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Diffstat (limited to 'src/mesa/program/prog_noise.c')
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diff --git a/src/mesa/program/prog_noise.c b/src/mesa/program/prog_noise.c new file mode 100644 index 00000000000..1713ddb5f34 --- /dev/null +++ b/src/mesa/program/prog_noise.c @@ -0,0 +1,638 @@ +/* + * Mesa 3-D graphics library + * Version: 6.5 + * + * Copyright (C) 2006 Brian Paul All Rights Reserved. + * + * Permission is hereby granted, free of charge, to any person obtaining a + * copy of this software and associated documentation files (the "Software"), + * to deal in the Software without restriction, including without limitation + * the rights to use, copy, modify, merge, publish, distribute, sublicense, + * and/or sell copies of the Software, and to permit persons to whom the + * Software is furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included + * in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS + * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL + * BRIAN PAUL BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN + * AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN + * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + */ + +/* + * SimplexNoise1234 + * Copyright (c) 2003-2005, Stefan Gustavson + * + * Contact: [email protected] + */ + +/** + * \file + * \brief C implementation of Perlin Simplex Noise over 1, 2, 3 and 4 dims. + * \author Stefan Gustavson ([email protected]) + * + * + * This implementation is "Simplex Noise" as presented by + * Ken Perlin at a relatively obscure and not often cited course + * session "Real-Time Shading" at Siggraph 2001 (before real + * time shading actually took on), under the title "hardware noise". + * The 3D function is numerically equivalent to his Java reference + * code available in the PDF course notes, although I re-implemented + * it from scratch to get more readable code. The 1D, 2D and 4D cases + * were implemented from scratch by me from Ken Perlin's text. + * + * This file has no dependencies on any other file, not even its own + * header file. The header file is made for use by external code only. + */ + + +#include "main/imports.h" +#include "prog_noise.h" + +#define FASTFLOOR(x) ( ((x)>0) ? ((int)x) : (((int)x)-1) ) + +/* + * --------------------------------------------------------------------- + * Static data + */ + +/** + * Permutation table. This is just a random jumble of all numbers 0-255, + * repeated twice to avoid wrapping the index at 255 for each lookup. + * This needs to be exactly the same for all instances on all platforms, + * so it's easiest to just keep it as static explicit data. + * This also removes the need for any initialisation of this class. + * + * Note that making this an int[] instead of a char[] might make the + * code run faster on platforms with a high penalty for unaligned single + * byte addressing. Intel x86 is generally single-byte-friendly, but + * some other CPUs are faster with 4-aligned reads. + * However, a char[] is smaller, which avoids cache trashing, and that + * is probably the most important aspect on most architectures. + * This array is accessed a *lot* by the noise functions. + * A vector-valued noise over 3D accesses it 96 times, and a + * float-valued 4D noise 64 times. We want this to fit in the cache! + */ +unsigned char perm[512] = { 151, 160, 137, 91, 90, 15, + 131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, 30, 69, 142, 8, + 99, 37, 240, 21, 10, 23, + 190, 6, 148, 247, 120, 