SimplexGaborNoiseIso.java

/**
 * K.jpg's Simplex-Gabor Noise, isotropic version.
 * Gabor-reminiscent noise, based on OpenSimplex 2, smooth variant ("SuperSimplex")
 *
 * Notes:
 * - Only supports basic (and approximated) sinusoidal kernels.
 * - Not normalized in its current version.
 * - For a slight speed improvement, you may be able to remove
 *   `+ permOffset2[pzi]` and `+ permOffset3[pzi]`, which just
 *   vary the phase offset of the kernels to increase variety.
 */
public class SimplexGaborNoiseIso {
	
	private static final int PSIZE = 2048;
	private static final int PMASK = 2047;

	private short[] perm;
	private Grad2[] permGrad2;
	private Grad3[] permGrad3;
	private double[] permOffset2;
	private double[] permOffset3;

	public SimplexGaborNoiseIso(long seed) {
		perm = new short[PSIZE];
		permGrad2 = new Grad2[PSIZE];
		permGrad3 = new Grad3[PSIZE];
		permOffset2 = new double[PSIZE];
		permOffset3 = new double[PSIZE];
		short[] source = new short[PSIZE]; 
		for (short i = 0; i < PSIZE; i++)
			source[i] = i;
		for (int i = PSIZE - 1; i >= 0; i--) {
			seed = seed * 6364136223846793005L + 1442695040888963407L;
			int r = (int)((seed + 31) % (i + 1));
			if (r < 0)
				r += (i + 1);
			perm[i] = source[r];
			permGrad2[i] = GRADIENTS_2D[perm[i]];
			permGrad3[i] = GRADIENTS_3D[perm[i]];
			permOffset2[i] = OFFSETS_2D[perm[i]];
			permOffset3[i] = OFFSETS_3D[perm[i]];
			source[r] = source[i];
		}
	}
	
	/*
	 * Noise Evaluators
	 */
	
	/**
	 * 2D SuperSimplex noise, standard lattice orientation.
	 */
	public double noise2(double x, double y, double waveFreq) {
		
		// Get points for A2* lattice
		double s = 0.366025403784439 * (x + y);
		double xs = x + s, ys = y + s;
		
		return noise2_Base(xs, ys, waveFreq);
	}
	
	/**
	 * 2D SuperSimplex noise, with Y pointing down the main diagonal.
	 * Might be better for a 2D sandbox style game, where Y is vertical.
	 * Probably slightly less optimal for heightmaps or continent maps.
	 */
	public double noise2_XBeforeY(double x, double y, double waveFreq) {
		
		// Skew transform and rotation baked into one.
		double xx = x * 0.7071067811865476;
		double yy = y * 1.224744871380249;
		
		return noise2_Base(yy + xx, yy - xx, waveFreq);
	}
	
	/**
	 * 2D SuperSimplex noise base.
	 * Lookup table implementation inspired by DigitalShadow.
	 */
	private double noise2_Base(double xs, double ys, double waveFreq) {
		double value = 0;
		
		// Get base points and offsets
		int xsb = fastFloor(xs), ysb = fastFloor(ys);
		double xsi = xs - xsb, ysi = ys - ysb;
		
		// Index to point list
		int a = (int)(xsi + ysi);
		int index =
			(a << 2) |
			(int)(xsi - ysi / 2 + 1 - a / 2.0) << 3 |
			(int)(ysi - xsi / 2 + 1 - a / 2.0) << 4;
		
		double ssi = (xsi + ysi) * -0.211324865405187;
		double xi = xsi + ssi, yi = ysi + ssi;

