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Aperiodic Improved Perlin Noise Example
//
// Aperiodic Improved Perlin Noise
// James Bird (jbrd.github.io)
//
// A version of Ken Perlin's Improved Perlin Noise, rewritten in C++ and
// expanded to use a higher precision (but more expensive) initial hashing
// function to overcome the 256-unit repetition in the reference code.
//
// Adapted from Ken Perlin's Improved Perlin Noise Code:
// http://mrl.nyu.edu/~perlin/noise/
//
#include <cmath>
namespace {
const int* build_permutation_table() {
static int p[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
};
for (int i=0; i < 256; i++) p[256+i] = p[i];
return p;
}
const int* p = build_permutation_table();
int initial_hash(int value) { // PEARSON HASHING FUNCTION
int result = 0;
for (int i = 0; i < sizeof(value); ++i, value >>= 8) {
result = p[result ^ (value & 0xff)];
}
return result;
}
double fade(double t) {
return t * t * t * (t * (t * 6 - 15) + 10);
}
double lerp(double t, double a, double b) {
return a + t * (b - a);
}
double grad(int hash, double x, double y, double z) {
int h = hash & 15; // CONVERT LO 4 BITS OF HASH CODE
double u = h<8 ? x : y, // INTO 12 GRADIENT DIRECTIONS.
v = h<4 ? y : h==12||h==14 ? x : z;
return ((h&1) == 0 ? u : -u) + ((h&2) == 0 ? v : -v);
}
}
double aperiodic_noise(double x, double y, double z) {
double FX = floor(x),
FY = floor(y),
FZ = floor(z);
int X = initial_hash((int)FX), // FIND UNIT CUBE THAT
Y = initial_hash((int)FY), // CONTAINS POINT.
Z = initial_hash((int)FZ);
int XX = initial_hash((int)FX+1), // FIND UNIT CUBE ADJACENT
YY = initial_hash((int)FY+1), // TO THIS POINT.
ZZ = initial_hash((int)FZ+1);
x -= FX; // FIND RELATIVE X,Y,Z
y -= FY; // OF POINT IN CUBE.
z -= FZ;
double u = fade(x), // COMPUTE FADE CURVES
v = fade(y), // FOR EACH OF X,Y,Z.
w = fade(z);
int A = p[X ], AA = p[A+Y], AB = p[A+YY], // HASH COORDINATES OF
B = p[XX], BA = p[B+Y], BB = p[B+YY]; // THE 8 CUBE CORNERS,
return lerp(w, lerp(v, lerp(u, grad(p[AA+Z ], x , y , z ), // AND ADD
grad(p[BA+Z ], x-1, y , z )), // BLENDED
lerp(u, grad(p[AB+Z ], x , y-1, z ), // RESULTS
grad(p[BB+Z ], x-1, y-1, z ))),// FROM 8
lerp(v, lerp(u, grad(p[AA+ZZ], x , y , z-1 ), // CORNERS
grad(p[BA+ZZ], x-1, y , z-1 )), // OF CUBE
lerp(u, grad(p[AB+ZZ], x , y-1, z-1 ),
grad(p[BB+ZZ], x-1, y-1, z-1 ))));
}
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