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  38.    <div id="projectname">Jolt Physics
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  40.    <div id="projectbrief">A multi core friendly Game Physics Engine</div>
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  108.   <div class="headertitle"><div class="title">Ellipse.h</div></div>
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    110. 

  110. <div class="contents">
    111. 

  111. <a href="_ellipse_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><span class="preprocessor">#include &lt;<a class="code" href="_float2_8h.html">Jolt/Math/Float2.h</a>&gt;</span></div>
    118. 

  118. <div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</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#ad14098b68b8c44ea6112601031268405">JPH_NAMESPACE_BEGIN</a></div>
    120. 

  120. <div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span> </div>
    121. 

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

  122. <div class="line"><a id="l00013" name="l00013"></a><span class="lineno"><a class="line" href="class_ellipse.html">   13</a></span><span class="keyword">class </span><a class="code hl_class" href="class_ellipse.html">Ellipse</a></div>
    123. 

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

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

  125. <div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span>    <a class="code hl_define" href="_memory_8h.html#a91074fb218fe28954a0938c099ddd9e0">JPH_OVERRIDE_NEW_DELETE</a></div>
    126. 

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

  127. <div class="line"><a id="l00019" name="l00019"></a><span class="lineno"><a class="line" href="class_ellipse.html#a35e3c1cc223333a5e227ea0ff9b120de">   19</a></span>                    <a class="code hl_function" href="class_ellipse.html#a35e3c1cc223333a5e227ea0ff9b120de">Ellipse</a>(<span class="keywordtype">float</span> inA, <span class="keywordtype">float</span> inB) : mA(inA), mB(inB) { <a class="code hl_define" href="_issue_reporting_8h.html#aaf6b1df827e11b7ca5f6f8778bd8f8cd">JPH_ASSERT</a>(inA &gt; 0.0f); <a class="code hl_define" href="_issue_reporting_8h.html#aaf6b1df827e11b7ca5f6f8778bd8f8cd">JPH_ASSERT</a>(inB &gt; 0.0f); }</div>
    128. 

  128. <div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span> </div>
    129. 

  129. <div class="foldopen" id="foldopen00022" data-start="{" data-end="}">
    130. 

  130. <div class="line"><a id="l00022" name="l00022"></a><span class="lineno"><a class="line" href="class_ellipse.html#a5592d2e8e6bb560567b3c9236babd545">   22</a></span>    <span class="keywordtype">bool</span>            <a class="code hl_function" href="class_ellipse.html#a5592d2e8e6bb560567b3c9236babd545">IsInside</a>(<span class="keyword">const</span> <a class="code hl_class" href="class_float2.html">Float2</a> &amp;inPoint)<span class="keyword"> const</span></div>
    131. 

  131. <div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="keyword">    </span>{</div>
    132. 

  132. <div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="_math_8h.html#a61379b8b743a16fe823daeebc1482570">Square</a>(inPoint.<a class="code hl_variable" href="class_float2.html#a9f4577102bc9a7bdf9355b5776301485">x</a> / mA) + <a class="code hl_function" href="_math_8h.html#a61379b8b743a16fe823daeebc1482570">Square</a>(inPoint.<a class="code hl_variable" href="class_float2.html#a53deb463e8335f53a8f5454c9c3c0503">y</a> / mB) &lt;= 1.0f;</div>
    133. 

  133. <div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span>    }</div>
    134. 

  134. </div>
    135. 

  135. <div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span> </div>
    136. 

  136. <div class="foldopen" id="foldopen00030" data-start="{" data-end="}">
    137. 

  137. <div class="line"><a id="l00030" name="l00030"></a><span class="lineno"><a class="line" href="class_ellipse.html#a07b49662cd16799da0e0b1a1d67a8d84">   30</a></span>    <a class="code hl_class" href="class_float2.html">Float2</a>          <a class="code hl_function" href="class_ellipse.html#a07b49662cd16799da0e0b1a1d67a8d84">GetClosestPoint</a>(<span class="keyword">const</span> <a class="code hl_class" href="class_float2.html">Float2</a> &amp;inPoint)<span class="keyword"> const</span></div>
    138. 

  138. <div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="keyword">    </span>{</div>
    139. 

  139. <div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>        <span class="keywordtype">float</span> a_sq = <a class="code hl_function" href="_math_8h.html#a61379b8b743a16fe823daeebc1482570">Square</a>(mA);</div>
    140. 