		// Point contributions
		for (int i = 0; i < 4; i++) {
			LatticePoint2D c = LOOKUP_2D[index + i];

			double dx = xi + c.dx, dy = yi + c.dy;
			double attn = 2.0 / 3.0 - dx * dx - dy * dy;
			if (attn <= 0) continue;

			int pxm = (xsb + c.xsv) & PMASK, pym = (ysb + c.ysv) & PMASK;
			int pyi = perm[pxm] ^ pym;
			Grad2 grad = permGrad2[pyi];
			double extrapolation = fastPseudoSine((grad.dx * dx + grad.dy * dy) * waveFreq + permOffset2[pyi]);
			
			attn = attn * attn * attn;
			value += attn * extrapolation;
		}
		
		return value;
	}
	
	/**
	 * 3D Re-oriented 8-point BCC noise, classic orientation
	 * Proper substitute for what 3D SuperSimplex would be,
	 * in light of Forbidden Formulae.
	 * Use noise3_XYBeforeZ or noise3_XZBeforeY instead, wherever appropriate.
	 */
	public double noise3_Classic(double x, double y, double z, double waveFreq) {
		
		// Re-orient the cubic lattices via rotation, to produce the expected look on cardinal planar slices.
		// If texturing objects that don't tend to have cardinal plane faces, you could even remove this.
		// Orthonormal rotation. Not a skew transform.
		double r = (2.0 / 3.0) * (x + y + z);
		double xr = r - x, yr = r - y, zr = r - z;
		
		// Evaluate both lattices to form a BCC lattice.
		return noise3_BCC(xr, yr, zr, waveFreq);
	}
	
	/**
	 * 3D Re-oriented 8-point BCC noise, with better visual isotropy in (X, Y).
	 * Recommended for 3D terrain and time-varied animations.
	 * The Z coordinate should always be the "different" coordinate in your use case.
	 * If Y is vertical in world coordinates, call noise3_XYBeforeZ(x, z, Y) or use noise3_XZBeforeY.
	 * If Z is vertical in world coordinates, call noise3_XYBeforeZ(x, y, Z).
	 * For a time varied animation, call noise3_XYBeforeZ(x, y, T).
	 */
	public double noise3_XYBeforeZ(double x, double y, double z, double waveFreq) {
		
		// Re-orient the cubic lattices without skewing, to make X and Y triangular like 2D.
		// Orthonormal rotation. Not a skew transform.
		double xy = x + y;
		double s2 = xy * -0.211324865405187;
		double zz = z * 0.577350269189626;
		double xr = x + s2 - zz, yr = y + s2 - zz;
		double zr = xy * 0.577350269189626 + zz;
		
		// Evaluate both lattices to form a BCC lattice.
		return noise3_BCC(xr, yr, zr, waveFreq);
	}
	
	/**
	 * 3D Re-oriented 8-point BCC noise, with better visual isotropy in (X, Z).
	 * Recommended for 3D terrain and time-varied animations.
	 * The Y coordinate should always be the "different" coordinate in your use case.
	 * If Y is vertical in world coordinates, call noise3_XZBeforeY(x, Y, z).
	 * If Z is vertical in world coordinates, call noise3_XZBeforeY(x, Z, y) or use noise3_XYBeforeZ.
	 * For a time varied animation, call noise3_XZBeforeY(x, T, y) or use noise3_XYBeforeZ.
	 */
	public double noise3_XZBeforeY(double x, double y, double z, double waveFreq) {
		
		// Re-orient the cubic lattices without skewing, to make X and Z triangular like 2D.
		// Orthonormal rotation. Not a skew transform.
		double xz = x + z;
		double s2 = xz * -0.211324865405187;
		double yy = y * 0.577350269189626;
		double xr = x + s2 - yy; double zr = z + s2 - yy;
		double yr = xz * 0.577350269189626 + yy;
		
		// Evaluate both lattices to form a BCC lattice.
		return noise3_BCC(xr, yr, zr, waveFreq);
	}
	
	/**
	 * Generate overlapping cubic lattices for 3D Re-oriented BCC noise.
	 * Lookup table implementation inspired by DigitalShadow.
	 * It was actually faster to narrow down the points in the loop itself,
	 * than to build up the index with enough info to isolate 8 points.
	 */
	private double noise3_BCC(double xr, double yr, double zr, double waveFreq) {
		
