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- <div class="headertitle"><div class="title">Trigonometry.h</div></div>
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- <div class="contents">
- <a href="_trigonometry_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>
- <div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// SPDX-FileCopyrightText: 2021 Jorrit Rouwe</span></div>
- <div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">// SPDX-License-Identifier: MIT</span></div>
- <div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span> </div>
- <div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="preprocessor">#pragma once</span></div>
- <div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span> </div>
- <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>
- <div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span> </div>
- <div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// Note that this file exists because std::sin etc. are not platform independent and will lead to non-deterministic simulation</span></div>
- <div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span> </div>
- <div class="foldopen" id="foldopen00012" data-start="{" data-end="}">
- <div class="line"><a id="l00012" name="l00012"></a><span class="lineno"><a class="line" href="_trigonometry_8h.html#a89091907eb3da97f690e324849d773cb"> 12</a></span>JPH_INLINE <span class="keywordtype">float</span> <a class="code hl_function" href="_trigonometry_8h.html#a89091907eb3da97f690e324849d773cb">Sin</a>(<span class="keywordtype">float</span> inX)</div>
- <div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span>{</div>
- <div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span> <a class="code hl_class" href="class_vec4.html">Vec4</a> s, c;</div>
- <div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> <a class="code hl_function" href="class_vec4.html#af18f350dd2885dc48ff7e7cbf4b8bc9d">Vec4::sReplicate</a>(inX).<a class="code hl_function" href="class_vec4.html#af7e7da5ada5c3e85aac45d62871a867c">SinCos</a>(s, c);</div>
- <div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> <span class="keywordflow">return</span> s.<a class="code hl_function" href="class_vec4.html#aad89aa3a9c4215f45c0dbe1fb65830c3">GetX</a>();</div>
- <div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span>}</div>
- </div>
- <div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> </div>
- <div class="foldopen" id="foldopen00020" data-start="{" data-end="}">
- <div class="line"><a id="l00020" name="l00020"></a><span class="lineno"><a class="line" href="_trigonometry_8h.html#a40fafb1c427199b6855d704fc79cd1cf"> 20</a></span>JPH_INLINE <span class="keywordtype">float</span> <a class="code hl_function" href="_trigonometry_8h.html#a40fafb1c427199b6855d704fc79cd1cf">Cos</a>(<span class="keywordtype">float</span> inX)</div>
- <div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span>{</div>
- <div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> <a class="code hl_class" href="class_vec4.html">Vec4</a> s, c;</div>
- <div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> <a class="code hl_function" href="class_vec4.html#af18f350dd2885dc48ff7e7cbf4b8bc9d">Vec4::sReplicate</a>(inX).<a class="code hl_function" href="class_vec4.html#af7e7da5ada5c3e85aac45d62871a867c">SinCos</a>(s, c);</div>
- <div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> <span class="keywordflow">return</span> c.<a class="code hl_function" href="class_vec4.html#aad89aa3a9c4215f45c0dbe1fb65830c3">GetX</a>();</div>
- <div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span>}</div>
- </div>
- <div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> </div>
- <div class="foldopen" id="foldopen00028" data-start="{" data-end="}">
- <div class="line"><a id="l00028" name="l00028"></a><span class="lineno"><a class="line" href="_trigonometry_8h.html#a138c843d7c7c5f89c1757b159a86eb00"> 28</a></span>JPH_INLINE <span class="keywordtype">float</span> <a class="code hl_function" href="_trigonometry_8h.html#a138c843d7c7c5f89c1757b159a86eb00">Tan</a>(<span class="keywordtype">float</span> inX)</div>
- <div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span>{</div>
- <div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> <span class="keywordflow">return</span> <a class="code hl_function" href="class_vec4.html#af18f350dd2885dc48ff7e7cbf4b8bc9d">Vec4::sReplicate</a>(inX).<a class="code hl_function" href="class_vec4.html#a3769f486156183d3cbecb6a37291fe5c">Tan</a>().<a class="code hl_function" href="class_vec4.html#aad89aa3a9c4215f45c0dbe1fb65830c3">GetX</a>();</div>
- <div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span>}</div>
