simplexnoise1234.cpp

// SimplexNoise1234
// Copyright ?2003-2011, Stefan Gustavson
//
// Contact: stegu@itn.liu.se
//
// This library is public domain software, released by the author
// into the public domain in February 2011. You may do anything
// you like with it. You may even remove all attributions,
// but of course I'd appreciate it if you kept my name somewhere.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// General Public License for more details.

/** \file
		\brief Implements the SimplexNoise1234 class for producing Perlin simplex noise.
		\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 is a highly reusable class. It has no dependencies
 * on any other file, apart from its own header file.
 */


#include	"simplexnoise1234.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!
 */
unsigned char SimplexNoise1234::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;
 */

float  SimplexNoise1234::grad( 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
}

float  SimplexNoise1234::grad( 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);
}

float  SimplexNoise1234::grad( 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);
}

float  SimplexNoise1234::grad( 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
float SimplexNoise1234::noise(float x) {

  int i0 = FASTFLOOR(x);
  int i1 = i0 + 1;
  float x0 = x - i0;
  float x1 = x0 - 1.0f;

  float n0, n1;

  float t0 = 1.0f - x0*x0;
//  if(t0 < 0.0f) t0 = 0.0f;
  t0 *= t0;
  n0 = t0 * t0 * grad(perm[i0 & 0xff], x0);

  float t1 = 1.0f - x1*x1;
//  if(t1 < 0.0f) t1 = 0.0f;
  t1 *= t1;
  n1 = t1 * t1 * grad(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
float SimplexNoise1234::noise(float x, float 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;

	// 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

	float x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
	float y1 = y0 - j1 + G2;
	float x2 = x0 - 1.0f + 2.0f * G2; // Offsets for last corner in (x,y) unskewed coords
	float y2 = y0 - 1.0f + 2.0f * G2;

	// Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
	int ii = i & 0xff;
	int jj = j & 0xff;

	// Calculate the contribution from the three corners
	float t0 = 0.5f - x0*x0-y0*y0;
	if(t0 < 0.0f) n0 = 0.0f;
	else {
	  t0 *= t0;
	  n0 = t0 * t0 * grad(perm[ii+perm[jj]], x0, y0); 
	}

	float t1 = 0.5f - x1*x1-y1*y1;
	if(t1 < 0.0f) n1 = 0.0f;
	else {
	  t1 *= t1;
	  n1 = t1 * t1 * grad(perm[ii+i1+perm[jj+j1]], x1, y1);
	}

	float t2 = 0.5f - x2*x2-y2*y2;
	if(t2 < 0.0f) n2 = 0.0f;
	else {
	  t2 *= t2;
	  n2 = t2 * t2 * grad(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
float SimplexNoise1234::noise(float x, float y, float 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;

	// 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

/* 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.

	float x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
	float y1 = y0 - j1 + G3;
	float z1 = z0 - k1 + G3;
	float x2 = x0 - i2 + 2.0f*G3; // Offsets for third corner in (x,y,z) coords
	float y2 = y0 - j2 + 2.0f*G3;
	float z2 = z0 - k2 + 2.0f*G3;
	float x3 = x0 - 1.0f + 3.0f*G3; // Offsets for last corner in (x,y,z) coords
	float y3 = y0 - 1.0f + 3.0f*G3;
	float z3 = z0 - 1.0f + 3.0f*G3;

	// Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
	int ii = i & 0xff;
	int jj = j & 0xff;
	int kk = k & 0xff;

	// Calculate the contribution from the four corners
	float t0 = 0.6f - x0*x0 - y0*y0 - z0*z0;
	if(t0 < 0.0f) n0 = 0.0f;
	else {
	  t0 *= t0;
	  n0 = t0 * t0 * grad(perm[ii+perm[jj+perm[kk]]], x0, y0, z0);
	}

	float t1 = 0.6f - x1*x1 - y1*y1 - z1*z1;
	if(t1 < 0.0f) n1 = 0.0f;
	else {
	  t1 *= t1;
	  n1 = t1 * t1 * grad(perm[ii+i1+perm[jj+j1+perm[kk+k1]]], x1, y1, z1);
	}

	float t2 = 0.6f - x2*x2 - y2*y2 - z2*z2;
	if(t2 < 0.0f) n2 = 0.0f;
	else {
	  t2 *= t2;
	  n2 = t2 * t2 * grad(perm[ii+i2+perm[jj+j2+perm[kk+k2]]], x2, y2, z2);
	}

	float t3 = 0.6f - x3*x3 - y3*y3 - z3*z3;
	if(t3<0.0f) n3 = 0.0f;
	else {
	  t3 *= t3;
	  n3 = t3 * t3 * grad(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
float SimplexNoise1234::noise(float x, float y, float z, float 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;

	int i1, j1, k1, l1; // The integer offsets for the second simplex corner
	int i2, j2, k2, l2; // The integer offsets for the third simplex corner
	int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner

	// 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.

	float x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
	float y1 = y0 - j1 + G4;
	float z1 = z0 - k1 + G4;
	float w1 = w0 - l1 + G4;
	float x2 = x0 - i2 + 2.0f*G4; // Offsets for third corner in (x,y,z,w) coords
	float y2 = y0 - j2 + 2.0f*G4;
	float z2 = z0 - k2 + 2.0f*G4;
	float w2 = w0 - l2 + 2.0f*G4;
	float x3 = x0 - i3 + 3.0f*G4; // Offsets for fourth corner in (x,y,z,w) coords
	float y3 = y0 - j3 + 3.0f*G4;
	float z3 = z0 - k3 + 3.0f*G4;
	float w3 = w0 - l3 + 3.0f*G4;
	float x4 = x0 - 1.0f + 4.0f*G4; // Offsets for last corner in (x,y,z,w) coords
	float y4 = y0 - 1.0f + 4.0f*G4;
	float z4 = z0 - 1.0f + 4.0f*G4;
	float w4 = w0 - 1.0f + 4.0f*G4;

	// Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
	int ii = i & 0xff;
	int jj = j & 0xff;
	int kk = k & 0xff;
	int ll = l & 0xff;

	// Calculate the contribution from the five corners
	float t0 = 0.6f - x0*x0 - y0*y0 - z0*z0 - w0*w0;
	if(t0 < 0.0f) n0 = 0.0f;
	else {
	  t0 *= t0;
	  n0 = t0 * t0 * grad(perm[ii+perm[jj+perm[kk+perm[ll]]]], x0, y0, z0, w0);
	}

   float t1 = 0.6f - x1*x1 - y1*y1 - z1*z1 - w1*w1;
	if(t1 < 0.0f) n1 = 0.0f;
	else {
	  t1 *= t1;
	  n1 = t1 * t1 * grad(perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]], x1, y1, z1, w1);
	}

   float t2 = 0.6f - x2*x2 - y2*y2 - z2*z2 - w2*w2;
	if(t2 < 0.0f) n2 = 0.0f;
	else {
	  t2 *= t2;
	  n2 = t2 * t2 * grad(perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]], x2, y2, z2, w2);
	}

   float t3 = 0.6f - x3*x3 - y3*y3 - z3*z3 - w3*w3;
	if(t3 < 0.0f) n3 = 0.0f;
	else {
	  t3 *= t3;
	  n3 = t3 * t3 * grad(perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]], x3, y3, z3, w3);
	}

   float t4 = 0.6f - x4*x4 - y4*y4 - z4*z4 - w4*w4;
	if(t4 < 0.0f) n4 = 0.0f;
	else {
	  t4 *= t4;
	  n4 = t4 * t4 * grad(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!
  }
//---------------------------------------------------------------------