678 lines
24 KiB
C++
678 lines
24 KiB
C++
#include "NoiseFunctionSimplex.h"
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/*
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* Simplex noise implementation.
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*
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* Based on Stefan Gustavson implementation.
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*/
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#include "Color.h"
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#include "Geometry.h"
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#include "Texture2D.h"
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#include "Vector3.h"
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#include <cmath>
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#include <cstdlib>
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#include <cstring>
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typedef struct {
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double x;
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double y;
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double z;
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} Grad3;
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typedef struct {
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double x;
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double y;
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double z;
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double w;
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} Grad4;
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static Grad3 _grad3[] = {{1, 1, 0}, {-1, 1, 0}, {1, -1, 0}, {-1, -1, 0}, {1, 0, 1}, {-1, 0, 1},
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{1, 0, -1}, {-1, 0, -1}, {0, 1, 1}, {0, -1, 1}, {0, 1, -1}, {0, -1, -1}};
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static Grad4 _grad4[] = {
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{0, 1, 1, 1}, {0, 1, 1, -1}, {0, 1, -1, 1}, {0, 1, -1, -1}, {0, -1, 1, 1}, {0, -1, 1, -1}, {0, -1, -1, 1},
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{0, -1, -1, -1}, {1, 0, 1, 1}, {1, 0, 1, -1}, {1, 0, -1, 1}, {1, 0, -1, -1}, {-1, 0, 1, 1}, {-1, 0, 1, -1},
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{-1, 0, -1, 1}, {-1, 0, -1, -1}, {1, 1, 0, 1}, {1, 1, 0, -1}, {1, -1, 0, 1}, {1, -1, 0, -1}, {-1, 1, 0, 1},
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{-1, 1, 0, -1}, {-1, -1, 0, 1}, {-1, -1, 0, -1}, {1, 1, 1, 0}, {1, 1, -1, 0}, {1, -1, 1, 0}, {1, -1, -1, 0},
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{-1, 1, 1, 0}, {-1, 1, -1, 0}, {-1, -1, 1, 0}, {-1, -1, -1, 0}};
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static short _permutations[] = {
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151, 160, 137, 91, 90, 15, 131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, 30, 69, 142,
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8, 99, 37, 240, 21, 10, 23, 190, 6, 148, 247, 120, 234, 75, 0, 26, 197, 62, 94, 252, 219, 203,
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117, 35, 11, 32, 57, 177, 33, 88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175, 74, 165,
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71, 134, 139, 48, 27, 166, 77, 146, 158, 231, 83, 111, 229, 122, 60, 211, 133, 230, 220, 105, 92, 41,
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55, 46, 245, 40, 244, 102, 143, 54, 65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89,
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18, 169, 200, 196, 135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186, 3, 64, 52, 217, 226, 250,
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124, 123, 5, 202, 38, 147, 118, 126, 255, 82, 85, 212, 207, 206, 59, 227, 47, 16, 58, 17, 182, 189,
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28, 42, 223, 183, 170, 213, 119, 248, 152, 2, 44, 154, 163, 70, 221, 153, 101, 155, 167, 43, 172, 9,
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129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224, 232, 178, 185, 112, 104, 218, 246, 97, 228, 251, 34,
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242, 193, 238, 210, 144, 12, 191, 179, 162, 241, 81, 51, 145, 235, 249, 14, 239, 107, 49, 192, 214, 31,
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181, 199, 106, 157, 184, 84, 204, 176, 115, 121, 50, 45, 127, 4, 150, 254, 138, 236, 205, 93, 222, 114,
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67, 29, 24, 72, 243, 141, 128, 195, 78, 66, 215, 61, 156, 180};
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static short _permutations2[512];
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static short _permutationsMod12[512];
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static double _F2;
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static double _G2;
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static double _F3;
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static double _G3;
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static double _F4;
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static double _G4;
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static inline int _fastfloor(double x) {
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int xi = trunc_to_int(x);
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return x < xi ? xi - 1 : xi;
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}
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static inline double _dot2(Grad3 g, double x, double y) {
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return g.x * x + g.y * y;
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}
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static inline double _dot3(Grad3 g, double x, double y, double z) {
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return g.x * x + g.y * y + g.z * z;
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}
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static inline double _dot4(Grad4 g, double x, double y, double z, double w) {
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return g.x * x + g.y * y + g.z * z + g.w * w;
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}
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static int noiseSimplexInit() {
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int i;
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/* To remove the need for index wrapping, double the permutation table length */