- </div>
- <div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> </div>
- <div class="foldopen" id="foldopen00035" data-start="{" data-end="}">
- <div class="line"><a id="l00035" name="l00035"></a><span class="lineno"><a class="line" href="_trigonometry_8h.html#a8d14d3276803ebb781ac40821491c959"> 35</a></span>JPH_INLINE <span class="keywordtype">float</span> <a class="code hl_function" href="_trigonometry_8h.html#a8d14d3276803ebb781ac40821491c959">ASin</a>(<span class="keywordtype">float</span> inX)</div>
- <div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span>{</div>
- <div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keywordflow">return</span> <a class="code hl_function" href="class_vec4.html#af18f350dd2885dc48ff7e7cbf4b8bc9d">Vec4::sReplicate</a>(inX).<a class="code hl_function" href="class_vec4.html#a2e71650ce94e6f72312f8820af419db5">ASin</a>().<a class="code hl_function" href="class_vec4.html#aad89aa3a9c4215f45c0dbe1fb65830c3">GetX</a>();</div>
- <div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span>}</div>
- </div>
- <div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> </div>
- <div class="foldopen" id="foldopen00042" data-start="{" data-end="}">
- <div class="line"><a id="l00042" name="l00042"></a><span class="lineno"><a class="line" href="_trigonometry_8h.html#a4d69678f84c03b333e32ca716998db39"> 42</a></span>JPH_INLINE <span class="keywordtype">float</span> <a class="code hl_function" href="_trigonometry_8h.html#a4d69678f84c03b333e32ca716998db39">ACos</a>(<span class="keywordtype">float</span> inX)</div>
- <div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span>{</div>
- <div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordflow">return</span> <a class="code hl_function" href="class_vec4.html#af18f350dd2885dc48ff7e7cbf4b8bc9d">Vec4::sReplicate</a>(inX).<a class="code hl_function" href="class_vec4.html#ae56c43bab7d034799def2a0cd588f971">ACos</a>().<a class="code hl_function" href="class_vec4.html#aad89aa3a9c4215f45c0dbe1fb65830c3">GetX</a>();</div>
- <div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span>}</div>
- </div>
- <div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
- <div class="foldopen" id="foldopen00048" data-start="{" data-end="}">
- <div class="line"><a id="l00048" name="l00048"></a><span class="lineno"><a class="line" href="_trigonometry_8h.html#a1dec7e1e2e84f4362a0a65d390a51ee0"> 48</a></span>JPH_INLINE <span class="keywordtype">float</span> <a class="code hl_function" href="_trigonometry_8h.html#a1dec7e1e2e84f4362a0a65d390a51ee0">ACosApproximate</a>(<span class="keywordtype">float</span> inX)</div>
- <div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span>{</div>
- <div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// See: https://www.johndcook.com/blog/2022/09/06/inverse-cosine-near-1/</span></div>
- <div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// See also: https://seblagarde.wordpress.com/2014/12/01/inverse-trigonometric-functions-gpu-optimization-for-amd-gcn-architecture/</span></div>
- <div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// Taylor of cos(x) = 1 - x^2 / 2 + ...</span></div>
- <div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="comment">// Substitute x = sqrt(2 y) we get: cos(sqrt(2 y)) = 1 - y</span></div>
- <div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// Substitute z = 1 - y we get: cos(sqrt(2 (1 - z))) = z <=> acos(z) = sqrt(2 (1 - z))</span></div>
- <div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// To avoid the discontinuity at 1, instead of using the Taylor expansion of acos(x) we use acos(x) / sqrt(2 (1 - x)) = 1 + (1 - x) / 12 + ...</span></div>
- <div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// Since the approximation was made at 1, it has quite a large error at 0 meaning that if we want to extend to the</span></div>
- <div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// range [-1, 1] by mirroring the range [0, 1], the value at 0+ is not the same as 0-.</span></div>
- <div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// So we observe that the form of the Taylor expansion is f(x) = sqrt(1 - x) * (a + b x) and we fit the function so that f(0) = pi / 2</span></div>
- <div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="comment">// this gives us a = pi / 2. f(1) = 0 regardless of b. We search for a constant b that minimizes the error in the range [0, 1].</span></div>
- <div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordtype">float</span> abs_x = min(abs(inX), 1.0f); <span class="comment">// Ensure that we don't get a value larger than 1</span></div>
