blender-archive/source/blender/draw/intern/shaders/common_math_lib.glsl

/* ---------------------------------------------------------------------- */
/** \name Common Math Utilities
 * \{ */

#define M_PI 3.14159265358979323846      /* pi */
#define M_2PI 6.28318530717958647692     /* 2*pi */
#define M_PI_2 1.57079632679489661923    /* pi/2 */
#define M_1_PI 0.318309886183790671538   /* 1/pi */
#define M_1_2PI 0.159154943091895335768  /* 1/(2*pi) */
#define M_1_PI2 0.101321183642337771443  /* 1/(pi^2) */
#define M_SQRT2 1.41421356237309504880   /* sqrt(2) */
#define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
#define FLT_MAX 3.402823e+38

vec3 mul(mat3 m, vec3 v)
{
  return m * v;
}
mat3 mul(mat3 m1, mat3 m2)
{
  return m1 * m2;
}
vec3 transform_direction(mat4 m, vec3 v)
{
  return mat3(m) * v;
}
vec3 transform_point(mat4 m, vec3 v)
{
  return (m * vec4(v, 1.0)).xyz;
}
vec3 project_point(mat4 m, vec3 v)
{
  vec4 tmp = m * vec4(v, 1.0);
  return tmp.xyz / tmp.w;
}

mat2 rot2_from_angle(float a)
{
  float c = cos(a);
  float s = sin(a);
  return mat2(c, -s, s, c);
}

#define min3(a, b, c) min(a, min(b, c))
#define min4(a, b, c, d) min(a, min3(b, c, d))
#define min5(a, b, c, d, e) min(a, min4(b, c, d, e))
#define min6(a, b, c, d, e, f) min(a, min5(b, c, d, e, f))
#define min7(a, b, c, d, e, f, g) min(a, min6(b, c, d, e, f, g))
#define min8(a, b, c, d, e, f, g, h) min(a, min7(b, c, d, e, f, g, h))
#define min9(a, b, c, d, e, f, g, h, i) min(a, min8(b, c, d, e, f, g, h, i))

#define max3(a, b, c) max(a, max(b, c))
#define max4(a, b, c, d) max(a, max3(b, c, d))
#define max5(a, b, c, d, e) max(a, max4(b, c, d, e))
#define max6(a, b, c, d, e, f) max(a, max5(b, c, d, e, f))
#define max7(a, b, c, d, e, f, g) max(a, max6(b, c, d, e, f, g))
#define max8(a, b, c, d, e, f, g, h) max(a, max7(b, c, d, e, f, g, h))
#define max9(a, b, c, d, e, f, g, h, i) max(a, max8(b, c, d, e, f, g, h, i))

#define avg3(a, b, c) (a + b + c) * (1.0 / 3.0)
#define avg4(a, b, c, d) (a + b + c + d) * (1.0 / 4.0)
#define avg5(a, b, c, d, e) (a + b + c + d + e) * (1.0 / 5.0)
#define avg6(a, b, c, d, e, f) (a + b + c + d + e + f) * (1.0 / 6.0)
#define avg7(a, b, c, d, e, f, g) (a + b + c + d + e + f + g) * (1.0 / 7.0)
#define avg8(a, b, c, d, e, f, g, h) (a + b + c + d + e + f + g + h) * (1.0 / 8.0)
#define avg9(a, b, c, d, e, f, g, h, i) (a + b + c + d + e + f + g + h + i) * (1.0 / 9.0)

/* clang-format off */
float min_v2(vec2 v) { return min(v.x, v.y); }
float min_v3(vec3 v) { return min(v.x, min(v.y, v.z)); }
float min_v4(vec4 v) { return min(min(v.x, v.y), min(v.z, v.w)); }
float max_v2(vec2 v) { return max(v.x, v.y); }
float max_v3(vec3 v) { return max(v.x, max(v.y, v.z)); }
float max_v4(vec4 v) { return max(max(v.x, v.y), max(v.z, v.w)); }

float sum(vec2 v) { return dot(vec2(1.0), v); }
float sum(vec3 v) { return dot(vec3(1.0), v); }
float sum(vec4 v) { return dot(vec4(1.0), v); }

