You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
572 lines
15 KiB
572 lines
15 KiB
/*****************************************************************************
|
|
* J3D.org Copyright (c) 2000
|
|
* Java Source
|
|
*
|
|
* This source is licensed under the GNU LGPL v2.1
|
|
* Please read http://www.gnu.org/copyleft/lgpl.html for more information
|
|
*
|
|
* This software comes with the standard NO WARRANTY disclaimer for any
|
|
* purpose. Use it at your own risk. If there's a problem you get to fix it.
|
|
*
|
|
****************************************************************************/
|
|
package mightypork.utils.math.noise;
|
|
|
|
|
|
import java.util.Random;
|
|
|
|
|
|
/**
|
|
* Computes Perlin Noise for three dimensions.
|
|
* <p>
|
|
* The result is a continuous function that interpolates a smooth path along a
|
|
* series random points. The function is consitent, so given the same
|
|
* parameters, it will always return the same value. The smoothing function is
|
|
* based on the Improving Noise paper presented at Siggraph 2002.
|
|
* <p>
|
|
* Computing noise for one and two dimensions can make use of the 3D problem
|
|
* space by just setting the un-needed dimensions to a fixed value.
|
|
*
|
|
* @author Justin Couch
|
|
* @edited by Ondřej Hruška
|
|
* @version $Revision: 1.4 $
|
|
* @source http://code.j3d.org/download.html
|
|
*/
|
|
public class PerlinNoiseGenerator {
|
|
|
|
// Constants for setting up the Perlin-1 noise functions
|
|
private static final int B = 0x1000;
|
|
private static final int BM = 0xff;
|
|
|
|
private static final int N = 0x1000;
|
|
|
|
/** Default seed to use for the random number generation */
|
|
private static final int DEFAULT_SEED = 100;
|
|
|
|
/** Default sample size to work with */
|
|
private static final int DEFAULT_SAMPLE_SIZE = 256;
|
|
|
|
private final Random rand = new Random(DEFAULT_SEED);
|
|
|
|
/** Permutation array for the improved noise function */
|
|
private final int[] p_imp;
|
|
|
|
/** P array for perline 1 noise */
|
|
private int[] p;
|
|
private double[][] g3;
|
|
private double[][] g2;
|
|
private double[] g1;
|
|
|
|
|
|
/**
|
|
* Create a new noise creator with the default seed value
|
|
*/
|
|
public PerlinNoiseGenerator() {
|
|
this(DEFAULT_SEED);
|
|
}
|
|
|
|
|
|
/**
|
|
* Create a new noise creator with the given seed value for the randomness
|
|
*
|
|
* @param seed The seed value to use
|
|
*/
|
|
public PerlinNoiseGenerator(long seed) {
|
|
p_imp = new int[DEFAULT_SAMPLE_SIZE << 1];
|
|
|
|
int i, j, k;
|
|
rand.setSeed(seed);
|
|
|
|
// Calculate the table of psuedo-random coefficients.
|
|
for (i = 0; i < DEFAULT_SAMPLE_SIZE; i++)
|
|
p_imp[i] = i;
|
|
|
|
// generate the psuedo-random permutation table.
|
|
while (--i > 0) {
|
|
k = p_imp[i];
|
|
j = (int) (rand.nextLong() & DEFAULT_SAMPLE_SIZE);
|
|
p_imp[i] = p_imp[j];
|
|
p_imp[j] = k;
|
|
}
|
|
|
|
initPerlin1();
|
|
}
|
|
|
|
|
|
/**
|
|
* Computes noise function for three dimensions at the point (x,y,z).
|
|
*
|
|
* @param x x dimension parameter
|
|
* @param y y dimension parameter
|
|
* @param z z dimension parameter
|
|
* @return the noise value at the point (x, y, z)
|
|
*/
|
|
public double improvedNoise(double x, double y, double z)
|
|
{
|
|
// Constraint the point to a unit cube
|
|
final int uc_x = (int) Math.floor(x) & 255;
|
|
final int uc_y = (int) Math.floor(y) & 255;
|
|
final int uc_z = (int) Math.floor(z) & 255;
|
|
|
|
// Relative location of the point in the unit cube
|
|
final double xo = x - Math.floor(x);
|
|
final double yo = y - Math.floor(y);
|
|
final double zo = z - Math.floor(z);
|
|
|
|
// Fade curves for x, y and z
|
|
final double u = fade(xo);
|
|
final double v = fade(yo);
|
|
final double w = fade(zo);
|
|
|
|
// Generate a hash for each coordinate to find out where in the cube
|
|
// it lies.
