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<div id="projectname">Gamedev Framework (gf)
 <span id="projectnumber">0.15.0</span>
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<div id="projectbrief">A C++14 framework for 2D games</div>
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<li class="navelem"><a class="el" href="dir_d44c64559bbebec7f509842c48db8b23.html">include</a></li><li class="navelem"><a class="el" href="dir_6d069d519ae9d12fa11dd8e685586b60.html">gf</a></li> </ul>
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<div class="title">Math.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"> * Gamedev Framework (gf)</span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> * Copyright (C) 2016-2019 Julien Bernard</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> *</span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> * This software is provided 'as-is', without any express or implied</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> * warranty. In no event will the authors be held liable for any damages</span></div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> * arising from the use of this software.</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> *</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> * Permission is granted to anyone to use this software for any purpose,</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> * including commercial applications, and to alter it and redistribute it</span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> * freely, subject to the following restrictions:</span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> *</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"> * 1. The origin of this software must not be misrepresented; you must not</span></div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"> * claim that you wrote the original software. If you use this software</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"> * in a product, an acknowledgment in the product documentation would be</span></div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"> * appreciated but is not required.</span></div><div class="line"><a name="l00017"></a><span class="lineno"> 17</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="l00018"></a><span class="lineno"> 18</span> <span class="comment"> * misrepresented as being the original software.</span></div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment"> * 3. This notice may not be removed or altered from any source distribution.</span></div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment"> */</span></div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#ifndef GF_MATH_H</span></div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#define GF_MATH_H</span></div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> </div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="preprocessor">#include <cmath></span></div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="preprocessor">#include <limits></span></div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span> </div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="preprocessor">#include "Portability.h"</span></div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span> </div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="keyword">namespace </span><a class="code" href="namespacegf.html">gf</a> {</div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="preprocessor">#ifndef DOXYGEN_SHOULD_SKIP_THIS</span></div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="keyword">inline</span> <span class="keyword">namespace </span>v1 {</div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span> </div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  constexpr</div><div class="line"><a name="l00040"></a><span class="lineno"><a class="line" href="group__core.html#gab69a18ba294adfcbf6bb27e1ae61ab67"> 40</a></span>  <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> <a class="code" href="group__core.html#gab69a18ba294adfcbf6bb27e1ae61ab67">pi</a>() {</div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keywordflow">return</span> <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a>(3.141592653589793238462643383279502884197169399<a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ad20caec3b48a1eef164cb4ca81ba2587">L</a>);</div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  }</div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span> </div><div class="line"><a name="l00048"></a><span class="lineno"><a class="line" href="group__core.html#gafea71ec62ea0c47eb8e65dba77940b40"> 