234, 75, 0, 26, 197, 62, 94, 252, 219, 203, 117, 35, + 11, 32, 57, 177, 33, + 88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175, 74, 165, 71, + 134, 139, 48, 27, 166, + 77, 146, 158, 231, 83, 111, 229, 122, 60, 211, 133, 230, 220, 105, 92, 41, + 55, 46, 245, 40, 244, + 102, 143, 54, 65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89, + 18, 169, 200, 196, + 135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186, 3, 64, 52, 217, + 226, 250, 124, 123, + 5, 202, 38, 147, 118, 126, 255, 82, 85, 212, 207, 206, 59, 227, 47, 16, 58, + 17, 182, 189, 28, 42, + 223, 183, 170, 213, 119, 248, 152, 2, 44, 154, 163, 70, 221, 153, 101, 155, + 167, 43, 172, 9, + 129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224, 232, 178, 185, 112, 104, + 218, 246, 97, 228, + 251, 34, 242, 193, 238, 210, 144, 12, 191, 179, 162, 241, 81, 51, 145, 235, + 249, 14, 239, 107, + 49, 192, 214, 31, 181, 199, 106, 157, 184, 84, 204, 176, 115, 121, 50, 45, + 127, 4, 150, 254, + 138, 236, 205, 93, 222, 114, 67, 29, 24, 72, 243, 141, 128, 195, 78, 66, + 215, 61, 156, 180, + 151, 160, 137, 91, 90, 15, + 131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, 30, 69, 142, 8, + 99, 37, 240, 21, 10, 23, + 190, 6, 148, 247, 120, 234, 75, 0, 26, 197, 62, 94, 252, 219, 203, 117, 35, + 11, 32, 57, 177, 33, + 88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175, 74, 165, 71, + 134, 139, 48, 27, 166, + 77, 146, 158, 231, 83, 111, 229, 122, 60, 211, 133, 230, 220, 105, 92, 41, + 55, 46, 245, 40, 244, + 102, 143, 54, 65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89, + 18, 169, 200, 196, + 135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186, 3, 64, 52, 217, + 226, 250, 124, 123, + 5, 202, 38, 147, 118, 126, 255, 82, 85, 212, 207, 206, 59, 227, 47, 16, 58, + 17, 182, 189, 28, 42, + 223, 183, 170, 213, 119, 248, 152, 2, 44, 154, 163, 70, 221, 153, 101, 155, + 167, 43, 172, 9, + 129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224, 232, 178, 185, 112, 104, + 218, 246, 97, 228, + 251, 34, 242, 193, 238, 210, 144, 12, 191, 179, 162, 241, 81, 51, 145, 235, + 249, 14, 239, 107, + 49, 192, 214, 31, 181, 199, 106, 157, 184, 84, 204, 176, 115, 121, 50, 45, + 127, 4, 150, 254, + 138, 236, 205, 93, 222, 114, 67, 29, 24, 72, 243, 141, 128, 195, 78, 66, + 215, 61, 156, 180 +}; + +/* + * --------------------------------------------------------------------- + */ + +/* + * Helper functions to compute gradients-dot-residualvectors (1D to 4D) + * Note that these generate gradients of more than unit length. To make + * a close match with the value range of classic Perlin noise, the final + * noise values need to be rescaled to fit nicely within [-1,1]. + * (The simplex noise functions as such also have different scaling.) + * Note also that these noise functions are the most practical and useful + * signed version of Perlin noise. To return values according to the + * RenderMan specification from the SL noise() and pnoise() functions, + * the noise values need to be scaled and offset to [0,1], like this: + * float SLnoise = (SimplexNoise1234::noise(x,y,z) + 1.0) * 0.5; + */ + +static float +grad1(int hash, float x) +{ + int h = hash & 15; + float grad = 1.0f + (h & 7); /* Gradient value 1.0, 2.0, ..., 8.0 */ + if (h & 8) + grad = -grad; /* Set a random sign for the gradient */ + return (grad * x); /* Multiply the gradient with the distance */ +} + +static float +grad2(int hash, float x, float y) +{ + int h = hash & 7; /* Convert low 3 bits of hash code */ + float u = h < 4 ? x : y; /* into 8 simple