|
|
final int a = p_imp[uc_x] + uc_y;
|
|
final int aa = p_imp[a] + uc_z;
|
|
final int ab = p_imp[a + 1] + uc_z;
|
|
|
|
final int b = p_imp[uc_x + 1] + uc_y;
|
|
final int ba = p_imp[b] + uc_z;
|
|
final int bb = p_imp[b + 1] + uc_z;
|
|
|
|
// blend results from the 8 corners based on the noise function
|
|
final double c1 = grad(p_imp[aa], xo, yo, zo);
|
|
final double c2 = grad(p_imp[ba], xo - 1, yo, zo);
|
|
final double c3 = grad(p_imp[ab], xo, yo - 1, zo);
|
|
final double c4 = grad(p_imp[bb], xo - 1, yo - 1, zo);
|
|
final double c5 = grad(p_imp[aa + 1], xo, yo, zo - 1);
|
|
final double c6 = grad(p_imp[ba + 1], xo - 1, yo, zo - 1);
|
|
final double c7 = grad(p_imp[ab + 1], xo, yo - 1, zo - 1);
|
|
final double c8 = grad(p_imp[bb + 1], xo - 1, yo - 1, zo - 1);
|
|
|
|
return lerp(w, lerp(v, lerp(u, c1, c2), lerp(u, c3, c4)), lerp(v, lerp(u, c5, c6), lerp(u, c7, c8)));
|
|
}
|
|
|
|
|
|
/**
|
|
* 1-D noise generation function using the original perlin algorithm.
|
|
*
|
|
* @param x Seed for the noise function
|
|
* @return The noisy output
|
|
*/
|
|
public double noise1(double x)
|
|
{
|
|
final double t = x + N;
|
|
final int bx0 = ((int) t) & BM;
|
|
final int bx1 = (bx0 + 1) & BM;
|
|
final double rx0 = t - (int) t;
|
|
final double rx1 = rx0 - 1;
|
|
|
|
final double sx = sCurve(rx0);
|
|
|
|
final double u = rx0 * g1[p[bx0]];
|
|
final double v = rx1 * g1[p[bx1]];
|
|
|
|
return lerp(sx, u, v);
|
|
}
|
|
|
|
|
|
/**
|
|
* Create noise in a 2D space using the orignal perlin noise algorithm.
|
|
*
|
|
* @param x The X coordinate of the location to sample
|
|
* @param y The Y coordinate of the location to sample
|
|
* @return A noisy value at the given position
|
|
*/
|
|
public double noise2(double x, double y)
|
|
{
|
|
double t = x + N;
|
|
final int bx0 = ((int) t) & BM;
|
|
final int bx1 = (bx0 + 1) & BM;
|
|
final double rx0 = t - (int) t;
|
|
final double rx1 = rx0 - 1;
|
|
|
|
t = y + N;
|
|
final int by0 = ((int) t) & BM;
|
|
final int by1 = (by0 + 1) & BM;
|
|
final double ry0 = t - (int) t;
|
|
final double ry1 = ry0 - 1;
|
|
|
|
final int i = p[bx0];
|
|
final int j = p[bx1];
|
|
|
|
final int b00 = p[i + by0];
|
|
final int b10 = p[j + by0];
|
|
final int b01 = p[i + by1];
|
|
final int b11 = p[j + by1];
|
|
|
|
final double sx = sCurve(rx0);
|
|
final double sy = sCurve(ry0);
|
|
|
|
double[] q = g2[b00];
|
|
double u = rx0 * q[0] + ry0 * q[1];
|
|
q = g2[b10];
|
|
double v = rx1 * q[0] + ry0 * q[1];
|
|
final double a = lerp(sx, u, v);
|
|
|
|
q = g2[b01];
|
|
u = rx0 * q[0] + ry1 * q[1];
|
|
q = g2[b11];
|
|
v = rx1 * q[0] + ry1 * q[1];
|
|
final double b = lerp(sx, u, v);
|
|
|
|
return lerp(sy, a, b);
|
|
}
|
|
|
|
|
|
/**
|
|
* Create noise in a 3D space using the orignal perlin noise algorithm.