48</a></span>  constexpr <span class="keywordtype">float</span> <a class="code" href="group__core.html#gafea71ec62ea0c47eb8e65dba77940b40">Pi</a> = pi<float>();</div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span> </div><div class="line"><a name="l00054"></a><span class="lineno"><a class="line" href="group__core.html#gaac3ad99d9b813b1cea8802abbfed6d80"> 54</a></span>  constexpr <span class="keywordtype">float</span> <a class="code" href="group__core.html#gaac3ad99d9b813b1cea8802abbfed6d80">Pi2</a> = Pi / 2;</div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span> </div><div class="line"><a name="l00060"></a><span class="lineno"><a class="line" href="group__core.html#gaab6d74eaf8f5a1744b6de68ad463edf2"> 60</a></span>  constexpr <span class="keywordtype">float</span> <a class="code" href="group__core.html#gaab6d74eaf8f5a1744b6de68ad463edf2">Pi4</a> = Pi / 4;</div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span> </div><div class="line"><a name="l00066"></a><span class="lineno"><a class="line" href="group__core.html#ga8aa2d6dc9c8fb96810fe47dff3c9b00a"> 66</a></span>  constexpr <span class="keywordtype">float</span> <a class="code" href="group__core.html#ga8aa2d6dc9c8fb96810fe47dff3c9b00a">Sqrt2</a> = 1.41421356237309504880f;</div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span> </div><div class="line"><a name="l00072"></a><span class="lineno"><a class="line" href="group__core.html#gab6ba065d81cdb7021ba7e47bea500580"> 72</a></span>  constexpr <span class="keywordtype">float</span> <a class="code" href="group__core.html#gab6ba065d81cdb7021ba7e47bea500580">InvSqrt2</a> = 1 / <a class="code" href="group__core.html#ga8aa2d6dc9c8fb96810fe47dff3c9b00a">Sqrt2</a>;</div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span> </div><div class="line"><a name="l00078"></a><span class="lineno"><a class="line" href="group__core.html#gad32b4a332d77de3d25eae25cfbcb3fb2"> 78</a></span>  constexpr <span class="keywordtype">float</span> <a class="code" href="group__core.html#gad32b4a332d77de3d25eae25cfbcb3fb2">Sqrt3</a> = 1.7320508075688772935f;</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span> </div><div class="line"><a name="l00084"></a><span class="lineno"><a class="line" href="group__core.html#gab4aa74a0cbea2a97c107bc5a1dc63a64"> 84</a></span>  constexpr <span class="keywordtype">float</span> <a class="code" href="group__core.html#gab4aa74a0cbea2a97c107bc5a1dc63a64">Epsilon</a> = std::numeric_limits<float>::epsilon();</div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span> </div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  constexpr</div><div class="line"><a name="l00098"></a><span class="lineno"><a class="line" href="group__core.html#ga9841a1fce2dd7019938c81d25ed8c136"> 98</a></span>  <span class="keywordtype">bool</span> <a class="code" href="group__core.html#ga9841a1fce2dd7019938c81d25ed8c136">almostEquals</a>(<a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> a, <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> b, <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> epsilon = std::numeric_limits<T>::epsilon()) {</div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keywordflow">if</span> (a == b) {</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  }</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span> </div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> diff = std::abs(a - b);</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>  <span class="keywordflow">if</span> (a == 0 || b == 0 || diff < std::numeric_limits<T>::denorm_min()) {</div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keywordflow">return</span> diff < (epsilon * std::numeric_limits<T>::denorm_min());</div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  }</div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span> </div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> sum = std::abs(a) + std::abs(b);</div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  sum = (sum < std::numeric_limits<T>::max()) ? sum : std::numeric_limits<T>::max();</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>  <span class="keywordflow">return</span> (diff / sum) < epsilon;</div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  }</div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span> </div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  constexpr</div><div class="line"><a name="l00125"></a><span class="lineno"><a class="line" href="group__core.html#ga1aa23f6b4c7a1e33f06fadf4a6c2b143"> 125</a></span>  <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> <a