- <div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keywordtype">float</span> val = sqrt(1.0f - abs_x) * (JPH_PI / 2 - 0.175394f * abs_x);</div>
- <div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> </div>
- <div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="comment">// Our approximation is valid in the range [0, 1], extend it to the range [-1, 1]</span></div>
- <div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keywordflow">return</span> inX < 0? JPH_PI - val : val;</div>
- <div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span>}</div>
- </div>
- <div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> </div>
- <div class="foldopen" id="foldopen00068" data-start="{" data-end="}">
- <div class="line"><a id="l00068" name="l00068"></a><span class="lineno"><a class="line" href="_trigonometry_8h.html#a8d7d50cdb10f600d1493bd8a36c4029e"> 68</a></span>JPH_INLINE <span class="keywordtype">float</span> <a class="code hl_function" href="_trigonometry_8h.html#a8d7d50cdb10f600d1493bd8a36c4029e">ATan</a>(<span class="keywordtype">float</span> inX)</div>
- <div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span>{</div>
- <div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keywordflow">return</span> <a class="code hl_function" href="class_vec4.html#af18f350dd2885dc48ff7e7cbf4b8bc9d">Vec4::sReplicate</a>(inX).<a class="code hl_function" href="class_vec4.html#a0c3d97968c479dcc0a08b98134c95e02">ATan</a>().<a class="code hl_function" href="class_vec4.html#aad89aa3a9c4215f45c0dbe1fb65830c3">GetX</a>();</div>
- <div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span>}</div>
- </div>
- <div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> </div>
- <div class="foldopen" id="foldopen00074" data-start="{" data-end="}">
- <div class="line"><a id="l00074" name="l00074"></a><span class="lineno"><a class="line" href="_trigonometry_8h.html#a64f4ce00d99917535c674ec5172ccf78"> 74</a></span>JPH_INLINE <span class="keywordtype">float</span> <a class="code hl_function" href="_trigonometry_8h.html#a64f4ce00d99917535c674ec5172ccf78">ATan2</a>(<span class="keywordtype">float</span> inY, <span class="keywordtype">float</span> inX)</div>
- <div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span>{</div>
- <div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordflow">return</span> <a class="code hl_function" href="class_vec4.html#a276178476f7db15b1925cae464f136cf">Vec4::sATan2</a>(<a class="code hl_function" href="class_vec4.html#af18f350dd2885dc48ff7e7cbf4b8bc9d">Vec4::sReplicate</a>(inY), <a class="code hl_function" href="class_vec4.html#af18f350dd2885dc48ff7e7cbf4b8bc9d">Vec4::sReplicate</a>(inX)).<a class="code hl_function" href="class_vec4.html#aad89aa3a9c4215f45c0dbe1fb65830c3">GetX</a>();</div>
- <div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span>}</div>
- </div>
- <div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> </div>
- <div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><a class="code hl_define" href="_core_8h.html#a73da8725998b00321a9db341202d650d">JPH_NAMESPACE_END</a></div>
- <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>
- <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>
- <div class="ttc" id="a_trigonometry_8h_html_a138c843d7c7c5f89c1757b159a86eb00"><div class="ttname"><a href="_trigonometry_8h.html#a138c843d7c7c5f89c1757b159a86eb00">Tan</a></div><div class="ttdeci">JPH_INLINE float Tan(float inX)</div><div class="ttdoc">Tangent of x (input in radians)</div><div class="ttdef"><b>Definition</b> Trigonometry.h:28</div></div>
- <div class="ttc" id="a_trigonometry_8h_html_a1dec7e1e2e84f4362a0a65d390a51ee0"><div class="ttname"><a href="_trigonometry_8h.html#a1dec7e1e2e84f4362a0a65d390a51ee0">ACosApproximate</a></div><div class="ttdeci">JPH_INLINE float ACosApproximate(float inX)</div><div class="ttdoc">An approximation of ACos, max error is 4.2e-3 over the entire range [-1, 1], is approximately 2....</div><div class="ttdef"><b>Definition</b> Trigonometry.h:48</div></div>
- <div class="ttc" id="a_trigonometry_8h_html_a40fafb1c427199b6855d704fc79cd1cf"><div class="ttname"><a href="_trigonometry_8h.html#a40fafb1c427199b6855d704fc79cd1cf">Cos</a></div><div class="ttdeci">JPH_INLINE float Cos(float inX)</div><div class="ttdoc">Cosine of x (input in radians)</div><div class="ttdef"><b>Definition</b> Trigonometry.h:20</div></div>
- <div class="ttc" id="a_trigonometry_8h_html_a4d69678f84c03b333e32ca716998db39"><div class="ttname"><a href="_trigonometry_8h.html#a4d69678f84c03b333e32ca716998db39">ACos</a></div><div class="ttdeci">JPH_INLINE float ACos(float inX)</div><div class="ttdef"><b>Definition</b> Trigonometry.h:42</div></div>
