/* Simplex.cpp
 *
 * Copyright 2007 Eliot Eshelman
 * battlestartux@6by9.net
 *
 *
 *  This file is part of Battlestar Tux.
 *
 *  Battlestar Tux is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; version 2 of the License.
 *
 *  Battlestar Tux 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.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with Battlestar Tux; if not, write to the Free Software
 *  Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
 *
 */


#include <math.h>

#include "Simplex.h"


// 2D Multi-octave Simplex noise.
//
// For each octave, a higher frequency/lower amplitude function will be added to the original.
// The higher the persistence [0-1], the more of each succeeding octave will be added.
double noise_simplex( const double octaves, const double persistence, const double scale, const double x, const double y ) {
	double total = 0;
	double frequency = scale;
	double amplitude = 1;

	// We have to keep track of the largest possible amplitude,
	// because each octave adds more, and we need a value in [-1, 1].
	double maxAmplitude = 0;

	for( int i=0; i < octaves; i++ ) {
		total += noise_simplex_raw( x * frequency, y * frequency ) * amplitude;

		frequency *= 2;
		maxAmplitude += amplitude;
		amplitude *= persistence;
	}

	return total / maxAmplitude;
}


// 3D Multi-octave Simplex noise.
//
// For each octave, a higher frequency/lower amplitude function will be added to the original.
// The higher the persistence [0-1], the more of each succeeding octave will be added.
double noise_simplex( const double octaves, const double persistence, const double scale, const double x, const double y, const double z ) {
	double total = 0;
	double frequency = scale;
	double amplitude = 1;

	// We have to keep track of the largest possible amplitude,
	// because each octave adds more, and we need a value in [-1, 1].
	double maxAmplitude = 0;

	for( int i=0; i < octaves; i++ ) {
		total += noise_simplex_raw( x * frequency, y * frequency, z * frequency ) * amplitude;

		frequency *= 2;
		maxAmplitude += amplitude;
		amplitude *= persistence;
	}

	return total / maxAmplitude;
}


// 4D Multi-octave Simplex noise.
//
// For each octave, a higher frequency/lower amplitude function will be added to the original.
// The higher the persistence [0-1], the more of each succeeding octave will be added.
double noise_simplex( const double octaves, const double persistence, const double scale, const double x, const double y, const double z, const double w ) {
	double total = 0;
	double frequency = scale;
	double amplitude = 1;

	// We have to keep track of the largest possible amplitude,
	// because each octave adds more, and we need a value in [-1, 1].
	double maxAmplitude = 0;

	for( int i=0; i < octaves; i++ ) {
		total += noise_simplex_raw( x * frequency, y * frequency, z * frequency, w * frequency ) * amplitude;

		frequency *= 2;
		maxAmplitude += amplitude;
		amplitude *= persistence;
	}

	return total / maxAmplitude;
}



// 2D Scaled Multi-octave Simplex noise.
//
// Returned value will be between loBound and hiBound.
double noise_simplex_scaled( const double octaves, const double persistence, const double scale, const double loBound, const double hiBound, const double x, const double y ) {
	return noise_simplex(octaves, persistence, scale, x, y) * (hiBound - loBound) / 2 + (hiBound + loBound) / 2;
}


// 3D Scaled Multi-octave Simplex noise.
//
// Returned value will be between loBound and hiBound.
double noise_simplex_scaled( const double octaves, const double persistence, const double scale, const double loBound, const double hiBound, const double x, const double y, const double z ) {
	return noise_simplex(octaves, persistence, scale, x, y, z) * (hiBound - loBound) / 2 + (hiBound + loBound) / 2;
}

// 4D Scaled Multi-octave Simplex noise.
//
// Returned value will be between loBound and hiBound.
double noise_simplex_scaled( const double octaves, const double persistence, const double scale, const double loBound, const double hiBound, const double x, const double y, const double z, const double w ) {
	return noise_simplex(octaves, persistence, scale, x, y, z, w) * (hiBound - loBound) / 2 + (hiBound + loBound) / 2;
}



// 2D Scaled Simplex raw noise.
//
// Returned value will be between loBound and hiBound.
double noise_simplex_raw_scaled( const double loBound, const double hiBound, const double x, const double y ) {
	return noise_simplex_raw(x, y) * (hiBound - loBound) / 2 + (hiBound + loBound) / 2;
}


// 3D Scaled Simplex raw noise.
//
// Returned value will be between loBound and hiBound.
double noise_simplex_raw_scaled( const double loBound, const double hiBound, const double x, const double y, const double z ) {
	return noise_simplex_raw(x, y, z) * (hiBound - loBound) / 2 + (hiBound + loBound) / 2;
}