		// Get base and offsets inside cube of first lattice.
		int xrb = fastFloor(xr), yrb = fastFloor(yr), zrb = fastFloor(zr);
		double xri = xr - xrb, yri = yr - yrb, zri = zr - zrb;
		
		// Identify which octant of the cube we're in. This determines which cell
		// in the other cubic lattice we're in, and also narrows down one point on each.
		int xht = (int)(xri + 0.5), yht = (int)(yri + 0.5), zht = (int)(zri + 0.5);
		int index = (xht << 0) | (yht << 1) | (zht << 2);
		
		// Point contributions
		double value = 0;
		LatticePoint3D c = LOOKUP_3D[index];
		while (c != null) {
			double dxr = xri + c.dxr, dyr = yri + c.dyr, dzr = zri + c.dzr;
			double attn = 0.75 - dxr * dxr - dyr * dyr - dzr * dzr;
			if (attn < 0) {
				c = c.nextOnFailure;
			} else {
				int pxm = (xrb + c.xrv) & PMASK, pym = (yrb + c.yrv) & PMASK, pzm = (zrb + c.zrv) & PMASK;
				int pzi = perm[perm[pxm] ^ pym] ^ pzm;
				Grad3 grad = permGrad3[pzi];
				double extrapolation = fastPseudoSine((grad.dx * dxr + grad.dy * dyr + grad.dz * dzr) * waveFreq + permOffset3[pzi]);
				
				attn = attn * attn * attn;
				value += attn * extrapolation;
				c = c.nextOnSuccess;
			}
		}
		return value;
	}
	
	/*
	 * Utility
	 */
	
	private static int fastFloor(double x) {
		int xi = (int)x;
		return x < xi ? xi - 1 : xi;
	}
	
	private static double fastPseudoSine(double x) {
		int xb = fastFloor(x);
		double t = x - xb;
		double part = t * (1 + t * t * (-2 + t));
		return (xb & 1) == 0 ? part : -part;
	}
	
	/*
	 * Definitions
	 */

	private static final LatticePoint2D[] LOOKUP_2D;
	private static final LatticePoint3D[] LOOKUP_3D;
	static {
		LOOKUP_2D = new LatticePoint2D[8 * 4];
		LOOKUP_3D = new LatticePoint3D[8];
		
		for (int i = 0; i < 8; i++) {
			int i1, j1, i2, j2;
			if ((i & 1) == 0) {
				if ((i & 2) == 0) { i1 = -1; j1 = 0; } else { i1 = 1; j1 = 0; }
				if ((i & 4) == 0) { i2 = 0; j2 = -1; } else { i2 = 0; j2 = 1; }
			} else {
				if ((i & 2) != 0) { i1 = 2; j1 = 1; } else { i1 = 0; j1 = 1; }
				if ((i & 4) != 0) { i2 = 1; j2 = 2; } else { i2 = 1; j2 = 0; }
			}
			LOOKUP_2D[i * 4 + 0] = new LatticePoint2D(0, 0);
			LOOKUP_2D[i * 4 + 1] = new LatticePoint2D(1, 1);
			LOOKUP_2D[i * 4 + 2] = new LatticePoint2D(i1, j1);
			LOOKUP_2D[i * 4 + 3] = new LatticePoint2D(i2, j2);
		}
		
		for (int i = 0; i < 8; i++) {
			int i1, j1, k1, i2, j2, k2;
			i1 = (i >> 0) & 1; j1 = (i >> 1) & 1; k1 = (i >> 2) & 1;
			i2 = i1 ^ 1; j2 = j1 ^ 1; k2 = k1 ^ 1;
			
			// The two points within this octant, one from each of the two cubic half-lattices.
			LatticePoint3D c0 = new LatticePoint3D(i1, j1, k1, 0);
			LatticePoint3D c1 = new LatticePoint3D(i1 + i2, j1 + j2, k1 + k2, 1);
			
			// (1, 0, 0) vs (0, 1, 1) away from octant.
			LatticePoint3D c2 = new LatticePoint3D(i1 ^ 1, j1, k1, 0);
			LatticePoint3D c3 = new LatticePoint3D(i1, j1 ^ 1, k1 ^ 1, 0);
			
