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September 28, 2023 00:45
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Shader Library: frequently used shader functions
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| /** | |
| First order approximation of acos() | |
| See https://seblagarde.wordpress.com/2014/12/01/inverse-trigonometric-functions-gpu-optimization-for-amd-gcn-architecture/ | |
| **/ | |
| float acosPoly1(float inX) { | |
| float x = abs(inX); | |
| float res = -0.156583 * x + 1.570796; | |
| res *= sqrt(1.0 - x); | |
| return (inX >= 0.0) ? res : (3.141593 - res); | |
| } | |
| float asinPoly1(float x) { | |
| return 1.570796 - acosPoly1(x); | |
| } | |
| /** | |
| Second order polynomial approximation of atan in the range -1 to 1 | |
| **/ | |
| float atanPoly2UnitRange(float inX) { | |
| float x = abs(inX); | |
| float p = (-0.269408 * x + 1.05863) * x; | |
| return inX < 0.0 ? -p : p; | |
| } | |
| vec2 atanPoly2UnitRange(vec2 inX) { | |
| vec2 x = abs(inX); | |
| vec2 p = (-0.269408 * x + 1.05863) * x; | |
| return sign(inX) * p; | |
| } | |
| vec3 atanPoly2UnitRange(vec3 inX) { | |
| vec3 x = abs(inX); | |
| vec3 p = (-0.269408 * x + 1.05863) * x; | |
| return sign(inX) * p; | |
| } | |
| /** | |
| Given a transform matrix, the adjugate matrix gives us the equivalent transform matrix for transforming surface normals | |
| The cofactor matrix is equivalent to transpose(adjugate(m)) | |
| **/ | |
| mat3 adjugate(in mat3 m) { | |
| return mat3( | |
| cross(m[1], m[2]), | |
| cross(m[2], m[0]), | |
| cross(m[0], m[1]) | |
| ); | |
| } |
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