gradient directions, */ + float v = h < 4 ? y : x; /* and compute the dot product with (x,y). */ + return ((h & 1) ? -u : u) + ((h & 2) ? -2.0f * v : 2.0f * v); +} + +static float +grad3(int hash, float x, float y, float z) +{ + int h = hash & 15; /* Convert low 4 bits of hash code into 12 simple */ + float u = h < 8 ? x : y; /* gradient directions, and compute dot product. */ + float v = h < 4 ? y : h == 12 || h == 14 ? x : z; /* Fix repeats at h = 12 to 15 */ + return ((h & 1) ? -u : u) + ((h & 2) ? -v : v); +} + +static float +grad4(int hash, float x, float y, float z, float t) +{ + int h = hash & 31; /* Convert low 5 bits of hash code into 32 simple */ + float u = h < 24 ? x : y; /* gradient directions, and compute dot product. */ + float v = h < 16 ? y : z; + float w = h < 8 ? z : t; + return ((h & 1) ? -u : u) + ((h & 2) ? -v : v) + ((h & 4) ? -w : w); +} + +/** + * A lookup table to traverse the simplex around a given point in 4D. + * Details can be found where this table is used, in the 4D noise method. + * TODO: This should not be required, backport it from Bill's GLSL code! + */ +static unsigned char simplex[64][4] = { + {0, 1, 2, 3}, {0, 1, 3, 2}, {0, 0, 0, 0}, {0, 2, 3, 1}, + {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {1, 2, 3, 0}, + {0, 2, 1, 3}, {0, 0, 0, 0}, {0, 3, 1, 2}, {0, 3, 2, 1}, + {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {1, 3, 2, 0}, + {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, + {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, + {1, 2, 0, 3}, {0, 0, 0, 0}, {1, 3, 0, 2}, {0, 0, 0, 0}, + {0, 0, 0, 0}, {0, 0, 0, 0}, {2, 3, 0, 1}, {2, 3, 1, 0}, + {1, 0, 2, 3}, {1, 0, 3, 2}, {0, 0, 0, 0}, {0, 0, 0, 0}, + {0, 0, 0, 0}, {2, 0, 3, 1}, {0, 0, 0, 0}, {2, 1, 3, 0}, + {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, + {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, + {2, 0, 1, 3}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, + {3, 0, 1, 2}, {3, 0, 2, 1}, {0, 0, 0, 0}, {3, 1, 2, 0}, + {2, 1, 0, 3}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, + {3, 1, 0, 2}, {0, 0, 0, 0}, {3, 2, 0, 1}, {3, 2, 1, 0} +}; + + +/** 1D simplex noise */ +GLfloat +_mesa_noise1(GLfloat x) +{ + int i0 = FASTFLOOR(x); + int i1 = i0 + 1; + float x0 = x - i0; + float x1 = x0 - 1.0f; + float t1 = 1.0f - x1 * x1; + float n0, n1; + + float t0 = 1.0f - x0 * x0; +/* if(t0 < 0.0f) t0 = 0.0f; // this never happens for the 1D case */ + t0 *= t0; + n0 = t0 * t0 * grad1(perm[i0 & 0xff], x0); + +/* if(t1 < 0.0f) t1 = 0.0f; // this never happens for the 1D case */ + t1 *= t1; + n1 = t1 * t1 * grad1(perm[i1 & 0xff], x1); + /* The maximum value of this noise is 8*(3/4)^4 = 2.53125 */ + /* A factor of 0.395 would scale to fit exactly within [-1,1], but */ + /* we want to match PRMan's 1D noise, so we scale it down some more. */ + return 0.25f * (n0 + n1); +} + + +/** 2D simplex noise */ +GLfloat +_mesa_noise2(GLfloat x, GLfloat y) +{ +#define F2 0.366025403f /* F2 = 0.5*(sqrt(3.0)-1.0) */ +#define G2 0.211324865f /* G2 = (3.0-Math.sqrt(3.0))/6.0 */ + + float n0, n1, n2; /* Noise contributions from the three corners */ + + /* Skew the input space to determine which simplex cell we're in */ + float s = (x + y) * F2; /* Hairy factor for 2D */ + float xs = x + s; + float ys = y + s; + int i = FASTFLOOR(xs); + int j = FASTFLOOR(ys); + + float t = (float) (i + j) * G2; + float X0 = i - t; /* Unskew the cell origin back to (x,y) space */ + float Y0 = j - t; + float x0 = x - X0; /* The x,y distances from the cell origin */ + float y0 = y - Y0; + + float