我想创建一个类似地形的3D噪音生成器，经过一些研究，我得出结论，Simplex噪音是迄今为止最好的噪音类型。
我觉得这个名字很有误导性，因为我很难找到关于这个主题的资源，而且我找到的资源往往写得不好。
我基本上想要的是一个好的资源/教程，一步一步地解释单纯形噪声是如何工作的，并解释如何将其实现到程序中。
我不是在寻找解释如何使用图书馆或其他什么的资源。
在教程推荐的路厄中，我将尝试解释如何使用现有的java源来创建单倍频程的单工噪声。
单工噪声码
这部分代码由Stefan Gustavson创建，并被置于公共领域。它可以在这里找到。这里引用它是为了方便
import java.awt.Color;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
import java.util.Random;
import javax.imageio.ImageIO;
/*
* A speed-improved simplex noise algorithm for 2D, 3D and 4D in Java.
*
* Based on example code by Stefan Gustavson (stegu@itn.liu.se).
* Optimisations by Peter Eastman (peastman@drizzle.stanford.edu).
* Better rank ordering method by Stefan Gustavson in 2012.
*
* This could be speeded up even further, but it's useful as it is.
*
* Version 2012-03-09
*
* This code was placed in the public domain by its original author,
* Stefan Gustavson. You may use it as you see fit, but
* attribution is appreciated.
*
*/
public class SimplexNoise_octave { // Simplex noise in 2D, 3D and 4D
public static int RANDOMSEED=0;
private static int NUMBEROFSWAPS=400;
private static Grad grad3[] = {new Grad(1,1,0),new Grad(-1,1,0),new Grad(1,-1,0),new Grad(-1,-1,0),
new Grad(1,0,1),new Grad(-1,0,1),new Grad(1,0,-1),new Grad(-1,0,-1),
new Grad(0,1,1),new Grad(0,-1,1),new Grad(0,1,-1),new Grad(0,-1,-1)};
private static Grad grad4[]= {new Grad(0,1,1,1),new Grad(0,1,1,-1),new Grad(0,1,-1,1),new Grad(0,1,-1,-1),
new Grad(0,-1,1,1),new Grad(0,-1,1,-1),new Grad(0,-1,-1,1),new Grad(0,-1,-1,-1),
new Grad(1,0,1,1),new Grad(1,0,1,-1),new Grad(1,0,-1,1),new Grad(1,0,-1,-1),
new Grad(-1,0,1,1),new Grad(-1,0,1,-1),new Grad(-1,0,-1,1),new Grad(-1,0,-1,-1),
new Grad(1,1,0,1),new Grad(1,1,0,-1),new Grad(1,-1,0,1),new Grad(1,-1,0,-1),
new Grad(-1,1,0,1),new Grad(-1,1,0,-1),new Grad(-1,-1,0,1),new Grad(-1,-1,0,-1),
new Grad(1,1,1,0),new Grad(1,1,-1,0),new Grad(1,-1,1,0),new Grad(1,-1,-1,0),
new Grad(-1,1,1,0),new Grad(-1,1,-1,0),new Grad(-1,-1,1,0),new Grad(-1,-1,-1,0)};
private static short p_supply[] = {151,160,137,91,90,15, //this contains all the numbers between 0 and 255, these are put in a random order depending upon the seed
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};
private short p[]=new short[p_supply.length];
// To remove the need for index wrapping, double the permutation table length
private short perm[] = new short[512];
private short permMod12[] = new short[512];
public SimplexNoise_octave(int seed) {
p=p_supply.clone();
if (seed==RANDOMSEED){
Random rand=new Random();
seed=rand.nextInt();
}
//the random for the swaps
Random rand=new Random(seed);
//the seed determines the swaps that occur between the default order and the order we're actually going to use
for(int i=0;i<NUMBEROFSWAPS;i++){
int swapFrom=rand.nextInt(p.length);
int swapTo=rand.nextInt(p.length);
short temp=p[swapFrom];
p[swapFrom]=p[swapTo];
p[swapTo]=temp;
}
for(int i=0; i<512; i++)
{
perm[i]=p[i & 255];
permMod12[i] = (short)(perm[i] % 12);
}
}