|
|
*
|
|
* @param x The X coordinate of the location to sample
|
|
* @param y The Y coordinate of the location to sample
|
|
* @param z The Z coordinate of the location to sample
|
|
* @return A noisy value at the given position
|
|
*/
|
|
public double noise3(double x, double y, double z)
|
|
{
|
|
double t = x + N;
|
|
final int bx0 = ((int) t) & BM;
|
|
final int bx1 = (bx0 + 1) & BM;
|
|
final double rx0 = t - (int) t;
|
|
final double rx1 = rx0 - 1;
|
|
|
|
t = y + N;
|
|
final int by0 = ((int) t) & BM;
|
|
final int by1 = (by0 + 1) & BM;
|
|
final double ry0 = t - (int) t;
|
|
final double ry1 = ry0 - 1;
|
|
|
|
t = z + N;
|
|
final int bz0 = ((int) t) & BM;
|
|
final int bz1 = (bz0 + 1) & BM;
|
|
final double rz0 = t - (int) t;
|
|
final double rz1 = rz0 - 1;
|
|
|
|
final int i = p[bx0];
|
|
final int j = p[bx1];
|
|
|
|
final int b00 = p[i + by0];
|
|
final int b10 = p[j + by0];
|
|
final int b01 = p[i + by1];
|
|
final int b11 = p[j + by1];
|
|
|
|
t = sCurve(rx0);
|
|
final double sy = sCurve(ry0);
|
|
final double sz = sCurve(rz0);
|
|
|
|
double[] q = g3[b00 + bz0];
|
|
double u = (rx0 * q[0] + ry0 * q[1] + rz0 * q[2]);
|
|
q = g3[b10 + bz0];
|
|
double v = (rx1 * q[0] + ry0 * q[1] + rz0 * q[2]);
|
|
double a = lerp(t, u, v);
|
|
|
|
q = g3[b01 + bz0];
|
|
u = (rx0 * q[0] + ry1 * q[1] + rz0 * q[2]);
|
|
q = g3[b11 + bz0];
|
|
v = (rx1 * q[0] + ry1 * q[1] + rz0 * q[2]);
|
|
double b = lerp(t, u, v);
|
|
|
|
final double c = lerp(sy, a, b);
|
|
|
|
q = g3[b00 + bz1];
|
|
u = (rx0 * q[0] + ry0 * q[1] + rz1 * q[2]);
|
|
q = g3[b10 + bz1];
|
|
v = (rx1 * q[0] + ry0 * q[1] + rz1 * q[2]);
|
|
a = lerp(t, u, v);
|
|
|
|
q = g3[b01 + bz1];
|
|
u = (rx0 * q[0] + ry1 * q[1] + rz1 * q[2]);
|
|
q = g3[b11 + bz1];
|
|
v = (rx1 * q[0] + ry1 * q[1] + rz1 * q[2]);
|
|
b = lerp(t, u, v);
|
|
|
|
final double d = lerp(sy, a, b);
|
|
|
|
return lerp(sz, c, d);
|
|
}
|
|
|
|
|
|
/**
|
|
* Create a turbulent noise output based on the core noise function. This
|
|
* uses the noise as a base function and is suitable for creating clouds,
|
|
* marble and explosion effects. For example, a typical marble effect would
|
|
* set the colour to be:
|
|
*
|
|
* <pre>
|
|
* sin(point + turbulence(point) * point.x);
|
|
* </pre>
|
|
*
|
|
* @param x
|
|
* @param y
|
|
* @param z
|
|
* @param loF
|
|
* @param hiF
|
|
* @return value
|
|
*/
|
|
public double imporvedTurbulence(double x, double y, double z, double loF, double hiF)
|
|
{
|
|
double p_x = x + 123.456f;
|
|
double p_y = y;
|
|
double p_z = z;
|
|
double t = 0;
|
|
double f;
|
|
|
|
for (f = loF; f < hiF; f *= 2) {
|
|
t += Math.abs(improvedNoise(p_x, p_y, p_z)) / f;
|
|
|
|
p_x *= 2;
|
|
p_y *= 2;
|
|
p_z *= 2;
|
|
}
|
|
|
|
return t - 0.3;
|
|
}
|
|
|
|
|
|
/**
|
|
* Create a turbulance function in 2D using the original perlin noise
|
|
* function.
|
|
*
|
|
* @param x The X coordinate of the location to sample
|
|
* @param y The Y coordinate of the location to sample
|
|
* @param freq The frequency of the turbluance to create
|
|
* @return The value at the given coordinates
|
|
*/
|
|
public double turbulence2(double x, double y, double freq)
|
|
{
|
|
double t = 0;
|
|
|
|
do {
|
|
t += noise2(freq * x, freq * y) / freq;
|
|
freq *= 0.5f;
|
|
} while (freq >= 1);
|
|
|
|
return t;
|
|
}
|
|
|
|
|
|
/**
|
|
* Create a turbulance function in 3D using the original perlin noise
|
|
* function.
