131 lines
3.7 KiB
GLSL
131 lines
3.7 KiB
GLSL
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/* ---------------------------------------------------------------------- */
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/** \name Common Math Utilities
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* \{ */
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#define M_PI 3.14159265358979323846 /* pi */
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#define M_2PI 6.28318530717958647692 /* 2*pi */
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#define M_PI_2 1.57079632679489661923 /* pi/2 */
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#define M_1_PI 0.318309886183790671538 /* 1/pi */
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#define M_1_2PI 0.159154943091895335768 /* 1/(2*pi) */
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#define M_1_PI2 0.101321183642337771443 /* 1/(pi^2) */
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#define FLT_MAX 3.402823e+38
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vec3 mul(mat3 m, vec3 v)
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{
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return m * v;
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}
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mat3 mul(mat3 m1, mat3 m2)
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{
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return m1 * m2;
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}
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vec3 transform_direction(mat4 m, vec3 v)
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{
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return mat3(m) * v;
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}
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vec3 transform_point(mat4 m, vec3 v)
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{
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return (m * vec4(v, 1.0)).xyz;
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}
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vec3 project_point(mat4 m, vec3 v)
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{
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vec4 tmp = m * vec4(v, 1.0);
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return tmp.xyz / tmp.w;
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}
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#define min3(a, b, c) min(a, min(b, c))
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#define min4(a, b, c, d) min(a, min3(b, c, d))
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#define min5(a, b, c, d, e) min(a, min4(b, c, d, e))
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#define min6(a, b, c, d, e, f) min(a, min5(b, c, d, e, f))
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#define min7(a, b, c, d, e, f, g) min(a, min6(b, c, d, e, f, g))
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#define min8(a, b, c, d, e, f, g, h) min(a, min7(b, c, d, e, f, g, h))
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#define min9(a, b, c, d, e, f, g, h, i) min(a, min8(b, c, d, e, f, g, h, i))
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#define max3(a, b, c) max(a, max(b, c))
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#define max4(a, b, c, d) max(a, max3(b, c, d))
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#define max5(a, b, c, d, e) max(a, max4(b, c, d, e))
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#define max6(a, b, c, d, e, f) max(a, max5(b, c, d, e, f))
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#define max7(a, b, c, d, e, f, g) max(a, max6(b, c, d, e, f, g))
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#define max8(a, b, c, d, e, f, g, h) max(a, max7(b, c, d, e, f, g, h))
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#define max9(a, b, c, d, e, f, g, h, i) max(a, max8(b, c, d, e, f, g, h, i))
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#define avg3(a, b, c) (a + b + c) * (1.0 / 3.0)
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#define avg4(a, b, c, d) (a + b + c + d) * (1.0 / 4.0)
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#define avg5(a, b, c, d, e) (a + b + c + d + e) * (1.0 / 5.0)
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#define avg6(a, b, c, d, e, f) (a + b + c + d + e + f) * (1.0 / 6.0)
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#define avg7(a, b, c, d, e, f, g) (a + b + c + d + e + f + g) * (1.0 / 7.0)
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#define avg8(a, b, c, d, e, f, g, h) (a + b + c + d + e + f + g + h) * (1.0 / 8.0)
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#define avg9(a, b, c, d, e, f, g, h, i) (a + b + c + d + e + f + g + h + i) * (1.0 / 9.0)
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/* clang-format off */
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float min_v2(vec2 v) { return min(v.x, v.y); }
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float min_v3(vec3 v) { return min(v.x, min(v.y, v.z)); }
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float min_v4(vec4 v) { return min(min(v.x, v.y), min(v.z, v.w)); }
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float max_v2(vec2 v) { return max(v.x, v.y); }
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float max_v3(vec3 v) { return max(v.x, max(v.y, v.z)); }
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float max_v4(vec4 v) { return max(max(v.x, v.y), max(v.z, v.w)); }
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float sum(vec2 v) { return dot(vec2(1.0), v); }
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float sum(vec3 v) { return dot(vec3(1.0), v); }
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float sum(vec4 v) { return dot(vec4(1.0), v); }
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float avg(vec2 v) { return dot(vec2(1.0 / 2.0), v); }
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float avg(vec3 v) { return dot(vec3(1.0 / 3.0), v); }
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float avg(vec4 v) { return dot(vec4(1.0 / 4.0), v); }
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/* clang-format on */
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#define saturate(a) clamp(a, 0.0, 1.0)
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float distance_squared(vec2 a, vec2 b)
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{
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a -= b;
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return dot(a, a);
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}
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float distance_squared(vec3 a, vec3 b)
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{
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a -= b;
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return dot(a, a);
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}
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float len_squared(vec3 a)
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{
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return dot(a, a);
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}
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/** \} */
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/* ---------------------------------------------------------------------- */
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/** \name Fast Math
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* \{ */
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/* [Drobot2014a] Low Level Optimizations for GCN */
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float fast_sqrt(float v)
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{
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return intBitsToFloat(0x1fbd1df5 + (floatBitsToInt(v) >> 1));
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}
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vec2 fast_sqrt(vec2 v)
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{
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return intBitsToFloat(0x1fbd1df5 + (floatBitsToInt(v) >> 1));
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}
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/* [Eberly2014] GPGPU Programming for Games and Science */
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float fast_acos(float v)
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{
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float res = -0.156583 * abs(v) + M_PI_2;
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res *= fast_sqrt(1.0 - abs(v));
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return (v >= 0) ? res : M_PI - res;
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}
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vec2 fast_acos(vec2 v)
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{
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vec2 res = -0.156583 * abs(v) + M_PI_2;
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res *= fast_sqrt(1.0 - abs(v));
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v.x = (v.x >= 0) ? res.x : M_PI - res.x;
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v.y = (v.y >= 0) ? res.y : M_PI - res.y;
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return v;
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}
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/** \} */
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