float avg(vec2 v) { return dot(vec2(1.0 / 2.0), v); }
float avg(vec3 v) { return dot(vec3(1.0 / 3.0), v); }
float avg(vec4 v) { return dot(vec4(1.0 / 4.0), v); }

float safe_rcp(float a) { return (a != 0.0) ? (1.0 / a) : 0.0; }
vec2 safe_rcp(vec2 a) { return mix(vec2(0.0), (1.0 / a), notEqual(a, vec2(0.0))); }
vec4 safe_rcp(vec4 a) { return mix(vec4(0.0), (1.0 / a), notEqual(a, vec4(0.0))); }

float safe_sqrt(float a) { return sqrt(max(a, 0.0)); }

float sqr(float a) { return a * a; }
vec2 sqr(vec2 a) { return a * a; }
vec3 sqr(vec3 a) { return a * a; }
vec4 sqr(vec4 a) { return a * a; }

/* Use manual powers for fixed powers. pow() can have unpredicatble results on some implementations.
 * (see T87369, T87541) */
float pow6(float x) { return sqr(sqr(x) * x); }
float pow8(float x) { return sqr(sqr(sqr(x))); }

float len_squared(vec3 a) { return dot(a, a); }
float len_squared(vec2 a) { return dot(a, a); }

#define weighted_sum(val0, val1, val2, val3, weights) ((val0 * weights[0] + val1 * weights[1] + val2 * weights[2] + val3 * weights[3]) * safe_rcp(sum(weights)));
#define weighted_sum_array(val, weights) ((val[0] * weights[0] + val[1] * weights[1] + val[2] * weights[2] + val[3] * weights[3]) * safe_rcp(sum(weights)));

/* clang-format on */

#define saturate(a) clamp(a, 0.0, 1.0)

float distance_squared(vec2 a, vec2 b)
{
  a -= b;
  return dot(a, a);
}

float distance_squared(vec3 a, vec3 b)
{
  a -= b;
  return dot(a, a);
}

vec3 safe_normalize(vec3 v)
{
  float len = length(v);
  if (isnan(len) || len == 0.0) {
    return vec3(1.0, 0.0, 0.0);
  }
  return v / len;
}

vec3 normalize_len(vec3 v, out float len)
{
  len = length(v);
  return v / len;
}

vec4 safe_color(vec4 c)
{
  /* Clamp to avoid black square artifacts if a pixel goes NaN. */
  return clamp(c, vec4(0.0), vec4(1e20)); /* 1e20 arbitrary. */
}

/** \} */

/* ---------------------------------------------------------------------- */
/** \name Fast Math
 * \{ */

/* [Drobot2014a] Low Level Optimizations for GCN */
float fast_sqrt(float v)
{
  return intBitsToFloat(0x1fbd1df5 + (floatBitsToInt(v) >> 1));
}

vec2 fast_sqrt(vec2 v)
{
  return intBitsToFloat(0x1fbd1df5 + (floatBitsToInt(v) >> 1));
}

/* [Eberly2014] GPGPU Programming for Games and Science */
float fast_acos(float v)
{
  float res = -0.156583 * abs(v) + M_PI_2;
  res *= fast_sqrt(1.0 - abs(v));
  return (v >= 0) ? res : M_PI - res;
}

vec2 fast_acos(vec2 v)
{
  vec2 res = -0.156583 * abs(v) + M_PI_2;
  res *= fast_sqrt(1.0 - abs(v));
  v.x = (v.x >= 0) ? res.x : M_PI - res.x;
  v.y = (v.y >= 0) ? res.y : M_PI - res.y;
  return v;
}

/** \} */

/*
 * For debugging purpose mainly.
 * From https://www.shadertoy.com/view/4dsSzr
 * By Morgan McGuire @morgan3d, http://graphicscodex.com
 * Reuse permitted under the BSD license.
 */
vec3 neon_gradient(float t)
{
  return clamp(vec3(t * 1.3 + 0.1, sqr(abs(0.43 - t) * 1.7), (1.0 - t) * 1.7), 0.0, 1.0);
}