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<div id="projectname">Gamedev Framework (gf)
 <span id="projectnumber">0.6.0</span>
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<div id="projectbrief">A C++11 framework for 2D games</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) 2016-2017 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">#</span><span class="preprocessor">ifndef</span> <span class="preprocessor">GF_MATH_H</span></div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#</span><span class="preprocessor">define</span> <span class="preprocessor">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">#</span><span class="preprocessor">include</span> <span class="preprocessor"><</span><span class="preprocessor">cmath</span><span class="preprocessor">></span></div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="preprocessor">#</span><span class="preprocessor">include</span> <span class="preprocessor"><</span><span class="preprocessor">limits</span><span class="preprocessor">></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">#</span><span class="preprocessor">include</span> <a class="code" href="_portability_8h.html">"Portability.h"</a></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">#</span><span class="preprocessor">ifndef</span> <span class="preprocessor">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">#</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="l00034"></a><span class="lineno"> 34</span>  <span class="comment">/**</span></div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment"> * @brief The @f$ \pi @f$ constant</span></div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment"> */</span></div><div class="line"><a name="l00038"></a><span class="lineno"><a class="line" href="group__core.html#gafea71ec62ea0c47eb8e65dba77940b40"> 38</a></span>  <span class="keyword">constexpr</span> <span class="keywordtype">float</span> <a class="code" href="group__core.html#gafea71ec62ea0c47eb8e65dba77940b40">Pi</a> = 3.14159265358979323846f;</div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span> </div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="comment">/**</span></div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment"> * @brief The @f$ \frac{\pi}{2} @f$ constant</span></div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment"> */</span></div><div class="line"><a name="l00044"></a><span class="lineno"><a class="line" href="group__core.html#gaac3ad99d9b813b1cea8802abbfed6d80"> 44</a></span>  <span class="keyword">constexpr</span> <span class="keywordtype">float</span> <a class="code" href="group__core.html#gaac3ad99d9b813b1cea8802abbfed6d80">Pi2</a> = <a class="code" href="group__core.html#gafea71ec62ea0c47eb8e65dba77940b40">Pi</a> / 2;</div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span> </div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="comment">/**</span></div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment"> * @brief The @f$ \frac{\pi}{4} @f$ constant</span></div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment"> */</span></div><div class="line"><a name="l00050"></a><span class="lineno"><a class="line" href="group__core.html#gaab6d74eaf8f5a1744b6de68ad463edf2"> 50</a></span>  <span class="keyword">constexpr</span> <span class="keywordtype">float</span> <a class="code" href="group__core.html#gaab6d74eaf8f5a1744b6de68ad463edf2">Pi4</a> = <a class="code" href="group__core.html#gafea71ec62ea0c47eb8e65dba77940b40">Pi</a> / 4;</div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span> </div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="comment">/**</span></div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment"> * @brief The @f$ \sqrt{2} @f$ constant</span></div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment"> */</span></div><div class="line"><a name="l00056"></a><span class="lineno"><a class="line" href="group__core.html#ga8aa2d6dc9c8fb96810fe47dff3c9b00a"> 56</a></span>  <span class="keyword">constexpr</span> <span class="keywordtype">float</span> <a class="code" href="group__core.html#ga8aa2d6dc9c8fb96810fe47dff3c9b00a">Sqrt2</a> = 1.41421356237309504880f;</div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span> </div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="comment">/**</span></div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment"> * @brief The @f$ \frac{1}{\sqrt{2}} @f$ constant</span></div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment"> */</span></div><div class="line"><a name="l00062"></a><span class="lineno"><a class="line" href="group__core.html#gab6ba065d81cdb7021ba7e47bea500580"> 62</a></span>  <span class="keyword">constexpr</span> <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="l00063"></a><span class="lineno"> 63</span> </div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="comment">/**</span></div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment"> * @brief The @f$ \sqrt{3} @f$ constant</span></div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment"> */</span></div><div class="line"><a name="l00068"></a><span class="lineno"><a class="line" href="group__core.html#gad32b4a332d77de3d25eae25cfbcb3fb2"> 68</a></span>  <span class="keyword">constexpr</span> <span class="keywordtype">float</span> <a class="code" href="group__core.html#gad32b4a332d77de3d25eae25cfbcb3fb2">Sqrt3</a> = 1.7320508075688772935f;</div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span> </div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="comment">/**</span></div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment"> * @brief Machine epsilon</span></div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment"> */</span></div><div class="line"><a name="l00074"></a><span class="lineno"><a class="line" href="group__core.html#gab4aa74a0cbea2a97c107bc5a1dc63a64"> 74</a></span>  <span class="keyword">constexpr</span> <span class="keywordtype">float</span> <a class="code" href="group__core.html#gab4aa74a0cbea2a97c107bc5a1dc63a64">Epsilon</a> = std::numeric_limits<<span class="keywordtype">float</span>>::epsilon();</div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span> </div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="comment">/**</span></div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment"> * @brief Compare two floats</span></div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment"> *</span></div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment"> * @param a The first float</span></div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment"> * @param b The second float</span></div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment"> * @param epsilon A small value that controls the equality