x1, y1, x2, y2; + int ii, jj; + float t0, t1, t2; + + /* For the 2D case, the simplex shape is an equilateral triangle. */ + /* Determine which simplex we are in. */ + int i1, j1; /* Offsets for second (middle) corner of simplex in (i,j) coords */ + if (x0 > y0) { + i1 = 1; + j1 = 0; + } /* lower triangle, XY order: (0,0)->(1,0)->(1,1) */ + else { + i1 = 0; + j1 = 1; + } /* upper triangle, YX order: (0,0)->(0,1)->(1,1) */ + + /* A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and */ + /* a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where */ + /* c = (3-sqrt(3))/6 */ + + x1 = x0 - i1 + G2; /* Offsets for middle corner in (x,y) unskewed coords */ + y1 = y0 - j1 + G2; + x2 = x0 - 1.0f + 2.0f * G2; /* Offsets for last corner in (x,y) unskewed coords */ + y2 = y0 - 1.0f + 2.0f * G2; + + /* Wrap the integer indices at 256, to avoid indexing perm[] out of bounds */ + ii = i % 256; + jj = j % 256; + + /* Calculate the contribution from the three corners */ + t0 = 0.5f - x0 * x0 - y0 * y0; + if (t0 < 0.0f) + n0 = 0.0f; + else { + t0 *= t0; + n0 = t0 * t0 * grad2(perm[ii + perm[jj]], x0, y0); + } + + t1 = 0.5f - x1 * x1 - y1 * y1; + if (t1 < 0.0f) + n1 = 0.0f; + else { + t1 *= t1; + n1 = t1 * t1 * grad2(perm[ii + i1 + perm[jj + j1]], x1, y1); + } + + t2 = 0.5f - x2 * x2 - y2 * y2; + if (t2 < 0.0f) + n2 = 0.0f; + else { + t2 *= t2; + n2 = t2 * t2 * grad2(perm[ii + 1 + perm[jj + 1]], x2, y2); + } + + /* Add contributions from each corner to get the final noise value. */ + /* The result is scaled to return values in the interval [-1,1]. */ + return 40.0f * (n0 + n1 + n2); /* TODO: The scale factor is preliminary! */ +} + + +/** 3D simplex noise */ +GLfloat +_mesa_noise3(GLfloat x, GLfloat y, GLfloat z) +{ +/* Simple skewing factors for the 3D case */ +#define F3 0.333333333f +#define G3 0.166666667f + + float n0, n1, n2, n3; /* Noise contributions from the four corners */ + + /* Skew the input space to determine which simplex cell we're in */ + float s = (x + y + z) * F3; /* Very nice and simple skew factor for 3D */ + float xs = x + s; + float ys = y + s; + float zs = z + s; + int i = FASTFLOOR(xs); + int j = FASTFLOOR(ys); + int k = FASTFLOOR(zs); + + float t = (float) (i + j + k) * G3; + float X0 = i - t; /* Unskew the cell origin back to (x,y,z) space */ + float Y0 = j - t; + float Z0 = k - t; + float x0 = x - X0; /* The x,y,z distances from the cell origin */ + float y0 = y - Y0; + float z0 = z - Z0; + + float x1, y1, z1, x2, y2, z2, x3, y3, z3; + int ii, jj, kk; + float t0, t1, t2, t3; + + /* For the 3D case, the simplex shape is a slightly irregular tetrahedron. */ + /* Determine which simplex we are in. */ + int i1, j1, k1; /* Offsets for second corner of simplex in (i,j,k) coords */ + int i2, j2, k2; /* Offsets for third corner of simplex in (i,j,k) coords */ + +/* This code would benefit from a backport from the GLSL version! */ + if (x0 >= y0) { + if (y0 >= z0) { + i1 = 1; + j1 = 0; + k1 = 0; + i2 = 1; + j2 = 1; + k2 = 0; + } /* X Y Z order */ + else if (x0 >= z0) { + i1 = 1; + j1 = 0; + k1 = 0; + i2 = 1; + j2 = 0; + k2 = 1; + } /* X Z Y order */ + else { + i1 = 0; + j1 = 0; + k1 = 1; + i2 = 1; + j2 = 0; + k2 = 1; + } /* Z X Y order */ + } + else { /* x0<y0 */ + if (y0 < z0) { + i1 = 0; + j1 = 0; + k1 = 1; + i2 = 0; + j2 = 1; + k2 = 1; + } /* Z Y X order */ + else if (x0 < z0) { + i1 = 0; + j1 = 1; + k1 = 0; + i2 = 0; + j2 = 1; + k2 = 1; + } /* Y Z X order */ + else { + i1 = 0; + j1 = 1; + k1 = 0; + i2 = 1; + j2 = 1; + k2 = 0; + } /* Y X Z order */ + } + + /* A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in + * (x,y,z), a step of (0,1,0) in (i,j,k) means a step of + * (-c,1-c,-c) in (x,y,z), and a step of (0,0,1) in (i,j,k) means a + * step of (-c,-c,1-c) in (x,y,z), where c = 1/6. + */ + + x1 = x0 - i1 + G3; /* Offsets for second corner in (x,y,z) coords */ + y1 = y0 - j1 + G3; + z1 = z0 - k1 + G3; + x2 = x0 - i2 + 2.0f * G3; /* Offsets for third corner in (x,y,z) coords */ + y2 = y0 - j2 + 2.0f * G3; + z2 = z0 - k2 + 2.0f * G3; + x3 = x0 - 1.0f + 3.0f * G3;/* Offsets for last corner in (x,y,z) coords */ + y3 = y0 - 1.0f + 3.0f * G3; + z3 = z0 - 1.0f + 3.0f * G3; + + /* Wrap the integer indices at 256 to avoid indexing perm[] out of bounds */ + ii = i % 256; + jj = j % 256; + kk = k % 256; + + /* Calculate the contribution from the four corners */ + t0 = 0.6f - x0 * x0 - y0 * y0 - z0 * z0; + if (t0 < 0.0f) + n0 = 0.0f; + else { + t0 *= t0; + n0 = t0 * t0 * grad3(perm[ii + perm[jj + perm[kk]]], x0, y0, z0); + } + + t1 = 0.6f - x1 * x1 - y1 * y1 - z1 * z1; + if (t1 < 0.0f) + n1 = 0.0f; + else { + t1 *= t1; + n1 = + t1 * t1 * grad3(perm[ii + i1 + perm[jj + j1 + perm[kk + k1]]], x1, + y1, z1); + } + + t2 = 0.6f - x2 * x2 - y2 * y2 - z2 * z2; + if (t2 < 0.0f) + n2 = 0.0f; + else { + t2 *= t2; + n2 = + t2 * t2 * grad3(perm[ii + i2 + perm[jj + j2 + perm[kk + k2]]], x2, + y2, z2); + } + + t3 = 0.6f - x3 * x3 - y3 * y3 - z3 * z3; + if (t3 < 0.0f) + n3 = 0.0f; + else { + t3 *= t3; + n3 = + t3 * t3 * grad3(perm[ii + 1 + perm[jj + 1 + perm[kk + 1]]], x3, y3, + z3); + } + + /* Add contributions from each corner to get the final noise value. + * The result is scaled to stay just inside [-1,1] + */ + return 32.0f * (n0 + n1 + n2 + n3); /* TODO: The scale factor is preliminary! */ +} + + +/** 4D simplex noise */ +GLfloat +_mesa_noise4(GLfloat x, GLfloat y, GLfloat z, GLfloat w) +{ + /* The skewing and unskewing factors are hairy again for the 4D case */ +#define F4 0.309016994f /* F4 = (Math.sqrt(5.0)-1.0)/4.0 */ +#define G4 0.138196601f /* G4 = (5.0-Math.sqrt(5.0))/20.0 */ + + float n0, n1, n2, n3, n4; /* Noise contributions from the five corners */ + + /* Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in */ + float s = (x + y + z + w) * F4; /* Factor for 4D skewing */ + float xs = x + s; + float ys = y + s; + float zs = z + s; + float ws = w + s; + int i = FASTFLOOR(xs); + int j = FASTFLOOR(ys); + int k = FASTFLOOR(zs); + int l = FASTFLOOR(ws); + + float t = (i + j + k + l) * G4; /* Factor for 4D unskewing */ + float X0 = i - t; /* Unskew the cell origin back to (x,y,z,w) space */ + float Y0 = j - t; + float Z0 = k - t; + float W0 = l - t; + + float x0 = x - X0; /* The x,y,z,w distances from the cell origin */ + float y0 = y - Y0; + float z0 = z - Z0; + float w0 = w - W0; + + /* For the 4D case, the simplex is a 4D shape I won't even try to describe. + * To find out which of the 24 possible simplices we're in, we need to + * determine the magnitude ordering of x0, y0, z0 and w0. + * The method below is a good way of finding the ordering of x,y,z,w and + * then find the correct traversal order for the simplex we're in. + * First, six pair-wise comparisons are performed between each possible pair + * of the four coordinates, and the results are used to add up binary bits + * for an integer index. + */ + int c1 = (x0 > y0) ? 32 : 0; + int c2 = (x0 > z0) ? 16 : 0; + int c3 = (y0 > z0) ? 8 : 0; + int c4 = (x0 > w0) ? 4 : 0; + int c5 = (y0 > w0) ? 2 : 0; + int c6 = (z0 > w0) ? 