  140. <div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>        <span class="keywordtype">float</span> b_sq = <a class="code hl_function" href="_math_8h.html#a61379b8b743a16fe823daeebc1482570">Square</a>(mB);</div>
    141. 

  141. <div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span> </div>
    142. 

  142. <div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>        <span class="comment">// Equation of ellipse: f(x, y) = (x/a)^2 + (y/b)^2 - 1 = 0                                         [1]</span></div>
    143. 

  143. <div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>        <span class="comment">// Normal on surface: (df/dx, df/dy) = (2 x / a^2, 2 y / b^2)</span></div>
    144. 

  144. <div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>        <span class="comment">// Closest point (x&#39;, y&#39;) on ellipse to point (x, y): (x&#39;, y&#39;) + t (x / a^2, y / b^2) = (x, y)</span></div>
    145. 

  145. <div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>        <span class="comment">// &lt;=&gt; (x&#39;, y&#39;) = (a^2 x / (t + a^2), b^2 y / (t + b^2))</span></div>
    146. 

  146. <div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>        <span class="comment">// Requiring point to be on ellipse (substituting into [1]): g(t) = (a x / (t + a^2))^2 + (b y / (t + b^2))^2 - 1 = 0</span></div>
    147. 

  147. <div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span> </div>
    148. 

  148. <div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>        <span class="comment">// Newton Raphson iteration, starting at t = 0</span></div>
    149. 

  149. <div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>        <span class="keywordtype">float</span> t = 0.0f;</div>
    150. 

  150. <div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>        <span class="keywordflow">for</span> (;;)</div>
    151. 

  151. <div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>        {</div>
    152. 

  152. <div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>            <span class="comment">// Calculate g(t)</span></div>
    153. 

  153. <div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>            <span class="keywordtype">float</span> t_plus_a_sq = t + a_sq;</div>
    154. 

  154. <div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>            <span class="keywordtype">float</span> t_plus_b_sq = t + b_sq;</div>
    155. 

  155. <div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>            <span class="keywordtype">float</span> gt = <a class="code hl_function" href="_math_8h.html#a61379b8b743a16fe823daeebc1482570">Square</a>(mA * inPoint.<a class="code hl_variable" href="class_float2.html#a9f4577102bc9a7bdf9355b5776301485">x</a> / t_plus_a_sq) + <a class="code hl_function" href="_math_8h.html#a61379b8b743a16fe823daeebc1482570">Square</a>(mB * inPoint.<a class="code hl_variable" href="class_float2.html#a53deb463e8335f53a8f5454c9c3c0503">y</a> / t_plus_b_sq) - 1.0f;</div>
    156. 

  156. <div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span> </div>
    157. 

  157. <div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>            <span class="comment">// Check if g(t) it is close enough to zero</span></div>
    158. 

  158. <div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>            <span class="keywordflow">if</span> (abs(gt) &lt; 1.0e-6f)</div>
    159. 

  159. <div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>                <span class="keywordflow">return</span> <a class="code hl_class" href="class_float2.html">Float2</a>(a_sq * inPoint.<a class="code hl_variable" href="class_float2.html#a9f4577102bc9a7bdf9355b5776301485">x</a> / t_plus_a_sq, b_sq * inPoint.<a class="code hl_variable" href="class_float2.html#a53deb463e8335f53a8f5454c9c3c0503">y</a> / t_plus_b_sq);</div>
    160. 

  160. <div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span> </div>
    161. 

  161. <div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>            <span class="comment">// Get derivative dg/dt = g&#39;(t) = -2 (b^2 y^2 / (t + b^2)^3 + a^2 x^2 / (t + a^2)^3)</span></div>
    162. 

  162. <div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>            <span class="keywordtype">float</span> gt_accent = -2.0f *</div>
    163. 

  163. <div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>                (a_sq * <a class="code hl_function" href="_math_8h.html#a61379b8b743a16fe823daeebc1482570">Square</a>(inPoint.<a class="code hl_variable" href="class_float2.html#a9f4577102bc9a7bdf9355b5776301485">x</a>) / <a class="code hl_function" href="_math_8h.html#a6a1a326c0e5f6b61307d2458bcce0eb8">Cubed</a>(t_plus_a_sq)</div>
    164. 