comparison</span></div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment"> *</span></div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment"> * @sa [Comparison - The Floating-Point Guide](http://floating-point-gui.de/errors/comparison/)</span></div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="comment"> */</span></div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keyword">inline</span></div><div class="line"><a name="l00088"></a><span class="lineno"><a class="line" href="group__core.html#ga7ed0adec6b897c228288a41a757b96a2"> 88</a></span>  <span class="keywordtype">bool</span> <a class="code" href="group__core.html#ga7ed0adec6b897c228288a41a757b96a2">almostEquals</a>(T a, T b, T epsilon = std::numeric_limits<T>::epsilon()) {</div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="keywordflow">if</span> (a == b) {</div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  }</div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span> </div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  T diff = std::abs(a - b);</div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span> </div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordflow">if</span> (a == 0 || b == 0 || diff < std::numeric_limits<T>::denorm_min()) {</div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keywordflow">return</span> diff < (epsilon * std::numeric_limits<T>::denorm_min());</div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  }</div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span> </div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  T sum = std::abs(a) + std::abs(b);</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  sum = (sum < std::numeric_limits<T>::max()) ? sum : std::numeric_limits<T>::max();</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>  <span class="keywordflow">return</span> (diff / sum) < epsilon;</div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  }</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="comment">/**</span></div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="comment"> * @brief Convert degrees to radians</span></div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="comment"> *</span></div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="comment"> * @param degrees An angle in degrees</span></div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment"> * @returns The angle in radians</span></div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="comment"> * @sa radiansToDegrees()</span></div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="comment"> */</span></div><div class="line"><a name="l00113"></a><span class="lineno"><a class="line" href="group__core.html#ga4f3a61189703ec2b8dc9e9a27a398bb5"> 113</a></span>  <span class="keyword">constexpr</span> <span class="keywordtype">float</span> <a class="code" href="group__core.html#ga4f3a61189703ec2b8dc9e9a27a398bb5">degreesToRadians</a>(<span class="keywordtype">float</span> degrees) {</div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="keywordflow">return</span> degrees * <a class="code" href="group__core.html#gafea71ec62ea0c47eb8e65dba77940b40">Pi</a> / 180.0f;</div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  }</div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span> </div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="comment">/**</span></div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="comment"> * @brief Convert radians to degrees</span></div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="comment"> *</span></div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span> <span class="comment"> * @param radians An angle in radians</span></div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="comment"> * @returns The angle in degrees</span></div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="comment"> * @sa degreesToRadians()</span></div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span> <span class="comment"> */</span></div><div class="line"><a name="l00125"></a><span class="lineno"><a class="line" href="group__core.html#ga1965ca9c0aa332a0a9fff72398f29c69"> 125</a></span>  <span class="keyword">constexpr</span> <span class="keywordtype">float</span> <a class="code" href="group__core.html#ga1965ca9c0aa332a0a9fff72398f29c69">radiansToDegrees</a>(<span class="keywordtype">float</span> radians) {</div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="keywordflow">return</span> radians * 180.0f / <a class="code" href="group__core.html#gafea71ec62ea0c47eb8e65dba77940b40">Pi</a>;</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="l00129"></a><span class="lineno"> 129</span>  <span class="comment">/**</span></div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="comment"> * @brief A step is a function with special features.</span></div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="comment"> *</span></div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span> <span class="comment"> * A step @f$ f @f$ is a (mathematical) function which has the following properties:</span></div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span> <span class="comment"> *</span></div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span> <span class="comment"> * - @f$ f(0) = 0 @f$</span></div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="comment"> * - @f$ f(1) = 1 @f$</span></div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="comment"> *</span></div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="comment"> * It can be used to smooth a linear interpolation.</span></div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="comment"> *</span></div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="comment"> * ~~~{.cc}</span></div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="comment"> * gf::Vector2f point1 = ...;</span></div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="comment"> * gf::Vector2f point2 = ...;</span></div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="comment"> * float t = ...;</span></div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span> <span class="comment"> * gf::Step<float> step = gf::cubicStep<float>;</span></div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="comment"> *</span></div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span> <span class="comment"> * gf::Vector2f interpolatedPoint = gf::lerp(point1, point2, t);</span></div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="comment"> * gf::Vector2f smoothedInterpolatedPoint = gf::lerp(point1, point2, step(t));</span></div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span> <span class="comment"> * ~~~</span></div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="comment"> *</span></div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span> <span