>
    276. 

  276. <div class="ttc" id="aclass_spring_part_html_a75d1d4a45e975a5b9b0ad99525c9f52f"><div class="ttname"><a href="class_spring_part.html#a75d1d4a45e975a5b9b0ad99525c9f52f">SpringPart::CalculateSpringPropertiesWithBias</a></div><div class="ttdeci">void CalculateSpringPropertiesWithBias(float inBias)</div><div class="ttdef"><b>Definition</b> SpringPart.h:71</div></div>
    277. 

  277. <div class="ttc" id="aclass_spring_part_html_a9dbe7d09f4a6aaf7f5edd106fb6fe335"><div class="ttname"><a href="class_spring_part.html#a9dbe7d09f4a6aaf7f5edd106fb6fe335">SpringPart::IsActive</a></div><div class="ttdeci">bool IsActive() const</div><div class="ttdoc">Returns if this spring is active.</div><div class="ttdef"><b>Definition</b> SpringPart.h:131</div></div>
    278. 

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