- <div class="ttc" id="a_trigonometry_8h_html_a64f4ce00d99917535c674ec5172ccf78"><div class="ttname"><a href="_trigonometry_8h.html#a64f4ce00d99917535c674ec5172ccf78">ATan2</a></div><div class="ttdeci">JPH_INLINE float ATan2(float inY, float inX)</div><div class="ttdoc">Arc tangent of y / x using the signs of the arguments to determine the correct quadrant (returns valu...</div><div class="ttdef"><b>Definition</b> Trigonometry.h:74</div></div>
- <div class="ttc" id="a_trigonometry_8h_html_a89091907eb3da97f690e324849d773cb"><div class="ttname"><a href="_trigonometry_8h.html#a89091907eb3da97f690e324849d773cb">Sin</a></div><div class="ttdeci">JPH_NAMESPACE_BEGIN JPH_INLINE float Sin(float inX)</div><div class="ttdoc">Sine of x (input in radians)</div><div class="ttdef"><b>Definition</b> Trigonometry.h:12</div></div>
- <div class="ttc" id="a_trigonometry_8h_html_a8d14d3276803ebb781ac40821491c959"><div class="ttname"><a href="_trigonometry_8h.html#a8d14d3276803ebb781ac40821491c959">ASin</a></div><div class="ttdeci">JPH_INLINE float ASin(float inX)</div><div class="ttdef"><b>Definition</b> Trigonometry.h:35</div></div>
- <div class="ttc" id="a_trigonometry_8h_html_a8d7d50cdb10f600d1493bd8a36c4029e"><div class="ttname"><a href="_trigonometry_8h.html#a8d7d50cdb10f600d1493bd8a36c4029e">ATan</a></div><div class="ttdeci">JPH_INLINE float ATan(float inX)</div><div class="ttdoc">Arc tangent of x (returns value in the range [-PI / 2, PI / 2])</div><div class="ttdef"><b>Definition</b> Trigonometry.h:68</div></div>
- <div class="ttc" id="aclass_vec4_html"><div class="ttname"><a href="class_vec4.html">Vec4</a></div><div class="ttdef"><b>Definition</b> Vec4.h:14</div></div>
- <div class="ttc" id="aclass_vec4_html_a0c3d97968c479dcc0a08b98134c95e02"><div class="ttname"><a href="class_vec4.html#a0c3d97968c479dcc0a08b98134c95e02">Vec4::ATan</a></div><div class="ttdeci">Vec4 ATan() const</div><div class="ttdoc">Calculate the arc tangent for each element of this vector (returns value in the range [-PI / 2,...</div><div class="ttdef"><b>Definition</b> Vec4.inl:1003</div></div>
- <div class="ttc" id="aclass_vec4_html_a276178476f7db15b1925cae464f136cf"><div class="ttname"><a href="class_vec4.html#a276178476f7db15b1925cae464f136cf">Vec4::sATan2</a></div><div class="ttdeci">static Vec4 sATan2(Vec4Arg inY, Vec4Arg inX)</div><div class="ttdoc">Calculate the arc tangent of y / x using the signs of the arguments to determine the correct quadrant...</div><div class="ttdef"><b>Definition</b> Vec4.inl:1037</div></div>
- <div class="ttc" id="aclass_vec4_html_a2e71650ce94e6f72312f8820af419db5"><div class="ttname"><a href="class_vec4.html#a2e71650ce94e6f72312f8820af419db5">Vec4::ASin</a></div><div class="ttdeci">Vec4 ASin() const</div><div class="ttdef"><b>Definition</b> Vec4.inl:962</div></div>
- <div class="ttc" id="aclass_vec4_html_a3769f486156183d3cbecb6a37291fe5c"><div class="ttname"><a href="class_vec4.html#a3769f486156183d3cbecb6a37291fe5c">Vec4::Tan</a></div><div class="ttdeci">Vec4 Tan() const</div><div class="ttdoc">Calculate the tangent for each element of this vector (input in radians)</div><div class="ttdef"><b>Definition</b> Vec4.inl:929</div></div>
- <div class="ttc" id="aclass_vec4_html_aad89aa3a9c4215f45c0dbe1fb65830c3"><div class="ttname"><a href="class_vec4.html#aad89aa3a9c4215f45c0dbe1fb65830c3">Vec4::GetX</a></div><div class="ttdeci">JPH_INLINE float GetX() const</div><div class="ttdoc">Get individual components.</div><div class="ttdef"><b>Definition</b> Vec4.h:119</div></div>
- <div class="ttc" id="aclass_vec4_html_ae56c43bab7d034799def2a0cd588f971"><div class="ttname"><a href="class_vec4.html#ae56c43bab7d034799def2a0cd588f971">Vec4::ACos</a></div><div class="ttdeci">Vec4 ACos() const</div><div class="ttdef"><b>Definition</b> Vec4.inl:997</div></div>
- <div class="ttc" id="aclass_vec4_html_af18f350dd2885dc48ff7e7cbf4b8bc9d"><div class="ttname"><a href="class_vec4.html#af18f350dd2885dc48ff7e7cbf4b8bc9d">Vec4::sReplicate</a></div><div class="ttdeci">static JPH_INLINE Vec4 sReplicate(float inV)</div><div class="ttdoc">Replicate inV across all components.</div><div class="ttdef"><b>Definition</b> Vec4.inl:74</div></div>
- <div class="ttc" id="aclass_vec4_html_af7e7da5ada5c3e85aac45d62871a867c"><div class="ttname"><a href="class_vec4.html#af7e7da5ada5c3e85aac45d62871a867c">Vec4::SinCos</a></div><div class="ttdeci">void SinCos(Vec4 &outSin, Vec4 &outCos) const</div><div class="ttdoc">Calculate the sine and cosine for each element of this vector (input in radians)</div><div class="ttdef"><b>Definition</b> Vec4.inl:867</div></div>
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