|
|
*
|
|
* @param x The X coordinate of the location to sample
|
|
* @param y The Y coordinate of the location to sample
|
|
* @param z The Z coordinate of the location to sample
|
|
* @param freq The frequency of the turbluance to create
|
|
* @return The value at the given coordinates
|
|
*/
|
|
public double turbulence3(double x, double y, double z, double freq)
|
|
{
|
|
double t = 0;
|
|
|
|
do {
|
|
t += noise3(freq * x, freq * y, freq * z) / freq;
|
|
freq *= 0.5f;
|
|
} while (freq >= 1);
|
|
|
|
return t;
|
|
}
|
|
|
|
|
|
/**
|
|
* Create a 1D tileable noise function for the given width.
|
|
*
|
|
* @param x The X coordinate to generate the noise for
|
|
* @param w The width of the tiled block
|
|
* @return The value of the noise at the given coordinate
|
|
*/
|
|
public double tileableNoise1(double x, double w)
|
|
{
|
|
return (noise1(x) * (w - x) + noise1(x - w) * x) / w;
|
|
}
|
|
|
|
|
|
/**
|
|
* Create a 2D tileable noise function for the given width and height.
|
|
*
|
|
* @param x The X coordinate to generate the noise for
|
|
* @param y The Y coordinate to generate the noise for
|
|
* @param w The width of the tiled block
|
|
* @param h The height of the tiled block
|
|
* @return The value of the noise at the given coordinate
|
|
*/
|
|
public double tileableNoise2(double x, double y, double w, double h)
|
|
{
|
|
return (noise2(x, y) * (w - x) * (h - y) + noise2(x - w, y) * x * (h - y) + noise2(x, y - h) * (w - x) * y + noise2(x - w, y - h) * x * y) / (w * h);
|
|
}
|
|
|
|
|
|
/**
|
|
* Create a 3D tileable noise function for the given width, height and
|
|
* depth.
|
|
*
|
|
* @param x The X coordinate to generate the noise for
|
|
* @param y The Y coordinate to generate the noise for
|
|
* @param z The Z coordinate to generate the noise for
|
|
* @param w The width of the tiled block
|
|
* @param h The height of the tiled block
|
|
* @param d The depth of the tiled block
|
|
* @return The value of the noise at the given coordinate
|
|
*/
|
|
public double tileableNoise3(double x, double y, double z, double w, double h, double d)
|
|
{
|
|
return (noise3(x, y, z) * (w - x) * (h - y) * (d - z) + noise3(x - w, y, z) * x * (h - y) * (d - z) + noise3(x, y - h, z) * (w - x) * y * (d - z) + noise3(x - w, y - h, z) * x * y * (d - z) + noise3(x, y, z - d) * (w - x) * (h - y) * z + noise3(x - w, y, z - d) * x * (h - y) * z + noise3(x, y - h, z - d) * (w - x) * y * z + noise3(x - w, y - h, z - d) * x * y * z) / (w * h * d);
|
|
}
|
|
|
|
|
|
/**
|
|
* Create a turbulance function that can be tiled across a surface in 2D.
|
|
*
|
|
* @param x The X coordinate of the location to sample
|
|
* @param y The Y coordinate of the location to sample
|
|
* @param w The width to tile over
|
|
* @param h The height to tile over
|
|
* @param freq The frequency of the turbluance to create
|
|
* @return The value at the given coordinates
|
|
*/
|
|
public double tileableTurbulence2(double x, double y, double w, double h, double freq)
|
|
{
|
|
double t = 0;
|
|
|
|
do {
|
|
t += tileableNoise2(freq * x, freq * y, w * freq, h * freq) / freq;
|
|
freq *= 0.5f;
|
|
} while (freq >= 1);
|
|
|
|
return t;
|
|
}
|
|
|
|
|
|
/**
|
|
* Create a turbulance function that can be tiled across a surface in 3D.