// Skewing and unskewing factors for 2, 3, and 4 dimensions
private static final double F2 = 0.5*(Math.sqrt(3.0)-1.0);
private static final double G2 = (3.0-Math.sqrt(3.0))/6.0;
private static final double F3 = 1.0/3.0;
private static final double G3 = 1.0/6.0;
private static final double F4 = (Math.sqrt(5.0)-1.0)/4.0;
private static final double G4 = (5.0-Math.sqrt(5.0))/20.0;
// This method is a *lot* faster than using (int)Math.floor(x)
private static int fastfloor(double x) {
int xi = (int)x;
return x<xi ? xi-1 : xi;
}
private static double dot(Grad g, double x, double y) {
return g.x*x + g.y*y; }
private static double dot(Grad g, double x, double y, double z) {
return g.x*x + g.y*y + g.z*z; }
private static double dot(Grad g, double x, double y, double z, double w) {
return g.x*x + g.y*y + g.z*z + g.w*w; }
// 2D simplex noise
public double noise(double xin, double yin) {
double n0, n1, n2; // Noise contributions from the three corners
// Skew the input space to determine which simplex cell we're in
double s = (xin+yin)*F2; // Hairy factor for 2D
int i = fastfloor(xin+s);
int j = fastfloor(yin+s);
double t = (i+j)*G2;
double X0 = i-t; // Unskew the cell origin back to (x,y) space
double Y0 = j-t;
double x0 = xin-X0; // The x,y distances from the cell origin
double y0 = yin-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 = permMod12[ii+perm[jj]];
int gi1 = permMod12[ii+i1+perm[jj+j1]];
int gi2 = permMod12[ii+1+perm[jj+1]];
// 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 simplex noise
public double noise(double xin, double yin, double zin) {
double n0, n1, n2, n3; // Noise contributions from the four corners
// Skew the input space to determine which simplex cell we're in
double s = (xin+yin+zin)*F3; // Very nice and simple skew factor for 3D
int i = fastfloor(xin+s);
int j = fastfloor(yin+s);
int k = fastfloor(zin+s);
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 = xin-X0; // The x,y,z distances from the cell origin
double y0 = yin-Y0;
double z0 = zin-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 = permMod12[ii+perm[jj+perm[kk]]];
int gi1 = permMod12[ii+i1+perm[jj+j1+perm[kk+k1]]];
int gi2 = permMod12[ii+i2+perm[jj+j2+perm[kk+k2]]];
int gi3 = permMod12[ii+1+perm[jj+1+perm[kk+1]]];
// 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 simplex noise, better simplex rank ordering method 2012-03-09
public double noise(double x, double y, double z, double w) {
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.
// Six pair-wise comparisons are performed between each possible pair
// of the four coordinates, and the results are used to rank the numbers.
int rankx = 0;
int ranky = 0;
int rankz = 0;
int rankw = 0;
if(x0 > y0) rankx++; else ranky++;
if(x0 > z0) rankx++; else rankz++;
if(x0 > w0) rankx++; else rankw++;
if(y0 > z0) ranky++; else rankz++;
if(y0 > w0) ranky++; else rankw++;
if(z0 > w0) rankz++; else rankw++;
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.
