text: #include "PerlinNoise.h"
  #include <cmath>
  #include <random>
  #include <algorithm>
  #include <numeric>
  
  // THIS IS A DIRECT TRANSLATION TO C++11 FROM THE REFERENCE
  // JAVA IMPLEMENTATION OF THE IMPROVED PERLIN FUNCTION (see http://mrl.nyu.edu/~perlin/noise/)
  // THE ORIGINAL JAVA IMPLEMENTATION IS COPYRIGHT 2002 KEN PERLIN
  
  // I ADDED AN EXTRA METHOD THAT GENERATES A NEW PERMUTATION VECTOR (THIS IS NOT PRESENT IN THE ORIGINAL IMPLEMENTATION)
  
  // Initialize with the reference values for the permutation vector
  PerlinNoise::PerlinNoise() {
  	
  	// Initialize the permutation vector with the reference values
  	p = {
  		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 };
      // Duplicate the permutation vector
  	p.insert(p.end(), p.begin(), p.end());
  }
  
  // Generate a new permutation vector based on the value of seed
  PerlinNoise::PerlinNoise(unsigned int seed) {
  	p.resize(256);
  
  	// Fill p with values from 0 to 255
  	std::iota(p.begin(), p.end(), 0);
  
  	// Initialize a random engine with seed
  	std::default_random_engine engine(seed);
  
  	// Suffle  using the above random engine
  	std::shuffle(p.begin(), p.end(), engine);
  
  	// Duplicate the permutation vector
  	p.insert(p.end(), p.begin(), p.end());
  }
  
  double PerlinNoise::noise(double x, double y, double z) {
  	// Find the unit cube that contains the point
  	int X = (int) floor(x) & 255;
  	int Y = (int) floor(y) & 255;
  	int Z = (int) floor(z) & 255;
  
  	// Find relative x, y,z of point in cube
  	x -= floor(x);
  	y -= floor(y);
  	z -= floor(z);
  
  	// Compute fade curves for each of x, y, z
  	double u = fade(x);
  	double v = fade(y);
  	double w = fade(z);
  
  	// Hash coordinates of the 8 cube corners
  	int A = p[X] + Y;
  	int AA = p[A] + Z;
  	int AB = p[A + 1] + Z;
  	int B = p[X + 1] + Y;
  	int BA = p[B] + Z;
  	int BB = p[B + 1] + Z;
  
  	// Add blended results from 8 corners of cube
  	double res = lerp(w, lerp(v, lerp(u, grad(p[AA], x, y, z), grad(p[BA], x-1, y, z)), lerp(u, grad(p[AB], x, y-1, z), grad(p[BB], x-1, y-1, z))),	lerp(v, lerp(u, grad(p[AA+1], x, y, z-1), grad(p[BA+1], x-1, y, z-1)), lerp(u, grad(p[AB+1], x, y-1, z-1),	grad(p[BB+1], x-1, y-1, z-1))));
  	return (res + 1.0)/2.0;
  }
  
  double PerlinNoise::fade(double t) { 
  	return t * t * t * (t * (t * 6 - 15) + 10);
  }
  
  double PerlinNoise::lerp(double t, double a, double b) { 
  	return a + t * (b - a); 
  }
  
  double PerlinNoise::grad(int hash, double x, double y, double z) {
  	int h = hash & 15;
  	// Convert lower 4 bits of hash into 12 gradient directions
  	double u = h < 8 ? x : y,
  		   v = h < 4 ? y : h == 12 || h == 14 ? x : z;
  	return ((h & 1) == 0 ? u : -u) + ((h & 2) == 0 ? v : -v);
  }
  