class="comment"> * @sa linearStep(), cubicStep(), quinticStep(), cosineStep()</span></div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="comment"> */</span></div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00153"></a><span class="lineno"><a class="line" href="group__core.html#ga44b429e4f47cceab994f3b20b811d681"> 153</a></span>  <span class="keyword">using</span> Step = T (*)(T);</div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span> </div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="comment">/**</span></div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="comment"> * @brief Linear step</span></div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="comment"> *</span></div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="comment"> * @f[ f(t) = t @f]</span></div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="comment"> *</span></div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span> <span class="comment"> * @sa gf::Step</span></div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="comment"> */</span></div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="keyword">constexpr</span></div><div class="line"><a name="l00165"></a><span class="lineno"><a class="line" href="group__core.html#gae4f9435d5873af1b503a277ddae35bd9"> 165</a></span>  T <a class="code" href="group__core.html#gae4f9435d5873af1b503a277ddae35bd9">linearStep</a>(T t) {</div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="keywordflow">return</span> t;</div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  }</div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span> </div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <span class="comment">/**</span></div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="comment"> * @brief Cubic step (smoothstep)</span></div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="comment"> *</span></div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="comment"> * @f[ f(t) = -2 * t^3 + 3 * t^2 @f]</span></div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span> <span class="comment"> *</span></div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="comment"> * Compared to a step, it has the following properties:</span></div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span> <span class="comment"> *</span></div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="comment"> * - @f$ f'(0) = 0 @f$</span></div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="comment"> * - @f$ f'(1) = 0 @f$</span></div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="comment"> *</span></div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="comment"> * This function is also known as [smoothstep](https://en.wikipedia.org/wiki/Smoothstep)</span></div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="comment"> *</span></div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="comment"> * @sa gf::Step</span></div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="comment"> */</span></div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="keyword">constexpr</span></div><div class="line"><a name="l00186"></a><span class="lineno"><a class="line" href="group__core.html#gab353056685420de64599bb422adaf701"> 186</a></span>  T <a class="code" href="group__core.html#gab353056685420de64599bb422adaf701">cubicStep</a>(T t) {</div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="keywordflow">return</span> (-2 * t + 3) * t * t;</div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  }</div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span> </div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <span class="comment">/**</span></div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span> <span class="comment"> * @brief Quintic step (smootherstep)</span></div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="comment"> *</span></div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span> <span class="comment"> * @f[ f(t) = 6 * t^5 - 15 * t^4 + 10 * t^3 @f]</span></div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span> <span class="comment"> *</span></div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span> <span class="comment"> * Compared to a step, it has the following properties:</span></div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span> <span class="comment"> *</span></div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span> <span class="comment"> * - @f$ f'(0) = 0 @f$</span></div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span> <span class="comment"> * - @f$ f'(1) = 0 @f$</span></div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="comment"> * - @f$ f''(0) = 0 @f$</span></div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span> <span class="comment"> * - @f$ f''(1) = 0 @f$</span></div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span> <span class="comment"> *</span></div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span> <span class="comment"> * This function is also known as [smootherstep](https://en.wikipedia.org/wiki/Smoothstep#Variations)</span></div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span> <span class="comment"> *</span></div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span> <span class="comment"> * @sa gf::Step</span></div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="comment"> */</span></div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="keyword">constexpr</span></div><div class="line"><a name="l00209"></a><span class="lineno"><a class="line" href="group__core.html#ga6f9ca6f1bc9622a4c7e68a3f956d8415"> 209</a></span>  T <a class="code" href="group__core.html#ga6f9ca6f1bc9622a4c7e68a3f956d8415">quinticStep</a>(T t) {</div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="keywordflow">return</span> ((6 * t - 15) * t + 10) * t * t * t;</div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  }</div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span> </div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="comment">/**</span></div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="comment"> * @brief Cosine step</span></div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="comment"> *</span></div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="comment"> * @f[ f(t) = (1 - \cos(\pi * t)) * 0.5 @f]</span></div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="comment"> *</span></div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span> <span class="comment"> * @sa gf::Step</span></div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span> <span class="comment"> */</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>  <span