Aperiodic Improved Perlin Noise Example

aperiodic-improved-perlin-noise.cpp

//
// 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 ))));
}