| 0,0 → 1,638 |
|---|
| /* |
| * Mesa 3-D graphics library |
| * |
| * 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 |
| * THE AUTHORS OR COPYRIGHT HOLDERS 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: stegu@itn.liu.se |
| */ |
| |
| /** |
| * \file |
| * \brief C implementation of Perlin Simplex Noise over 1, 2, 3 and 4 dims. |
| * \author Stefan Gustavson (stegu@itn.liu.se) |
| * |
| * |
| * 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! |
| */ |
| static const 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; |
| unsigned int ii, jj; |
| float t0, t1, t2; |
| |
| /* For the 2D case, the simplex shape is an equilateral triangle. */ |
| /* Determine which simplex we are in. */ |
| unsigned 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 & 0xff; |
| jj = j & 0xff; |
| |
| /* 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; |
| unsigned 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. */ |
| unsigned int i1, j1, k1; /* Offsets for second corner of simplex in (i,j,k) coords */ |
| unsigned 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 & 0xff; |
| jj = j & 0xff; |
| kk = k & 0xff; |
| |
| /* 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; |
| |
| unsigned int i1, j1, k1, l1; /* The integer offsets for the second simplex corner */ |
| unsigned int i2, j2, k2, l2; /* The integer offsets for the third simplex corner */ |
| unsigned 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; |
| unsigned 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 & 0xff; |
| jj = j & 0xff; |
| kk = k & 0xff; |
| ll = l & 0xff; |
| |
| /* 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! */ |
| } |