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for (i = 0; i < 512; i++) {
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_permutations2[i] = _permutations[i & 255];
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_permutationsMod12[i] = (short)(_permutations2[i] % 12);
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}
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/* Skewing and unskewing factors for 2, 3, and 4 dimensions */
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_F2 = 0.5 * (sqrt(3.0) - 1.0);
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_G2 = (3.0 - sqrt(3.0)) / 6.0;
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_F3 = 1.0 / 3.0;
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_G3 = 1.0 / 6.0;
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_F4 = (sqrt(5.0) - 1.0) / 4.0;
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_G4 = (5.0 - sqrt(5.0)) / 20.0;
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return 1;
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}
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static int _inited = noiseSimplexInit();
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double noiseSimplexGet1DValue(double x) {
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/* TODO Find custom function */
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return noiseSimplexGet2DValue(x, 0.0);
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}
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double noiseSimplexGet2DValue(double x, double y) {
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// FIXME duplicated
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double n0, n1, n2; /* Noise contributions from the three corners */
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/* Skew the input space to determine which simplex cell we're in */
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double s = (x + y) * _F2; /* Hairy factor for 2D */
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int i = _fastfloor(x + s);
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int j = _fastfloor(y + s);
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double t = (i + j) * _G2;
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double X0 = i - t; /* Unskew the cell origin back to (x,y) space */
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double Y0 = j - t;
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double x0 = x - X0; /* The x,y distances from the cell origin */
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double y0 = y - Y0;
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/* For the 2D case, the simplex shape is an equilateral triangle.
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Determine which simplex we are in. */
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int i1, j1; /* Offsets for second (middle) corner of simplex in (i,j) coords */
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if (x0 > y0) {
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i1 = 1;
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j1 = 0;
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} /* lower triangle, XY order: (0,0)->(1,0)->(1,1) */
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else {
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i1 = 0;
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j1 = 1;
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} /* upper triangle, YX order: (0,0)->(0,1)->(1,1) */
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/* A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
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a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
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c = (3-sqrt(3))/6 */
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double x1 = x0 - i1 + _G2; /* Offsets for middle corner in (x,y) unskewed coords */
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double y1 = y0 - j1 + _G2;
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double x2 = x0 - 1.0 + 2.0 * _G2; /* Offsets for last corner in (x,y) unskewed coords */
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double y2 = y0 - 1.0 + 2.0 * _G2;
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/* Work out the hashed gradient indices of the three simplex corners */
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int ii = i & 255;
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int jj = j & 255;
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int gi0 = _permutationsMod12[ii + _permutations2[jj]];
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int gi1 = _permutationsMod12[ii + i1 + _permutations2[jj + j1]];
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int gi2 = _permutationsMod12[ii + 1 + _permutations2[jj + 1]];
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/* Calculate the contribution from the three corners */
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double t0 = 0.5 - x0 * x0 - y0 * y0;
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if (t0 < 0)
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n0 = 0.0;
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else {
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t0 *= t0;
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n0 = t0 * t0 * _dot2(_grad3[gi0], x0, y0); /* (x,y) of _grad3 used for 2D gradient */
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}
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double t1 = 0.5 - x1 * x1 - y1 * y1;
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if (t1 < 0)
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n1 = 0.0;
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else {
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t1 *= t1;
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n1 = t1 * t1 * _dot2(_grad3[gi1], x1, y1);
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}
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double t2 = 0.5 - x2 * x2 - y2 * y2;
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if (t2 < 0)
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n2 = 0.0;
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else {
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t2 *= t2;
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n2 = t2 * t2 * _dot2(_grad3[gi2], x2, y2);
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}
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/* Add contributions from each corner to get the final noise value.