|
|
*
|
|
* @param x The X coordinate of the location to sample
|
|
* @param y The Y coordinate of the location to sample
|
|
* @param z The Z coordinate of the location to sample
|
|
* @param w The width to tile over
|
|
* @param h The height to tile over
|
|
* @param d The depth to tile over
|
|
* @param freq The frequency of the turbluance to create
|
|
* @return The value at the given coordinates
|
|
*/
|
|
public double tileableTurbulence3(double x, double y, double z, double w, double h, double d, double freq)
|
|
{
|
|
double t = 0;
|
|
|
|
do {
|
|
t += tileableNoise3(freq * x, freq * y, freq * z, w * freq, h * freq, d * freq) / freq;
|
|
freq *= 0.5f;
|
|
} while (freq >= 1);
|
|
|
|
return t;
|
|
}
|
|
|
|
|
|
/**
|
|
* Simple lerp function using doubles.
|
|
*/
|
|
private double lerp(double t, double a, double b)
|
|
{
|
|
return a + t * (b - a);
|
|
}
|
|
|
|
|
|
/**
|
|
* Fade curve calculation which is 6t^5 - 15t^4 + 10t^3. This is the new
|
|
* algorithm, where the old one used to be 3t^2 - 2t^3.
|
|
*
|
|
* @param t The t parameter to calculate the fade for
|
|
* @return the drop-off amount.
|
|
*/
|
|
private double fade(double t)
|
|
{
|
|
return t * t * t * (t * (t * 6 - 15) + 10);
|
|
}
|
|
|
|
|
|
/**
|
|
* Calculate the gradient function based on the hash code.
|
|
*/
|
|
private double grad(int hash, double x, double y, double z)
|
|
{
|
|
// Convert low 4 bits of hash code into 12 gradient directions.
|
|
final int h = hash & 15;
|
|
final double u = (h < 8 || h == 12 || h == 13) ? x : y;
|
|
final double v = (h < 4 || h == 12 || h == 13) ? y : z;
|
|
|
|
return ((h & 1) == 0 ? u : -u) + ((h & 2) == 0 ? v : -v);
|
|
}
|
|
|
|
|
|
/**
|
|
* S-curve function for value distribution for Perlin-1 noise function.
|
|
*/
|
|
private double sCurve(double t)
|
|
{
|
|
return (t * t * (3 - 2 * t));
|
|
}
|
|
|
|
|
|
/**
|
|
* 2D-vector normalisation function.
|
|
*/
|
|
private void normalize2(double[] v)
|
|
{
|
|
final double s = 1 / Math.sqrt(v[0] * v[0] + v[1] * v[1]);
|
|
v[0] *= s;
|
|
v[1] *= s;
|
|
}
|
|
|
|
|
|
/**
|
|
* 3D-vector normalisation function.
|
|
*/
|
|
private void normalize3(double[] v)
|
|
{
|
|
final double s = 1 / Math.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
|
|
v[0] *= s;
|
|
v[1] *= s;
|
|
v[2] *= s;
|
|
}
|
|
|
|
|
|
/**
|
|
* Initialise the lookup arrays used by Perlin 1 function.
|
|
*/
|
|
private void initPerlin1()
|
|
{
|
|
p = new int[B + B + 2];
|
|
g3 = new double[B + B + 2][3];
|
|
g2 = new double[B + B + 2][2];
|
|
g1 = new double[B + B + 2];
|
|
int i, j, k;
|
|
|
|
for (i = 0; i < B; i++) {
|
|
p[i] = i;
|
|
|
|
g1[i] = (((rand.nextDouble() * Integer.MAX_VALUE) % (B + B)) - B) / B;
|
|
|
|
for (j = 0; j < 2; j++)
|
|
g2[i][j] = (((rand.nextDouble() * Integer.MAX_VALUE) % (B + B)) - B) / B;
|
|
normalize2(g2[i]);
|
|
|
|
for (j = 0; j < 3; j++)
|
|
g3[i][j] = (((rand.nextDouble() * Integer.MAX_VALUE) % (B + B)) - B) / B;
|
|
normalize3(g3[i]);
|
|
}
|
|
|
|
while (--i > 0) {
|
|
k = p[i];
|
|
j = (int) ((rand.nextDouble() * Integer.MAX_VALUE) % B);
|
|
p[i] = p[j];
|
|
p[j] = k;
|
|
}
|
|
|
|
for (i = 0; i < B + 2; i++) {
|
|
p[B + i] = p[i];
|
|
g1[B + i] = g1[i];
|
|
for (j = 0; j < 2; j++)
|
|
g2[B + i][j] = g2[i][j];
|
|
for (j = 0; j < 3; j++)
|
|
g3[B + i][j] = g3[i][j];
|
|
}
|
|
}
|
|
}
|
|
|