  164. <div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>                + b_sq * <a class="code hl_function" href="_math_8h.html#a61379b8b743a16fe823daeebc1482570">Square</a>(inPoint.<a class="code hl_variable" href="class_float2.html#a53deb463e8335f53a8f5454c9c3c0503">y</a>) / <a class="code hl_function" href="_math_8h.html#a6a1a326c0e5f6b61307d2458bcce0eb8">Cubed</a>(t_plus_b_sq));</div>
    165. 

  165. <div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span> </div>
    166. 

  166. <div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>            <span class="comment">// Calculate t for next iteration: tn+1 = tn - g(t) / g&#39;(t)</span></div>
    167. 

  167. <div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>            <span class="keywordtype">float</span> tn = t - gt / gt_accent;</div>
    168. 

  168. <div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>            t = tn;</div>
    169. 

  169. <div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        }</div>
    170. 

  170. <div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>    }</div>
    171. 

  171. </div>
    172. 

  172. <div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span> </div>
    173. 

  173. <div class="foldopen" id="foldopen00066" data-start="{" data-end="}">
    174. 

  174. <div class="line"><a id="l00066" name="l00066"></a><span class="lineno"><a class="line" href="class_ellipse.html#a827cce3196e44e983b0fb525eb9d52ac">   66</a></span>    <a class="code hl_class" href="class_float2.html">Float2</a>          <a class="code hl_function" href="class_ellipse.html#a827cce3196e44e983b0fb525eb9d52ac">GetNormal</a>(<span class="keyword">const</span> <a class="code hl_class" href="class_float2.html">Float2</a> &amp;inPoint)<span class="keyword"> const</span></div>
    175. 

  175. <div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span><span class="keyword">    </span>{</div>
    176. 

  176. <div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>        <span class="comment">// Calculated by [d/dx f(x, y), d/dy f(x, y)], where f(x, y) is the ellipse equation from above</span></div>
    177. 

  177. <div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>        <span class="keywordflow">return</span> <a class="code hl_class" href="class_float2.html">Float2</a>(inPoint.<a class="code hl_variable" href="class_float2.html#a9f4577102bc9a7bdf9355b5776301485">x</a> / <a class="code hl_function" href="_math_8h.html#a61379b8b743a16fe823daeebc1482570">Square</a>(mA), inPoint.<a class="code hl_variable" href="class_float2.html#a53deb463e8335f53a8f5454c9c3c0503">y</a> / <a class="code hl_function" href="_math_8h.html#a61379b8b743a16fe823daeebc1482570">Square</a>(mB));</div>
    178. 

  178. <div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>    }</div>
    179. 

  179. </div>
    180. 

  180. <div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span> </div>
    181. 

  181. <div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span><span class="keyword">private</span>:</div>
    182. 

  182. <div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <span class="keywordtype">float</span>           mA;             </div>
    183. 

  183. <div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    <span class="keywordtype">float</span>           mB;             </div>
    184. 

  184. <div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>};</div>
    185. 

  185. </div>
    186. 

  186. <div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span> </div>
    187. 

  187. <div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span><a class="code hl_define" href="_core_8h.html#a73da8725998b00321a9db341202d650d">JPH_NAMESPACE_END</a></div>
    188. 

  188. <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>
    189. 

  189. <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>
    190. 

  190. <div class="ttc" id="a_float2_8h_html"><div class="ttname"><a href="_float2_8h.html">Float2.h</a></div></div>
    191. 

  191. <div class="ttc" id="a_issue_reporting_8h_html_aaf6b1df827e11b7ca5f6f8778bd8f8cd"><div class="ttname"><a href="_issue_reporting_8h.html#aaf6b1df827e11b7ca5f6f8778bd8f8cd">JPH_ASSERT</a></div><div class="ttdeci">#define JPH_ASSERT(...)</div><div class="ttdef"><b>Definition</b> IssueReporting.h:33</div></div>
    192. 

  192. <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>
    193. 

  193. <div class="ttc" id="a_math_8h_html_a6a1a326c0e5f6b61307d2458bcce0eb8"><div class="ttname"><a href="_math_8h.html#a6a1a326c0e5f6b61307d2458bcce0eb8">Cubed</a></div><div class="ttdeci">JPH_INLINE constexpr T Cubed(T inV)</div><div class="ttdoc">Returns .</div><div class="ttdef"><b>Definition</b> Math.h:62</div></div>
    194. 