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The result is scaled to return values in the interval [-0.5,0.5]. */
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return 35.0 * (n0 + n1 + n2) + 0.5;
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}
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double noiseSimplexGet3DValue(double x, double y, double z) {
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// FIXME duplicated
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double n0, n1, n2, n3; /* Noise contributions from the four corners */
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/* Skew the input space to determine which simplex cell we're in */
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double s = (x + y + z) * _F3; /* Very nice and simple skew factor for 3D */
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int i = _fastfloor(x + s);
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int j = _fastfloor(y + s);
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int k = _fastfloor(z + s);
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double t = (i + j + k) * _G3;
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double X0 = i - t; /* Unskew the cell origin back to (x,y,z) space */
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double Y0 = j - t;
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double Z0 = k - t;
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double x0 = x - X0; /* The x,y,z distances from the cell origin */
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double y0 = y - Y0;
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double z0 = z - Z0;
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/* For the 3D case, the simplex shape is a slightly irregular tetrahedron.
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Determine which simplex we are in. */
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int i1, j1, k1; /* Offsets for second corner of simplex in (i,j,k) coords */
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int i2, j2, k2; /* Offsets for third corner of simplex in (i,j,k) coords */
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if (x0 >= y0) {
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if (y0 >= z0) {
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i1 = 1;
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j1 = 0;
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k1 = 0;
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i2 = 1;
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j2 = 1;
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k2 = 0;
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} /* X Y Z order */
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else if (x0 >= z0) {
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i1 = 1;
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j1 = 0;
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k1 = 0;
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i2 = 1;
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j2 = 0;
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k2 = 1;
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} /* X Z Y order */
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else {
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i1 = 0;
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j1 = 0;
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k1 = 1;
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i2 = 1;
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j2 = 0;
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k2 = 1;
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} /* Z X Y order */
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} else { /* x0<y0 */
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if (y0 < z0) {
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i1 = 0;
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j1 = 0;
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k1 = 1;
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i2 = 0;
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j2 = 1;
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k2 = 1;
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} /* Z Y X order */
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else if (x0 < z0) {
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i1 = 0;
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j1 = 1;
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k1 = 0;
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i2 = 0;
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j2 = 1;
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k2 = 1;
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} /* Y Z X order */
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else {
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i1 = 0;
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j1 = 1;
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k1 = 0;
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i2 = 1;
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j2 = 1;
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k2 = 0;
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} /* Y X Z order */
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}
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/* A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
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a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
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a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
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c = 1/6. */
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double x1 = x0 - i1 + _G3; /* Offsets for second corner in (x,y,z) coords */
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double y1 = y0 - j1 + _G3;
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double z1 = z0 - k1 + _G3;
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double x2 = x0 - i2 + 2.0 * _G3; /* Offsets for third corner in (x,y,z) coords */
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double y2 = y0 - j2 + 2.0 * _G3;
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double z2 = z0 - k2 + 2.0 * _G3;
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double x3 = x0 - 1.0 + 3.0 * _G3; /* Offsets for last corner in (x,y,z) coords */
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double y3 = y0 - 1.0 + 3.0 * _G3;
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double z3 = z0 - 1.0 + 3.0 * _G3;
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/* Work out the hashed gradient indices of the four simplex corners */
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int ii = i & 255;
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int jj = j & 255;
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int kk = k & 255;
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int gi0 = _permutationsMod12[ii + _permutations2[jj + _permutations2[kk]]];
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int gi1 = _permutationsMod12[ii + i1 + _permutations2[jj + j1 + _permutations2[kk + k1]]];
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int gi2 = _permutationsMod12[ii + i2 + _permutations2[jj + j2 + _permutations2[kk + k2]]];
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int gi3 = _permutationsMod12[ii + 1 + _permutations2[jj + 1 + _permutations2[kk + 1]]];
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/* Calculate the contribution from the four corners */
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double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
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if (t0 < 0)
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n0 = 0.0;
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else {
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t0 *= t0;
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n0 = t0 * t0 * _dot3(_grad3[gi0], x0, y0, z0);
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}
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double t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
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if (t1 < 0)
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n1 = 0.0;
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else {
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t1 *= t1;
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n1 = t1 * t1 * _dot3(_grad3[gi1], x1, y1, z1);
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}
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double t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
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if (t2 < 0)
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n2 = 0.0;
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else {
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t2 *= t2;
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n2 = t2 * t2 * _dot3(_grad3[gi2], x2, y2, z2);
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}
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double t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
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if (t3 < 0)
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n3 = 0.0;
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else {
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t3 *= t3;
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n3 = t3 * t3 * _dot3(_grad3[gi3], x3, y3, z3);
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}
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/* Add contributions from each corner to get the final noise value.