			// (1, 0, 0) vs (0, 1, 1) away from octant, on second half-lattice.
			LatticePoint3D c4 = new LatticePoint3D(i1 + (i2 ^ 1), j1 + j2, k1 + k2, 1);
			LatticePoint3D c5 = new LatticePoint3D(i1 + i2, j1 + (j2 ^ 1), k1 + (k2 ^ 1), 1);
			
			// (0, 1, 0) vs (1, 0, 1) away from octant.
			LatticePoint3D c6 = new LatticePoint3D(i1, j1 ^ 1, k1, 0);
			LatticePoint3D c7 = new LatticePoint3D(i1 ^ 1, j1, k1 ^ 1, 0);
			
			// (0, 1, 0) vs (1, 0, 1) away from octant, on second half-lattice.
			LatticePoint3D c8 = new LatticePoint3D(i1 + i2, j1 + (j2 ^ 1), k1 + k2, 1);
			LatticePoint3D c9 = new LatticePoint3D(i1 + (i2 ^ 1), j1 + j2, k1 + (k2 ^ 1), 1);
			
			// (0, 0, 1) vs (1, 1, 0) away from octant.
			LatticePoint3D cA = new LatticePoint3D(i1, j1, k1 ^ 1, 0);
			LatticePoint3D cB = new LatticePoint3D(i1 ^ 1, j1 ^ 1, k1, 0);
			
			// (0, 0, 1) vs (1, 1, 0) away from octant, on second half-lattice.
			LatticePoint3D cC = new LatticePoint3D(i1 + i2, j1 + j2, k1 + (k2 ^ 1), 1);
			LatticePoint3D cD = new LatticePoint3D(i1 + (i2 ^ 1), j1 + (j2 ^ 1), k1 + k2, 1);
			
			// First two points are guaranteed.
			c0.nextOnFailure = c0.nextOnSuccess = c1;
			c1.nextOnFailure = c1.nextOnSuccess = c2;
			
			// If c2 is in range, then we know c3 and c4 are not.
			c2.nextOnFailure = c3; c2.nextOnSuccess = c5;
			c3.nextOnFailure = c4; c3.nextOnSuccess = c4;
			
			// If c4 is in range, then we know c5 is not.
			c4.nextOnFailure = c5; c4.nextOnSuccess = c6;
			c5.nextOnFailure = c5.nextOnSuccess = c6;
			
			// If c6 is in range, then we know c7 and c8 are not.
			c6.nextOnFailure = c7; c6.nextOnSuccess = c9;
			c7.nextOnFailure = c8; c7.nextOnSuccess = c8;
			
			// If c8 is in range, then we know c9 is not.
			c8.nextOnFailure = c9; c8.nextOnSuccess = cA;
			c9.nextOnFailure = c9.nextOnSuccess = cA;
			
			// If cA is in range, then we know cB and cC are not.
			cA.nextOnFailure = cB; cA.nextOnSuccess = cD;
			cB.nextOnFailure = cC; cB.nextOnSuccess = cC;
			
			// If cC is in range, then we know cD is not.
			cC.nextOnFailure = cD; cC.nextOnSuccess = null;
			cD.nextOnFailure = cD.nextOnSuccess = null;
			
			LOOKUP_3D[i] = c0;
			
		}
	}
	
	private static class LatticePoint2D {
		int xsv, ysv;
		double dx, dy;
		public LatticePoint2D(int xsv, int ysv) {
			this.xsv = xsv; this.ysv = ysv;
			double ssv = (xsv + ysv) * -0.211324865405187;
			this.dx = -xsv - ssv;
			this.dy = -ysv - ssv;
		}
	}
	
	private static class LatticePoint3D {
		public double dxr, dyr, dzr;
		public int xrv, yrv, zrv;
		LatticePoint3D nextOnFailure, nextOnSuccess;
		public LatticePoint3D(int xrv, int yrv, int zrv, int lattice) {
			this.dxr = -xrv + lattice * 0.5; this.dyr = -yrv + lattice * 0.5; this.dzr = -zrv + lattice * 0.5;
			this.xrv = xrv + lattice * 1024; this.yrv = yrv + lattice * 1024; this.zrv = zrv + lattice * 1024;
		}
	}
	