// 4D Scaled Simplex raw noise.
//
// Returned value will be between loBound and hiBound.
double noise_simplex_raw_scaled( const double loBound, const double hiBound, const double x, const double y, const double z, const double w ) {
	return noise_simplex_raw(x, y, z, w) * (hiBound - loBound) / 2 + (hiBound + loBound) / 2;
}



// 2D raw Simplex noise
double noise_simplex_raw( const double x, const double y ) {
	// Noise contributions from the three corners
	double n0, n1, n2;

	// Skew the input space to determine which simplex cell we're in
	double F2 = 0.5 * (sqrt(3.0) - 1.0);
	// Hairy factor for 2D
	double s = (x + y) * F2;
	int i = fastfloor( x + s );
	int j = fastfloor( y + s );

	double G2 = (3.0 - sqrt(3.0)) / 6.0;
	double t = (i + j) * G2;
	// Unskew the cell origin back to (x,y) space
	double X0 = i-t;
	double Y0 = j-t;
	// The x,y distances from the cell origin
	double x0 = x-X0;
	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 = perm[ii+perm[jj]] % 12;
	int gi1 = perm[ii+i1+perm[jj+j1]] % 12;
	int gi2 = perm[ii+1+perm[jj+1]] % 12;

	// 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 * dot(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 * dot(grad3[gi1], x1, y1);
	}

	double t2 = 0.5 - x2*x2-y2*y2;
	if(t2<0) n2 = 0.0;
	else {
	t2 *= t2;
	n2 = t2 * t2 * dot(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 [-1,1].
	return 70.0 * (n0 + n1 + n2);
}


// 3D raw Simplex noise
double noise_simplex_raw( const double x, const double y, const double z ) {
	double n0, n1, n2, n3; // Noise contributions from the four corners

	// Skew the input space to determine which simplex cell we're in
	double F3 = 1.0/3.0;
	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 G3 = 1.0/6.0; // Very nice and simple unskew factor, too
	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 = perm[ii+perm[jj+perm[kk]]] % 12;
	int gi1 = perm[ii+i1+perm[jj+j1+perm[kk+k1]]] % 12;
	int gi2 = perm[ii+i2+perm[jj+j2+perm[kk+k2]]] % 12;
	int gi3 = perm[ii+1+perm[jj+1+perm[kk+1]]] % 12;

	// 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 * dot(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 * dot(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 * dot(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 * dot(grad3[gi3], 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 32.0*(n0 + n1 + n2 + n3);
}


// 4D raw Simplex noise
double noise_simplex_raw( const double x, const double y, const double z, const double w ) {
	// The skewing and unskewing factors are hairy again for the 4D case
	double F4 = (sqrt(5.0)-1.0)/4.0;
	double G4 = (5.0-sqrt(5.0))/20.0;
	double 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
	double s = (x + y + z + w) * F4; // Factor for 4D skewing
	int i = fastfloor(x + s);
	int j = fastfloor(y + s);
	int k = fastfloor(z + s);
	int l = fastfloor(w + s);
	double t = (i + j + k + l) * G4; // Factor for 4D unskewing
	double X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
	double Y0 = j - t;
	double Z0 = k - t;
	double W0 = l - t;

	double x0 = x - X0; // The x,y,z,w distances from the cell origin
	double y0 = y - Y0;
	double z0 = z - Z0;
	double 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.

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

	// Work out the hashed gradient indices of the five simplex corners
	int ii = i & 255;
	int jj = j & 255;
	int kk = k & 255;
	int ll = l & 255;
	int gi0 = perm[ii+perm[jj+perm[kk+perm[ll]]]] % 32;
	int gi1 = perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]] % 32;
	int gi2 = perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]] % 32;
	int gi3 = perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]] % 32;
	int gi4 = perm[ii+1+perm[jj+1+perm[kk+1+perm[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 * dot(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 * dot(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 * dot(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 * dot(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 * dot(grad4[gi4], x4, y4, z4, w4);
	}

	// Sum up and scale the result to cover the range [-1,1]
	return 27.0 * (n0 + n1 + n2 + n3 + n4);
}


int fastfloor( const double x ) { return x > 0 ? (int) x : (int) x - 1; }

double dot( const int* g, const double x, const double y ) { return g[0]*x + g[1]*y; }
double dot( const int* g, const double x, const double y, const double z ) { return g[0]*x + g[1]*y + g[2]*z; }
double dot( const int* g, const double x, const double y, const double z, const double w ) { return g[0]*x + g[1]*y + g[2]*z + g[3]*w; }