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The result is scaled to stay just inside [-0.5,0.5] */
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return 16.0 * (n0 + n1 + n2 + n3) + 0.5;
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}
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double noiseSimplexGet4DValue(double x, double y, double z, double w) {
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double n0, n1, n2, n3, n4; /* Noise contributions from the five corners */
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/* Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in */
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double s = (x + y + z + w) * _F4; /* Factor for 4D skewing */
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int i = _fastfloor(x + s);
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int j = _fastfloor(y + s);
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int k = _fastfloor(z + s);
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int l = _fastfloor(w + s);
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double t = (i + j + k + l) * _G4; /* Factor for 4D unskewing */
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double X0 = i - t; /* Unskew the cell origin back to (x,y,z,w) space */
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double Y0 = j - t;
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double Z0 = k - t;
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double W0 = l - t;
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double x0 = x - X0; /* The x,y,z,w distances from the cell origin */
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double y0 = y - Y0;
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double z0 = z - Z0;
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double w0 = w - W0;
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/* For the 4D case, the simplex is a 4D shape I won't even try to describe.
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To find out which of the 24 possible simplices we're in, we need to
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determine the magnitude ordering of x0, y0, z0 and w0.
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Six pair-wise comparisons are performed between each possible pair
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of the four coordinates, and the results are used to rank the numbers. */
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int rankx = 0;
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int ranky = 0;
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int rankz = 0;
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int rankw = 0;
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if (x0 > y0)
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rankx++;
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else
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ranky++;
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if (x0 > z0)
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rankx++;
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else
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rankz++;
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if (x0 > w0)
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rankx++;
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else
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rankw++;
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if (y0 > z0)
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ranky++;
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else
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rankz++;
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if (y0 > w0)
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ranky++;
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else
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rankw++;
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if (z0 > w0)
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rankz++;
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else