  194. <div class="ttc" id="a_memory_8h_html_a91074fb218fe28954a0938c099ddd9e0"><div class="ttname"><a href="_memory_8h.html#a91074fb218fe28954a0938c099ddd9e0">JPH_OVERRIDE_NEW_DELETE</a></div><div class="ttdeci">#define JPH_OVERRIDE_NEW_DELETE</div><div class="ttdoc">Macro to override the new and delete functions.</div><div class="ttdef"><b>Definition</b> Memory.h:50</div></div>
    195. 

  195. <div class="ttc" id="aclass_ellipse_html"><div class="ttname"><a href="class_ellipse.html">Ellipse</a></div><div class="ttdef"><b>Definition</b> Ellipse.h:14</div></div>
    196. 

  196. <div class="ttc" id="aclass_ellipse_html_a07b49662cd16799da0e0b1a1d67a8d84"><div class="ttname"><a href="class_ellipse.html#a07b49662cd16799da0e0b1a1d67a8d84">Ellipse::GetClosestPoint</a></div><div class="ttdeci">Float2 GetClosestPoint(const Float2 &amp;inPoint) const</div><div class="ttdef"><b>Definition</b> Ellipse.h:30</div></div>
    197. 

  197. <div class="ttc" id="aclass_ellipse_html_a35e3c1cc223333a5e227ea0ff9b120de"><div class="ttname"><a href="class_ellipse.html#a35e3c1cc223333a5e227ea0ff9b120de">Ellipse::Ellipse</a></div><div class="ttdeci">JPH_OVERRIDE_NEW_DELETE Ellipse(float inA, float inB)</div><div class="ttdoc">Construct ellipse with radius A along the X-axis and B along the Y-axis.</div><div class="ttdef"><b>Definition</b> Ellipse.h:19</div></div>
    198. 

  198. <div class="ttc" id="aclass_ellipse_html_a5592d2e8e6bb560567b3c9236babd545"><div class="ttname"><a href="class_ellipse.html#a5592d2e8e6bb560567b3c9236babd545">Ellipse::IsInside</a></div><div class="ttdeci">bool IsInside(const Float2 &amp;inPoint) const</div><div class="ttdoc">Check if inPoint is inside the ellipse.</div><div class="ttdef"><b>Definition</b> Ellipse.h:22</div></div>
    199. 

  199. <div class="ttc" id="aclass_ellipse_html_a827cce3196e44e983b0fb525eb9d52ac"><div class="ttname"><a href="class_ellipse.html#a827cce3196e44e983b0fb525eb9d52ac">Ellipse::GetNormal</a></div><div class="ttdeci">Float2 GetNormal(const Float2 &amp;inPoint) const</div><div class="ttdoc">Get normal at point inPoint (non-normalized vector)</div><div class="ttdef"><b>Definition</b> Ellipse.h:66</div></div>
    200. 

  200. <div class="ttc" id="aclass_float2_html"><div class="ttname"><a href="class_float2.html">Float2</a></div><div class="ttdoc">Class that holds 2 floats, used as a storage class mainly.</div><div class="ttdef"><b>Definition</b> Float2.h:11</div></div>
    201. 

  201. <div class="ttc" id="aclass_float2_html_a53deb463e8335f53a8f5454c9c3c0503"><div class="ttname"><a href="class_float2.html#a53deb463e8335f53a8f5454c9c3c0503">Float2::y</a></div><div class="ttdeci">float y</div><div class="ttdef"><b>Definition</b> Float2.h:31</div></div>
    202. 

  202. <div class="ttc" id="aclass_float2_html_a9f4577102bc9a7bdf9355b5776301485"><div class="ttname"><a href="class_float2.html#a9f4577102bc9a7bdf9355b5776301485">Float2::x</a></div><div class="ttdeci">float x</div><div class="ttdef"><b>Definition</b> Float2.h:30</div></div>
    203. 

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    204. 

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    207. 

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  208.     <li class="navelem"><a class="el" href="dir_d99289a5d3c46cf26f14ff6c90658d9f.html">Jolt</a></li><li class="navelem"><a class="el" href="dir_2d88bf03bf4a7a62918727c0f2ee34eb.html">Geometry</a></li><li class="navelem"><a class="el" href="_ellipse_8h.html">Ellipse.h</a></li>
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