class="keyword">inline</span></div><div class="line"><a name="l00223"></a><span class="lineno"><a class="line" href="group__core.html#ga0e9fce6526516ba6bee65bf802888cd3"> 223</a></span>  T <a class="code" href="group__core.html#ga0e9fce6526516ba6bee65bf802888cd3">cosineStep</a>(T t) {</div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="keywordflow">return</span> (1 - std::cos(<a class="code" href="group__core.html#gafea71ec62ea0c47eb8e65dba77940b40">Pi</a> * t)) * 0.5;</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="l00227"></a><span class="lineno"> 227</span>  <span class="comment">/**</span></div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span> <span class="comment"> * @brief Linear interpolation function</span></div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span> <span class="comment"> *</span></div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span> <span class="comment"> * This functions returns an interpolated value between two values `lhs` and</span></div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span> <span class="comment"> * `rhs` according to a parameter @f$ t @f$. When @f$ t = 0 @f$ then `lhs`</span></div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span> <span class="comment"> * is returned, and when @f$ t = 1 @f$ then `rhs` is returned.</span></div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span> <span class="comment"> *</span></div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span> <span class="comment"> * @param lhs The first value</span></div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span> <span class="comment"> * @param rhs The second value</span></div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span> <span class="comment"> * @param t The interpolation parameter, generally in the interval @f$ [0,1] @f$</span></div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span> <span class="comment"> * @returns A value between the first and second value</span></div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span> <span class="comment"> */</span></div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T, <span class="keyword">typename</span> U></div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="keyword">inline</span></div><div class="line"><a name="l00242"></a><span class="lineno"><a class="line" href="group__core.html#gac274bd90d63716ed5b514331c90288e9"> 242</a></span>  T <a class="code" href="group__core.html#gac274bd90d63716ed5b514331c90288e9">lerp</a>(T lhs, T rhs, U t) {</div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="keywordflow">return</span> (1 - t) * lhs + t * rhs;</div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  }</div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span> </div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <span class="comment">/**</span></div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span> <span class="comment"> * @brief Clamping function</span></div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span> <span class="comment"> *</span></div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span> <span class="comment"> * This function takes a value and returns it if it is in a specified range.</span></div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span> <span class="comment"> * If not, the returned value is the nearest value in the range.</span></div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span> <span class="comment"> *</span></div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span> <span class="comment"> * @param val The value to clamp</span></div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span> <span class="comment"> * @param lo The minimum accepted value</span></div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span> <span class="comment"> * @param hi The maximum accepted value</span></div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span> <span class="comment"> * @returns The clamped value</span></div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span> <span class="comment"> */</span></div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="keyword">constexpr</span></div><div class="line"><a name="l00260"></a><span class="lineno"><a class="line" href="group__core.html#ga671bdda5a52c335e68d391147c70cc16"> 260</a></span>  T <a class="code" href="group__core.html#ga671bdda5a52c335e68d391147c70cc16">clamp</a>(T val, T lo, T hi) {</div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  <span class="keywordflow">return</span> val < lo ? lo : (val > hi ? hi : val);</div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  }</div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span> </div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  <span class="comment">/**</span></div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span> <span class="comment"> * @brief Square function</span></div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span> <span class="comment"> *</span></div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span> <span class="comment"> * For a value @f$ x @f$, the square value is @f$ x^2 @f$.</span></div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span> <span class="comment"> *</span></div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span> <span class="comment"> * @param val A value</span></div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span> <span class="comment"> * @returns The square of the value</span></div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span> <span class="comment"> */</span></div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  <span class="keyword">constexpr</span></div><div class="line"><a name="l00275"></a><span class="lineno"><a class="line" href="group__core.html#ga0e22be4ddd625e4c235dbf0ef2d1f43f"> 275</a></span>  T <a class="code" href="group__core.html#ga0e22be4ddd625e4c235dbf0ef2d1f43f">square</a>(T val) {</div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <span class="keywordflow">return</span> val * val;</div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  }</div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span> </div><div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <span class="comment">/**</span></div><div class="line"><a name="l00280"></a><span class="lineno"> 280</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span> <span class="comment"> * @brief Sign function</span></div><div class="line"><a name="l00282"></a><span class="lineno"> 282</span> <span class="comment"> *</span></div><div class="line"><a name="l00283"></a><span class="lineno"> 283</span> <span class="comment"> * The sign function of @f$ x @f$ is:</span></div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span> <span