	/*
	 * Gradients
	 */
	
	public static class Grad2 {
		double dx, dy;
		public Grad2(double dx, double dy) {
			this.dx = dx; this.dy = dy;
		}
	}
	
	public static class Grad3 {
		double dx, dy, dz;
		public Grad3(double dx, double dy, double dz) {
			this.dx = dx; this.dy = dy; this.dz = dz;
		}
	}
	
	private static final Grad2[] GRADIENTS_2D;
	private static final Grad3[] GRADIENTS_3D;
	private static final double[] OFFSETS_2D;
	private static final double[] OFFSETS_3D;
	static {
		GRADIENTS_2D = new Grad2[PSIZE];
		OFFSETS_2D = new double[PSIZE];
		Grad2[] grad2 = {
			new Grad2( 0.130526192220052,  0.99144486137381),
			new Grad2( 0.38268343236509,   0.923879532511287),
			new Grad2( 0.608761429008721,  0.793353340291235),
			new Grad2( 0.793353340291235,  0.608761429008721),
			new Grad2( 0.923879532511287,  0.38268343236509),
			new Grad2( 0.99144486137381,   0.130526192220051),
			new Grad2( 0.99144486137381,  -0.130526192220051),
			new Grad2( 0.923879532511287, -0.38268343236509),
			new Grad2( 0.793353340291235, -0.60876142900872),
			new Grad2( 0.608761429008721, -0.793353340291235),
			new Grad2( 0.38268343236509,  -0.923879532511287),
			new Grad2( 0.130526192220052, -0.99144486137381),
			new Grad2(-0.130526192220052, -0.99144486137381),
			new Grad2(-0.38268343236509,  -0.923879532511287),
			new Grad2(-0.608761429008721, -0.793353340291235),
			new Grad2(-0.793353340291235, -0.608761429008721),
			new Grad2(-0.923879532511287, -0.38268343236509),
			new Grad2(-0.99144486137381,  -0.130526192220052),
			new Grad2(-0.99144486137381,   0.130526192220051),
			new Grad2(-0.923879532511287,  0.38268343236509),
			new Grad2(-0.793353340291235,  0.608761429008721),
			new Grad2(-0.608761429008721,  0.793353340291235),
			new Grad2(-0.38268343236509,   0.923879532511287),
			new Grad2(-0.130526192220052,  0.99144486137381)
		};
		Grad2[] grad2XBeforeY = new Grad2[grad2.length];
		/*for (int i = 0; i < grad2.length; i++) {
			double norm = Math.sqrt(grad2[i].dx * grad2[i].dx + grad2[i].dy * grad2[i].dy);
			grad2[i].dx /= norm; grad2[i].dy /= norm;
		}*/
		double offsetNormalize2 = 1.0 / Math.round(PSIZE * 1.0 / grad2.length);
		for (int i = 0; i < PSIZE; i++) {
			GRADIENTS_2D[i] = grad2[i % grad2.length];
			OFFSETS_2D[i] = (((i / grad2.length) * offsetNormalize2) % 1) * 2;
		}
		