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rankw++;
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int i1, j1, k1, l1; /* The integer offsets for the second simplex corner */
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int i2, j2, k2, l2; /* The integer offsets for the third simplex corner */
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int i3, j3, k3, l3; /* The integer offsets for the fourth simplex corner */
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/* simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
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Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
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impossible. Only the 24 indices which have non-zero entries make any sense.
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We use a thresholding to set the coordinates in turn from the largest magnitude.
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Rank 3 denotes the largest coordinate. */
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i1 = rankx >= 3 ? 1 : 0;
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j1 = ranky >= 3 ? 1 : 0;
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k1 = rankz >= 3 ? 1 : 0;
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l1 = rankw >= 3 ? 1 : 0;
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/* Rank 2 denotes the second largest coordinate. */
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i2 = rankx >= 2 ? 1 : 0;
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j2 = ranky >= 2 ? 1 : 0;
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k2 = rankz >= 2 ? 1 : 0;
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l2 = rankw >= 2 ? 1 : 0;
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/* Rank 1 denotes the second smallest coordinate. */
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i3 = rankx >= 1 ? 1 : 0;
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j3 = ranky >= 1 ? 1 : 0;
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k3 = rankz >= 1 ? 1 : 0;
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l3 = rankw >= 1 ? 1 : 0;
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/* The fifth corner has all coordinate offsets = 1, so no need to compute that. */
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double x1 = x0 - i1 + _G4; /* Offsets for second corner in (x,y,z,w) coords */
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double y1 = y0 - j1 + _G4;
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double z1 = z0 - k1 + _G4;
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double w1 = w0 - l1 + _G4;
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double x2 = x0 - i2 + 2.0 * _G4; /* Offsets for third corner in (x,y,z,w) coords */
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double y2 = y0 - j2 + 2.0 * _G4;
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double z2 = z0 - k2 + 2.0 * _G4;
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double w2 = w0 - l2 + 2.0 * _G4;
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double x3 = x0 - i3 + 3.0 * _G4; /* Offsets for fourth corner in (x,y,z,w) coords */
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double y3 = y0 - j3 + 3.0 * _G4;
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double z3 = z0 - k3 + 3.0 * _G4;
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double w3 = w0 - l3 + 3.0 * _G4;
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double x4 = x0 - 1.0 + 4.0 * _G4; /* Offsets for last corner in (x,y,z,w) coords */
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double y4 = y0 - 1.0 + 4.0 * _G4;
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double z4 = z0 - 1.0 + 4.0 * _G4;
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double w4 = w0 - 1.0 + 4.0 * _G4;
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/* Work out the hashed gradient indices of the five simplex corners */
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int ii = i & 255;
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int jj = j & 255;