1 : 0; + int c = c1 + c2 + c3 + c4 + c5 + c6; + + int i1, j1, k1, l1; /* The integer offsets for the second simplex corner */ + int i2, j2, k2, l2; /* The integer offsets for the third simplex corner */ + int i3, j3, k3, l3; /* The integer offsets for the fourth simplex corner */ + + float x1, y1, z1, w1, x2, y2, z2, w2, x3, y3, z3, w3, x4, y4, z4, w4; + int ii, jj, kk, ll; + float t0, t1, t2, t3, t4; + + /* + * simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some + * order. Many values of c will never occur, since e.g. x>y>z>w + * makes x<z, y<w and x<w impossible. Only the 24 indices which + * have non-zero entries make any sense. We use a thresholding to + * set the coordinates in turn from the largest magnitude. The + * number 3 in the "simplex" array is at the position of the + * largest coordinate. + */ + i1 = simplex[c][0] >= 3 ? 1 : 0; + j1 = simplex[c][1] >= 3 ? 1 : 0; + k1 = simplex[c][2] >= 3 ? 1 : 0; + l1 = simplex[c][3] >= 3 ? 1 : 0; + /* The number 2 in the "simplex" array is at the second largest coordinate. */ + i2 = simplex[c][0] >= 2 ? 1 : 0; + j2 = simplex[c][1] >= 2 ? 1 : 0; + k2 = simplex[c][2] >= 2 ? 1 : 0; + l2 = simplex[c][3] >= 2 ? 1 : 0; + /* The number 1 in the "simplex" array is at the second smallest coordinate. */ + i3 = simplex[c][0] >= 1 ? 1 : 0; + j3 = simplex[c][1] >= 1 ? 1 : 0; + k3 = simplex[c][2] >= 1 ? 1 : 0; + l3 = simplex[c][3] >= 1 ? 1 : 0; + /* The fifth corner has all coordinate offsets = 1, so no need to look that up. */ + + x1 = x0 - i1 + G4; /* Offsets for second corner in (x,y,z,w) coords */ + y1 = y0 - j1 + G4; + z1 = z0 - k1 + G4; + w1 = w0 - l1 + G4; + x2 = x0 - i2 + 2.0f * G4; /* Offsets for third corner in (x,y,z,w) coords */ + y2 = y0 - j2 + 2.0f * G4; + z2 = z0 - k2 + 2.0f * G4; + w2 = w0 - l2 + 2.0f * G4; + x3 = x0 - i3 + 3.0f * G4; /* Offsets for fourth corner in (x,y,z,w) coords */ + y3 = y0 - j3 + 3.0f * G4; + z3 = z0 - k3 + 3.0f * G4; + w3 = w0 - l3 + 3.0f * G4; + x4 = x0 - 1.0f + 4.0f * G4; /* Offsets for last corner in (x,y,z,w) coords */ + y4 = y0 - 1.0f + 4.0f * G4; + z4 = z0 - 1.0f + 4.0f * G4; + w4 = w0 - 1.0f + 4.0f * G4; + + /* Wrap the integer indices at 256, to avoid indexing perm[] out of bounds */ + ii = i % 256; + jj = j % 256; + kk = k % 256; + ll = l % 256; + + /* Calculate the contribution from the five corners */ + t0 = 0.6f - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0; + if (t0 < 0.0f) + n0 = 0.0f; + else { + t0 *= t0; + n0 = + t0 * t0 * grad4(perm[ii + perm[jj + perm[kk + perm[ll]]]], x0, y0, + z0, w0); + } + + t1 = 0.6f - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1; + if (t1 < 0.0f) + n1 = 0.0f; + else { + t1 *= t1; + n1 = + t1 * t1 * + grad4(perm[ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]]], + x1, y1, z1, w1); + } + + t2 = 0.6f - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2; + if (t2 < 0.0f) + n2 = 0.0f; + else { + t2 *= t2; + n2 = + t2 * t2 * + grad4(perm[ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]]], + x2, y2, z2, w2); + } + + t3 = 0.6f - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3; + if (t3 < 0.0f) + n3 = 0.0f; + else { + t3 *= t3; + n3 = + t3 * t3 * + grad4(perm[ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]]], + x3, y3, z3, w3); + } + + t4 = 0.6f - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4; + if (t4 < 0.0f) + n4 = 0.0f; + else { + t4 *= t4; + n4 = + t4 * t4 * + grad4(perm[ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]]], x4, + y4, z4, w4); + } + + /* Sum up and scale the result to cover the range [-1,1] */ + return 27.0f * (n0 + n1 + n2 + n3 + n4); /* TODO: The scale factor is preliminary! */ +} |