class="code" href="group__core.html#ga1aa23f6b4c7a1e33f06fadf4a6c2b143">degreesToRadians</a>(<a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> degrees) {</div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="keywordflow">return</span> degrees * gf::pi<T>() / <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a>(180);</div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  }</div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span> </div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  constexpr</div><div class="line"><a name="l00139"></a><span class="lineno"><a class="line" href="group__core.html#ga2076bbbd889489ac7f2f6e1d212f6c7c"> 139</a></span>  <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> <a class="code" href="group__core.html#ga2076bbbd889489ac7f2f6e1d212f6c7c">radiansToDegrees</a>(<a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> radians) {</div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keywordflow">return</span> radians * <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a>(180) / gf::pi<T>();</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="l00166"></a><span class="lineno"> 166</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00167"></a><span class="lineno"><a class="line" href="group__core.html#ga44b429e4f47cceab994f3b20b811d681"> 167</a></span>  <span class="keyword">using</span> <a class="code" href="group__core.html#ga44b429e4f47cceab994f3b20b811d681">Step</a> = <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> (*)(<a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a>);</div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span> </div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  constexpr</div><div class="line"><a name="l00179"></a><span class="lineno"><a class="line" href="group__core.html#gae4f9435d5873af1b503a277ddae35bd9"> 179</a></span>  <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> <a class="code" href="group__core.html#gae4f9435d5873af1b503a277ddae35bd9">linearStep</a>(<a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> t) {</div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="keywordflow">return</span> t;</div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  }</div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span> </div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  constexpr</div><div class="line"><a name="l00200"></a><span class="lineno"><a class="line" href="group__core.html#gab353056685420de64599bb422adaf701"> 200</a></span>  <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> <a class="code" href="group__core.html#gab353056685420de64599bb422adaf701">cubicStep</a>(<a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> t) {</div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="keywordflow">return</span> (-<a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a>(2) * t + <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a>(3)) * t * t;</div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  }</div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span> </div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  constexpr</div><div class="line"><a name="l00223"></a><span class="lineno"><a class="line" href="group__core.html#ga6f9ca6f1bc9622a4c7e68a3f956d8415"> 223</a></span>  <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> <a class="code" href="group__core.html#ga6f9ca6f1bc9622a4c7e68a3f956d8415">quinticStep</a>(<a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> t) {</div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="keywordflow">return</span> ((<a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a>(6) * t - <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a>(15)) * t + <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a>(10)) * t * t * t;</div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  }</div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span> </div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="keyword">inline</span></div><div class="line"><a name="l00237"></a><span class="lineno"><a class="line" href="group__core.html#ga0e9fce6526516ba6bee65bf802888cd3"> 237</a></span>  <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> <a class="code" href="group__core.html#ga0e9fce6526516ba6bee65bf802888cd3">cosineStep</a>(<a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> t) {</div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="keywordflow">return</span> (<a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a>(1) - std::cos(gf::pi<T>() * t)) * <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a>(0.5);</div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  }</div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span> </div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T, <span class="keyword">typename</span> U></div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  constexpr</div><div class="line"><a name="l00256"></a><span class="lineno"><a class="line" href="group__core.html#ga9cff790079bfedb8b24a26de940a051f"> 256</a></span>  <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> <a class="code" href="group__core.html#ga9cff790079bfedb8b24a26de940a051f">lerp</a>(<a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> lhs, <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> rhs, <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626a4c614360da93c0a041b22e537de151eb">U</a> t) {</div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="keywordflow">return</span> (<a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626a4c614360da93c0a041b22e537de151eb">U</a>(1) - t) * lhs + t * rhs;</div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  }</div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span> </div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  constexpr</div><div class="line"><a name="l00274"></a><span class="lineno"><a class="line" href="group__core.html#ga671bdda5a52c335e68d391147c70cc16"> 274</a></span>  <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> <a class="code" href="group__core.html#ga671bdda5a52c335e68d391147c70cc16">clamp</a>(<a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> val, <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> lo, <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> hi) {</div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  <span class="keywordflow">return</span> val < lo ? lo : (val > hi ? hi : val);</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="l00287"></a><span class="lineno"> 287</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  constexpr</div><div class="line"><a name="l00289"></a><span class="lineno"><a class="line" href="group__core.html#ga0e22be4ddd625e4c235dbf0ef2d1f43f"> 289</a></span>  <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> <a class="code" href="group__core.html#ga0e22be4ddd625e4c235dbf0ef2d1f43f">square</a>(<a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> val) {</div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <span class="keywordflow">return</span> val * val;</div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  }</div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span> </div><div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  constexpr</div><div class="line"><a name="l00304"></a><span class="lineno"><a class="line" href="group__core.html#ga79f9c3327331a94c9b239d2cee745ff2"> 304</a></span>  <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> <a class="code" href="group__core.html#ga79f9c3327331a94c9b239d2cee745ff2">cube</a>(<a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> val) {</div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <span class="keywordflow">return</span> val * val * val;</div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  }</div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span> </div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  constexpr</div><div class="line"><a name="l00324"></a><span class="lineno"><a class="line" href="group__core.html#ga55d7afb6ae7f894776bb0244465ac497"> 324</a></span>  <span class="keywordtype">int</span> <a class="code" href="group__core.html#ga55d7afb6ae7f894776bb0244465ac497">sign</a>(<a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> val) {</div><div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  <span class="keywordflow">return</span> (val > <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a>(0)) - (val < <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a>(0));</div><div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  }</div><div class="line"><a name="l00327"></a><span class="lineno"> 327</span> </div><div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  constexpr</div><div class="line"><a name="l00342"></a><span class="lineno"><a class="line" href="group__core.html#ga162af6026bb8a59762e87c918f634006"> 342</a></span>  <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> <a class="code" href="group__core.html#ga162af6026bb8a59762e87c918f634006">absdiff</a>(<a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> lhs, <a class="code" href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">T</a> rhs) {</div><div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  <span class="keywordflow">return</span> lhs > rhs ? lhs - rhs : rhs - lhs;</div><div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  }</div><div class="line"><a name="l00345"></a><span class="lineno"> 345</span> </div><div class="line"><a name="l00346"></a><span class="lineno"> 346</span> <span class="preprocessor">#ifndef DOXYGEN_SHOULD_SKIP_THIS</span></div><div class="line"><a name="l00347"></a><span class="lineno"> 347</span> }</div><div class="line"><a name="l00348"></a><span class="lineno"> 348</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00349"></a><span class="lineno"> 349</span> }</div><div class="line"><a name="l00350"></a><span class="lineno"> 350</span> </div><div class="line"><a name="l00351"></a><span class="lineno"> 351</span> <span class="preprocessor">#endif // GF_MATH_H</span></div><div class="ttc" id="group__core_html_gaac3ad99d9b813b1cea8802abbfed6d80"><div class="ttname"><a href="group__core.html#gaac3ad99d9b813b1cea8802abbfed6d80">gf::Pi2</a></div><div class="ttdeci">constexpr float Pi2</div><div class="ttdoc">The constant. </div><div class="ttdef"><b>Definition:</b> Math.h:54</div></div>
<div class="ttc" id="group__core_html_ga9cff790079bfedb8b24a26de940a051f"><div class="ttname"><a href="group__core.html#ga9cff790079bfedb8b24a26de940a051f">gf::lerp</a></div><div class="ttdeci">constexpr T lerp(T lhs, T rhs, U t)</div><div class="ttdoc">Linear interpolation function. </div><div class="ttdef"><b>Definition:</b> Math.h:256</div></div>
<div class="ttc" id="group__core_html_gab4aa74a0cbea2a97c107bc5a1dc63a64"><div class="ttname"><a href="group__core.html#gab4aa74a0cbea2a97c107bc5a1dc63a64">gf::Epsilon</a></div><div class="ttdeci">constexpr float Epsilon</div><div class="ttdoc">Machine epsilon. </div><div class="ttdef"><b>Definition:</b> Math.h:84</div></div>
<div class="ttc" id="group__window_html_gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3"><div class="ttname"><a href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ab9ece18c950afbfa6b0fdbfa4ff731d3">gf::Scancode::T</a></div></div>
<div class="ttc" id="group__core_html_ga79f9c3327331a94c9b239d2cee745ff2"><div class="ttname"><a href="group__core.html#ga79f9c3327331a94c9b239d2cee745ff2">gf::cube</a></div><div class="ttdeci">constexpr T cube(T val)</div><div class="ttdoc">Cube function. </div><div class="ttdef"><b>Definition:</b> Math.h:304</div></div>
<div class="ttc" id="group__core_html_gab6ba065d81cdb7021ba7e47bea500580"><div class="ttname"><a href="group__core.html#gab6ba065d81cdb7021ba7e47bea500580">gf::InvSqrt2</a></div><div class="ttdeci">constexpr float InvSqrt2</div><div class="ttdoc">The constant. </div><div class="ttdef"><b>Definition:</b> Math.h:72</div></div>
<div class="ttc" id="group__core_html_ga162af6026bb8a59762e87c918f634006"><div class="ttname"><a href="group__core.html#ga162af6026bb8a59762e87c918f634006">gf::absdiff</a></div><div class="ttdeci">constexpr T absdiff(T lhs, T rhs)</div><div class="ttdoc">Absolute difference of two values. </div><div class="ttdef"><b>Definition:</b> Math.h:342</div></div>
<div class="ttc" id="group__window_html_gga795d7d5e2f2a4f38b16b95e0e78cb626ad20caec3b48a1eef164cb4ca81ba2587"><div class="ttname"><a href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626ad20caec3b48a1eef164cb4ca81ba2587">gf::Scancode::L</a></div></div>
<div class="ttc" id="group__core_html_ga0e22be4ddd625e4c235dbf0ef2d1f43f"><div class="ttname"><a href="group__core.html#ga0e22be4ddd625e4c235dbf0ef2d1f43f">gf::square</a></div><div class="ttdeci">constexpr T square(T val)</div><div class="ttdoc">Square function. </div><div class="ttdef"><b>Definition:</b> Math.h:289</div></div>
<div class="ttc" id="group__core_html_ga671bdda5a52c335e68d391147c70cc16"><div class="ttname"><a href="group__core.html#ga671bdda5a52c335e68d391147c70cc16">gf::clamp</a></div><div class="ttdeci">constexpr T clamp(T val, T lo, T hi)</div><div class="ttdoc">Clamping function. </div><div class="ttdef"><b>Definition:</b> Math.h:274</div></div>
<div class="ttc" id="group__window_html_gga795d7d5e2f2a4f38b16b95e0e78cb626a4c614360da93c0a041b22e537de151eb"><div class="ttname"><a href="group__window.html#gga795d7d5e2f2a4f38b16b95e0e78cb626a4c614360da93c0a041b22e537de151eb">gf::Scancode::U</a></div></div>
<div class="ttc" id="group__core_html_ga8aa2d6dc9c8fb96810fe47dff3c9b00a"><div class="ttname"><a href="group__core.html#ga8aa2d6dc9c8fb96810fe47dff3c9b00a">gf::Sqrt2</a></div><div class="ttdeci">constexpr float Sqrt2</div><div class="ttdoc">The constant. </div><div class="ttdef"><b>Definition:</b> Math.h:66</div></div>