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int kk = k & 255;
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int ll = l & 255;
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int gi0 = _permutations2[ii + _permutations2[jj + _permutations2[kk + _permutations2[ll]]]] % 32;
|
|
int gi1 =
|
|
_permutations2[ii + i1 + _permutations2[jj + j1 + _permutations2[kk + k1 + _permutations2[ll + l1]]]] % 32;
|
|
int gi2 =
|
|
_permutations2[ii + i2 + _permutations2[jj + j2 + _permutations2[kk + k2 + _permutations2[ll + l2]]]] % 32;
|
|
int gi3 =
|
|
_permutations2[ii + i3 + _permutations2[jj + j3 + _permutations2[kk + k3 + _permutations2[ll + l3]]]] % 32;
|
|
int gi4 = _permutations2[ii + 1 + _permutations2[jj + 1 + _permutations2[kk + 1 + _permutations2[ll + 1]]]] % 32;
|
|
/* Calculate the contribution from the five corners */
|
|
double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
|
|
if (t0 < 0)
|
|
n0 = 0.0;
|
|
else {
|
|
t0 *= t0;
|
|
n0 = t0 * t0 * _dot4(_grad4[gi0], x0, y0, z0, w0);
|
|
}
|
|
double t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
|
|
if (t1 < 0)
|
|
n1 = 0.0;
|
|
else {
|
|
t1 *= t1;
|
|
n1 = t1 * t1 * _dot4(_grad4[gi1], x1, y1, z1, w1);
|
|
}
|
|
double t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
|
|
if (t2 < 0)
|
|
n2 = 0.0;
|
|
else {
|
|
t2 *= t2;
|
|
n2 = t2 * t2 * _dot4(_grad4[gi2], x2, y2, z2, w2);
|
|
}
|
|
double t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
|
|
if (t3 < 0)
|
|
n3 = 0.0;
|
|
else {
|
|
t3 *= t3;
|
|
n3 = t3 * t3 * _dot4(_grad4[gi3], x3, y3, z3, w3);
|
|
}
|
|
double t4 = 0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
|
|
if (t4 < 0)
|
|
n4 = 0.0;
|
|
else {
|
|
t4 *= t4;
|
|
n4 = t4 * t4 * _dot4(_grad4[gi4], x4, y4, z4, w4);
|
|
}
|
|
/* Sum up and scale the result to cover the range [-0.5,0.5] */
|
|
return 13.5 * (n0 + n1 + n2 + n3 + n4) + 0.5;
|
|
}
|
|
|
|
double NoiseFunctionSimplex::getBase2d(double x, double y) const {
|
|
double n0, n1, n2; /* Noise contributions from the three corners */
|
|
/* Skew the input space to determine which simplex cell we're in */
|
|
double s = (x + y) * _F2; /* Hairy factor for 2D */
|
|
int i = _fastfloor(x + s);
|
|
int j = _fastfloor(y + s);
|
|
double t = (i + j) * _G2;
|
|
double X0 = i - t; /* Unskew the cell origin back to (x,y) space */
|
|
double Y0 = j - t;
|
|
double x0 = x - X0; /* The x,y distances from the cell origin */
|
|
double y0 = y - Y0;
|
|
/* 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 */
|
|
double x1 = x0 - i1 + _G2; /* Offsets for middle corner in (x,y) unskewed coords */
|
|
double y1 = y0 - j1 + _G2;
|
|
double x2 = x0 - 1.0 + 2.0 * _G2; /* Offsets for last corner in (x,y) unskewed coords */
|
|
double y2 = y0 - 1.0 + 2.0 * _G2;
|
|
/* Work out the hashed gradient indices of the three simplex corners */
|
|
int ii = i & 255;
|
|
int jj = j & 255;
|
|
int gi0 = _permutationsMod12[ii + _permutations2[jj]];
|
|
int gi1 = _permutationsMod12[ii + i1 + _permutations2[jj + j1]];
|
|
int gi2 = _permutationsMod12[ii + 1 + _permutations2[jj + 1]];
|
|
/* Calculate the contribution from the three corners */
|
|
double t0 = 0.5 - x0 * x0 - y0 * y0;
|
|
if (t0 < 0)
|
|
n0 = 0.0;
|
|
else {
|
|
t0 *= t0;
|
|
n0 = t0 * t0 * _dot2(_grad3[gi0], x0, y0); /* (x,y) of _grad3 used for 2D gradient */
|
|
}
|
|
double t1 = 0.5 - x1 * x1 - y1 * y1;
|
|
if (t1 < 0)
|
|
n1 = 0.0;
|
|
else {
|
|
t1 *= t1;
|
|
n1 = t1 * t1 * _dot2(_grad3[gi1], x1, y1);
|
|
}
|
|
double t2 = 0.5 - x2 * x2 - y2 * y2;
|
|
if (t2 < 0)
|
|
n2 = 0.0;
|
|
else {
|
|
t2 *= t2;
|
|
n2 = t2 * t2 * _dot2(_grad3[gi2], x2, y2);
|
|
}
|
|
/* Add contributions from each corner to get the final noise value.
|
|
The result is scaled to return values in the interval [-0.5,0.5]. */
|
|
return 35.0 * (n0 + n1 + n2);
|
|
}
|
|
|
|
double NoiseFunctionSimplex::getBase3d(double x, double y, double z) const {
|
|
double n0, n1, n2, n3; /* Noise contributions from the four corners */
|
|
/* Skew the input space to determine which simplex cell we're in */
|
|
double s = (x + y + z) * _F3; /* Very nice and simple skew factor for 3D */
|
|
int i = _fastfloor(x + s);
|
|
int j = _fastfloor(y + s);