		GRADIENTS_3D = new Grad3[PSIZE];
		OFFSETS_3D = new double[PSIZE];
		Grad3[] grad3 = {
			new Grad3(-2.22474487139,      -2.22474487139,      -1.0),
			new Grad3(-2.22474487139,      -2.22474487139,       1.0),
			new Grad3(-3.0862664687972017, -1.1721513422464978,  0.0),
			new Grad3(-1.1721513422464978, -3.0862664687972017,  0.0),
			new Grad3(-2.22474487139,      -1.0,                -2.22474487139),
			new Grad3(-2.22474487139,       1.0,                -2.22474487139),
			new Grad3(-1.1721513422464978,  0.0,                -3.0862664687972017),
			new Grad3(-3.0862664687972017,  0.0,                -1.1721513422464978),
			new Grad3(-2.22474487139,      -1.0,                 2.22474487139),
			new Grad3(-2.22474487139,       1.0,                 2.22474487139),
			new Grad3(-3.0862664687972017,  0.0,                 1.1721513422464978),
			new Grad3(-1.1721513422464978,  0.0,                 3.0862664687972017),
			new Grad3(-2.22474487139,       2.22474487139,      -1.0),
			new Grad3(-2.22474487139,       2.22474487139,       1.0),
			new Grad3(-1.1721513422464978,  3.0862664687972017,  0.0),
			new Grad3(-3.0862664687972017,  1.1721513422464978,  0.0),
			new Grad3(-1.0,                -2.22474487139,      -2.22474487139),
			new Grad3( 1.0,                -2.22474487139,      -2.22474487139),
			new Grad3( 0.0,                -3.0862664687972017, -1.1721513422464978),
			new Grad3( 0.0,                -1.1721513422464978, -3.0862664687972017),
			new Grad3(-1.0,                -2.22474487139,       2.22474487139),
			new Grad3( 1.0,                -2.22474487139,       2.22474487139),
			new Grad3( 0.0,                -1.1721513422464978,  3.0862664687972017),
			new Grad3( 0.0,                -3.0862664687972017,  1.1721513422464978),
			new Grad3(-1.0,                 2.22474487139,      -2.22474487139),
			new Grad3( 1.0,                 2.22474487139,      -2.22474487139),
			new Grad3( 0.0,                 1.1721513422464978, -3.0862664687972017),
			new Grad3( 0.0,                 3.0862664687972017, -1.1721513422464978),
			new Grad3(-1.0,                 2.22474487139,       2.22474487139),
			new Grad3( 1.0,                 2.22474487139,       2.22474487139),
			new Grad3( 0.0,                 3.0862664687972017,  1.1721513422464978),
			new Grad3( 0.0,                 1.1721513422464978,  3.0862664687972017),
			new Grad3( 2.22474487139,      -2.22474487139,      -1.0),
			new Grad3( 2.22474487139,      -2.22474487139,       1.0),
			new Grad3( 1.1721513422464978, -3.0862664687972017,  0.0),
			new Grad3( 3.0862664687972017, -1.1721513422464978,  0.0),
			new Grad3( 2.22474487139,      -1.0,                -2.22474487139),
			new Grad3( 2.22474487139,       1.0,                -2.22474487139),
			new Grad3( 3.0862664687972017,  0.0,                -1.1721513422464978),
			new Grad3( 1.1721513422464978,  0.0,                -3.0862664687972017),
			new Grad3( 2.22474487139,      -1.0,                 2.22474487139),
			new Grad3( 2.22474487139,       1.0,                 2.22474487139),
			new Grad3( 1.1721513422464978,  0.0,                 3.0862664687972017),
			new Grad3( 3.0862664687972017,  0.0,                 1.1721513422464978),
			new Grad3( 2.22474487139,       2.22474487139,      -1.0),
			new Grad3( 2.22474487139,       2.22474487139,       1.0),
			new Grad3( 3.0862664687972017,  1.1721513422464978,  0.0),
			new Grad3( 1.1721513422464978,  3.0862664687972017,  0.0)
		};
		for (int i = 0; i < grad3.length; i++) {
			double norm = Math.sqrt(grad3[i].dx * grad3[i].dx + grad3[i].dy * grad3[i].dy + grad3[i].dz * grad3[i].dz);
			grad3[i].dx /= norm; grad3[i].dy /= norm; grad3[i].dz /= norm;
		}
		double offsetNormalize3 = 1.0 / Math.round(PSIZE * 1.0 / grad3.length);
		for (int i = 0; i < PSIZE; i++) {
			GRADIENTS_3D[i] = grad3[i % grad3.length];
			OFFSETS_3D[i] = (((i / grad3.length) * offsetNormalize3) % 1) * 2;
		}
	}
}