<div class="ttc" id="group__core_html_ga2076bbbd889489ac7f2f6e1d212f6c7c"><div class="ttname"><a href="group__core.html#ga2076bbbd889489ac7f2f6e1d212f6c7c">gf::radiansToDegrees</a></div><div class="ttdeci">constexpr T radiansToDegrees(T radians)</div><div class="ttdoc">Convert radians to degrees. </div><div class="ttdef"><b>Definition:</b> Math.h:139</div></div>
<div class="ttc" id="group__core_html_gab353056685420de64599bb422adaf701"><div class="ttname"><a href="group__core.html#gab353056685420de64599bb422adaf701">gf::cubicStep</a></div><div class="ttdeci">constexpr T cubicStep(T t)</div><div class="ttdoc">Cubic step (smoothstep) </div><div class="ttdef"><b>Definition:</b> Math.h:200</div></div>
<div class="ttc" id="namespacegf_html"><div class="ttname"><a href="namespacegf.html">gf</a></div><div class="ttdoc">The namespace for gf classes. </div><div class="ttdef"><b>Definition:</b> Action.h:35</div></div>
<div class="ttc" id="group__core_html_ga0e9fce6526516ba6bee65bf802888cd3"><div class="ttname"><a href="group__core.html#ga0e9fce6526516ba6bee65bf802888cd3">gf::cosineStep</a></div><div class="ttdeci">T cosineStep(T t)</div><div class="ttdoc">Cosine step. </div><div class="ttdef"><b>Definition:</b> Math.h:237</div></div>
<div class="ttc" id="group__core_html_ga1aa23f6b4c7a1e33f06fadf4a6c2b143"><div class="ttname"><a href="group__core.html#ga1aa23f6b4c7a1e33f06fadf4a6c2b143">gf::degreesToRadians</a></div><div class="ttdeci">constexpr T degreesToRadians(T degrees)</div><div class="ttdoc">Convert degrees to radians. </div><div class="ttdef"><b>Definition:</b> Math.h:125</div></div>
<div class="ttc" id="group__core_html_gafea71ec62ea0c47eb8e65dba77940b40"><div class="ttname"><a href="group__core.html#gafea71ec62ea0c47eb8e65dba77940b40">gf::Pi</a></div><div class="ttdeci">constexpr float Pi</div><div class="ttdoc">The constant. </div><div class="ttdef"><b>Definition:</b> Math.h:48</div></div>
<div class="ttc" id="group__core_html_ga9841a1fce2dd7019938c81d25ed8c136"><div class="ttname"><a href="group__core.html#ga9841a1fce2dd7019938c81d25ed8c136">gf::almostEquals</a></div><div class="ttdeci">constexpr bool almostEquals(T a, T b, T epsilon=std::numeric_limits< T >::epsilon())</div><div class="ttdoc">Compare two floats. </div><div class="ttdef"><b>Definition:</b> Math.h:98</div></div>
<div class="ttc" id="group__core_html_gae4f9435d5873af1b503a277ddae35bd9"><div class="ttname"><a href="group__core.html#gae4f9435d5873af1b503a277ddae35bd9">gf::linearStep</a></div><div class="ttdeci">constexpr T linearStep(T t)</div><div class="ttdoc">Linear step. </div><div class="ttdef"><b>Definition:</b> Math.h:179</div></div>
<div class="ttc" id="group__core_html_gad32b4a332d77de3d25eae25cfbcb3fb2"><div class="ttname"><a href="group__core.html#gad32b4a332d77de3d25eae25cfbcb3fb2">gf::Sqrt3</a></div><div class="ttdeci">constexpr float Sqrt3</div><div class="ttdoc">The constant. </div><div class="ttdef"><b>Definition:</b> Math.h:78</div></div>
<div class="ttc" id="group__core_html_ga55d7afb6ae7f894776bb0244465ac497"><div class="ttname"><a href="group__core.html#ga55d7afb6ae7f894776bb0244465ac497">gf::sign</a></div><div class="ttdeci">constexpr int sign(T val)</div><div class="ttdoc">Sign function. </div><div class="ttdef"><b>Definition:</b> Math.h:324</div></div>
<div class="ttc" id="group__core_html_ga44b429e4f47cceab994f3b20b811d681"><div class="ttname"><a href="group__core.html#ga44b429e4f47cceab994f3b20b811d681">gf::Step</a></div><div class="ttdeci">T(*)(T) Step</div><div class="ttdoc">A step is a function with special features. </div><div class="ttdef"><b>Definition:</b> Math.h:167</div></div>
<div class="ttc" id="group__core_html_ga6f9ca6f1bc9622a4c7e68a3f956d8415"><div class="ttname"><a href="group__core.html#ga6f9ca6f1bc9622a4c7e68a3f956d8415">gf::quinticStep</a></div><div class="ttdeci">constexpr T quinticStep(T t)</div><div class="ttdoc">Quintic step (smootherstep) </div><div class="ttdef"><b>Definition:</b> Math.h:223</div></div>
<div class="ttc" id="group__core_html_gab69a18ba294adfcbf6bb27e1ae61ab67"><div class="ttname"><a href="group__core.html#gab69a18ba294adfcbf6bb27e1ae61ab67">gf::pi</a></div><div class="ttdeci">constexpr T pi()</div><div class="ttdoc">Templated value of . </div><div class="ttdef"><b>Definition:</b> Math.h:40</div></div>
<div class="ttc" id="group__core_html_gaab6d74eaf8f5a1744b6de68ad463edf2"><div class="ttname"><a href="group__core.html#gaab6d74eaf8f5a1744b6de68ad463edf2">gf::Pi4</a></div><div class="ttdeci">constexpr float Pi4</div><div class="ttdoc">The constant. </div><div class="ttdef"><b>Definition:</b> Math.h:60</div></div>
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