|
|
int k = _fastfloor(z + s);
|
|
double t = (i + j + k) * _G3;
|
|
double X0 = i - t; /* Unskew the cell origin back to (x,y,z) space */
|
|
double Y0 = j - t;
|
|
double Z0 = k - t;
|
|
double x0 = x - X0; /* The x,y,z distances from the cell origin */
|
|
double y0 = y - Y0;
|
|
double z0 = z - Z0;
|
|
/* 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 */
|
|
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. */
|
|
double x1 = x0 - i1 + _G3; /* Offsets for second corner in (x,y,z) coords */
|
|
double y1 = y0 - j1 + _G3;
|
|
double z1 = z0 - k1 + _G3;
|
|
double x2 = x0 - i2 + 2.0 * _G3; /* Offsets for third corner in (x,y,z) coords */
|
|
double y2 = y0 - j2 + 2.0 * _G3;
|
|
double z2 = z0 - k2 + 2.0 * _G3;
|
|
double x3 = x0 - 1.0 + 3.0 * _G3; /* Offsets for last corner in (x,y,z) coords */
|
|
double y3 = y0 - 1.0 + 3.0 * _G3;
|
|
double z3 = z0 - 1.0 + 3.0 * _G3;
|
|
/* Work out the hashed gradient indices of the four simplex corners */
|
|
int ii = i & 255;
|
|
int jj = j & 255;
|
|
int kk = k & 255;
|
|
int gi0 = _permutationsMod12[ii + _permutations2[jj + _permutations2[kk]]];
|
|
int gi1 = _permutationsMod12[ii + i1 + _permutations2[jj + j1 + _permutations2[kk + k1]]];
|
|
int gi2 = _permutationsMod12[ii + i2 + _permutations2[jj + j2 + _permutations2[kk + k2]]];
|
|
int gi3 = _permutationsMod12[ii + 1 + _permutations2[jj + 1 + _permutations2[kk + 1]]];
|
|
/* Calculate the contribution from the four corners */
|
|
double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
|
|
if (t0 < 0)
|
|
n0 = 0.0;
|
|
else {
|
|
t0 *= t0;
|
|
n0 = t0 * t0 * _dot3(_grad3[gi0], x0, y0, z0);
|
|
}
|
|
double t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
|
|
if (t1 < 0)
|
|
n1 = 0.0;
|
|
else {
|
|
t1 *= t1;
|
|
n1 = t1 * t1 * _dot3(_grad3[gi1], x1, y1, z1);
|
|
}
|
|
double t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
|
|
if (t2 < 0)
|
|
n2 = 0.0;
|
|
else {
|
|
t2 *= t2;
|
|
n2 = t2 * t2 * _dot3(_grad3[gi2], x2, y2, z2);
|
|
}
|
|
double t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
|
|
if (t3 < 0)
|
|
n3 = 0.0;
|
|
else {
|
|
t3 *= t3;
|
|
n3 = t3 * t3 * _dot3(_grad3[gi3], x3, y3, z3);
|
|
}
|
|
/* Add contributions from each corner to get the final noise value.
|
|
The result is scaled to stay just inside [-0.5,0.5] */
|
|
return 16.0 * (n0 + n1 + n2 + n3);
|
|
}
|
|
|
|
static constexpr double TEXTURE_SCALING = 15.0;
|
|
static Texture2D *_valueTexture = NULL;
|
|
|
|
const Texture2D *NoiseFunctionSimplex::getValueTexture() {
|
|
if (!_valueTexture) {
|
|
const int width = 2048;
|
|
const int height = 2048;
|
|
|
|
_valueTexture = new Texture2D(width, height);
|
|
|
|
for (int x = 0; x < width; x++) {
|
|
for (int z = 0; z < height; z++) {
|
|
// TODO Make texture tileable
|
|
double dx = to_double(x) / to_double(width);
|
|
double dz = to_double(z) / to_double(height);
|
|
double val = noiseSimplexGet2DValue(TEXTURE_SCALING * dx, TEXTURE_SCALING * dz);
|
|
_valueTexture->setPixel(x, z, Color(val, val, val));
|
|
}
|
|
}
|
|
}
|
|
|
|
return _valueTexture;
|
|
}
|
|
|
|
static Texture2D *_normalTexture = NULL;
|
|
|
|
const Texture2D *NoiseFunctionSimplex::getNormalTexture() {
|
|
if (!_normalTexture) {
|
|
const int width = 2048;
|
|
const int height = 2048;
|
|
|
|
_normalTexture = new Texture2D(width, height);
|
|
|
|
double scale = TEXTURE_SCALING;
|
|
double offset = scale * 0.1;
|
|
|
|
for (int x = 0; x < width; x++) {
|
|
for (int z = 0; z < height; z++) {
|
|
// TODO Make texture tileable
|
|
double dx = to_double(x) / to_double(width);
|
|
double dz = to_double(z) / to_double(height);
|
|
double vcenter = noiseSimplexGet2DValue(scale * dx, scale * dz);
|
|
double vsouth = noiseSimplexGet2DValue(scale * dx, scale * dz + offset);
|
|
double veast = noiseSimplexGet2DValue(scale * dx + offset, scale * dz);
|
|
|
|
Vector3 normal = Geometry::getNormalFromTriangle(
|
|
Vector3(0.0, vcenter, 0.0), Vector3(0.0, vsouth, offset), Vector3(offset, veast, 0.0));
|
|
|
|
_normalTexture->setPixel(x, z, Color(normal.x * 0.5 + 0.5, normal.y * 0.5 + 0.5, normal.z * 0.5 + 0.5));
|
|
}
|
|
}
|
|
}
|
|
|
|
return _normalTexture;
|
|
}
|