class="comment"> *</span></div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span> <span class="comment"> * - @f$ -1 @f$ if @f$ x < 0 @f$</span></div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span> <span class="comment"> * - @f$ 0 @f$ if @f$ x = 0 @f$</span></div><div class="line"><a name="l00287"></a><span class="lineno"> 287</span> <span class="comment"> * - @f$ 1 @f$ if @f$ x > 0 @f$</span></div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span> <span class="comment"> *</span></div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span> <span class="comment"> * @param val A value</span></div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span> <span class="comment"> * @returns The sign of the value</span></div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span> <span class="comment"> * @sa [Sign function](https://en.wikipedia.org/wiki/Sign_function)</span></div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span> <span class="comment"> */</span></div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <span class="keyword">constexpr</span></div><div class="line"><a name="l00295"></a><span class="lineno"><a class="line" href="group__core.html#ga55d7afb6ae7f894776bb0244465ac497"> 295</a></span>  <span class="keywordtype">int</span> <a class="code" href="group__core.html#ga55d7afb6ae7f894776bb0244465ac497">sign</a>(T val) {</div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <span class="keywordflow">return</span> (val > T(0)) - (val < T(0));</div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  }</div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span> </div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="comment">/**</span></div><div class="line"><a name="l00300"></a><span class="lineno"> 300</span> <span class="comment"> * @ingroup core</span></div><div class="line"><a name="l00301"></a><span class="lineno"> 301</span> <span class="comment"> * @brief Absolute difference of two values</span></div><div class="line"><a name="l00302"></a><span class="lineno"> 302</span> <span class="comment"> *</span></div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span> <span class="comment"> * This function is defined as:</span></div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span> <span class="comment"> *</span></div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span> <span class="comment"> * @f[ \text{absdiff}(a, b) = | a - b | @f]</span></div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span> <span class="comment"> *</span></div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span> <span class="comment"> * @param lhs The first value</span></div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span> <span class="comment"> * @param rhs The second value</span></div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span> <span class="comment"> * @returns The absolute difference between the two values</span></div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span> <span class="comment"> */</span></div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T></div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="keyword">constexpr</span></div><div class="line"><a name="l00313"></a><span class="lineno"><a class="line" href="group__core.html#ga162af6026bb8a59762e87c918f634006"> 313</a></span>  T <a class="code" href="group__core.html#ga162af6026bb8a59762e87c918f634006">absdiff</a>(T lhs, T rhs) {</div><div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <span class="keywordflow">return</span> lhs > rhs ? lhs - rhs : rhs - lhs;</div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  }</div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span> </div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span> <span class="preprocessor">#</span><span class="preprocessor">ifndef</span> <span class="preprocessor">DOXYGEN_SHOULD_SKIP_THIS</span></div><div class="line"><a name="l00318"></a><span class="lineno"> 318</span> }</div><div class="line"><a name="l00319"></a><span class="lineno"> 319</span> <span class="preprocessor">#</span><span class="preprocessor">endif</span></div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span> }</div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span> </div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span> <span class="preprocessor">#</span><span class="preprocessor">endif</span> <span class="comment">// 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:44</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:74</div></div>
<div class="ttc" id="group__core_html_ga1965ca9c0aa332a0a9fff72398f29c69"><div class="ttname"><a href="group__core.html#ga1965ca9c0aa332a0a9fff72398f29c69">gf::radiansToDegrees</a></div><div class="ttdeci">constexpr float radiansToDegrees(float radians)</div><div class="ttdoc">Convert radians to degrees. </div><div class="ttdef"><b>Definition:</b> Math.h:125</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:62</div></div>
<div class="ttc" id="group__core_html_ga4f3a61189703ec2b8dc9e9a27a398bb5"><div class="ttname"><a href="group__core.html#ga4f3a61189703ec2b8dc9e9a27a398bb5">gf::degreesToRadians</a></div><div class="ttdeci">constexpr float degreesToRadians(float degrees)</div><div class="ttdoc">Convert degrees to radians. </div><div class="ttdef"><b>Definition:</b> Math.h:113</div></div>
<div class="ttc" id="group__core_html_gac274bd90d63716ed5b514331c90288e9"><div class="ttname"><a href="group__core.html#gac274bd90d63716ed5b514331c90288e9">gf::lerp</a></div><div class="ttdeci">T lerp(T lhs, T rhs, U t)</div><div class="ttdoc">Linear interpolation function. </div><div class="ttdef"><b>Definition:</b> Math.h:242</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:313</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:275</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:260</div></div>
<div class="ttc" id="group__core_html_ga7ed0adec6b897c228288a41a757b96a2"><div class="ttname"><a href="group__core.html#ga7ed0adec6b897c228288a41a757b96a2">gf::almostEquals</a></div><div class="ttdeci">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:88</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:56</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:186</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:34</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:223</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:38</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:165</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:68</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:295</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:209</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:50</div></div>
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