// Rank 3 denotes the largest coordinate.
i1 = rankx >= 3 ? 1 : 0;
j1 = ranky >= 3 ? 1 : 0;
k1 = rankz >= 3 ? 1 : 0;
l1 = rankw >= 3 ? 1 : 0;
// Rank 2 denotes the second largest coordinate.
i2 = rankx >= 2 ? 1 : 0;
j2 = ranky >= 2 ? 1 : 0;
k2 = rankz >= 2 ? 1 : 0;
l2 = rankw >= 2 ? 1 : 0;
// Rank 1 denotes the second smallest coordinate.
i3 = rankx >= 1 ? 1 : 0;
j3 = ranky >= 1 ? 1 : 0;
k3 = rankz >= 1 ? 1 : 0;
l3 = rankw >= 1 ? 1 : 0;
// The fifth corner has all coordinate offsets = 1, so no need to compute that.
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);
}
// Inner class to speed upp gradient computations
// (array access is a lot slower than member access)
private static class Grad
{
double x, y, z, w;
Grad(double x, double y, double z)
{
this.x = x;
this.y = y;
this.z = z;
}
Grad(double x, double y, double z, double w)
{
this.x = x;
this.y = y;
this.z = z;
this.w = w;
}
}
}
坦率地说，我认为整个类是一个带有公共构造函数public SimplexNoise_octave(int seed)和3个公共方法public double noise(double xin, double yin)、public double noise(double xin, double yin, double zin)和public double noise(double x, double y, double z, double w)的黑盒。
您可以使用这些方法，就像使用perlin噪波等效方法一样。
SimplexNoise_octave(int seed)
为你想要的每个倍频程创建1个SimplexNoise_octave，每个倍频程都应该有自己的种子
public double noise(double xin, double yin)
调用以获取该八度音阶在这些坐标下的特定噪声值。笔记坐标应该被预先缩放（稍后）。其他CCD_ 5函数是相同的，但用于更高维。
创建八度音阶
就像在perlin噪波中一样，你通常会将几个八度音阶的噪波组合起来创建分形噪波（这会给你带来类似地形的特征）。请注意，三维地形高度是由二维噪波创建的。
使用以下比率组合几个八度音阶
frequency = 2^i
amplitude = persistence^i
对于每个倍频程（i），您将输入坐标除以频率，并将结果乘以振幅；这给人一种类似地形的外观。持久性用于影响地形的外观，高持久性（朝向1）会产生多岩石的山地地形。低持续性（接近0）会产生缓慢变化的平坦地形。有关更多详细信息，请参阅标记页。
以下是如何使用的示例：
import java.util.Random;
public class SimplexNoise {
SimplexNoise_octave[] octaves;
double[] frequencys;
double[] amplitudes;
int largestFeature;
double persistence;
int seed;
public SimplexNoise(int largestFeature,double persistence, int seed){
this.largestFeature=largestFeature;
this.persistence=persistence;
this.seed=seed;
//recieves a number (eg 128) and calculates what power of 2 it is (eg 2^7)
int numberOfOctaves=(int)Math.ceil(Math.log10(largestFeature)/Math.log10(2));
octaves=new SimplexNoise_octave[numberOfOctaves];
frequencys=new double[numberOfOctaves];
amplitudes=new double[numberOfOctaves];
Random rnd=new Random(seed);
for(int i=0;i<numberOfOctaves;i++){
octaves[i]=new SimplexNoise_octave(rnd.nextInt());
frequencys[i] = Math.pow(2,i);
amplitudes[i] = Math.pow(persistence,octaves.length-i);
}
}
public double getNoise(int x, int y){
double result=0;
for(int i=0;i<octaves.length;i++){
//double frequency = Math.pow(2,i);
//double amplitude = Math.pow(persistence,octaves.length-i);
result=result+octaves[i].noise(x/frequencys[i], y/frequencys[i])* amplitudes[i];
}
return result;
}
public double getNoise(int x,int y, int z){
double result=0;
for(int i=0;i<octaves.length;i++){
double frequency = Math.pow(2,i);
double amplitude = Math.pow(persistence,octaves.length-i);
result=result+octaves[i].noise(x/frequency, y/frequency,z/frequency)* amplitude;
}
return result;
}
}
这创建了八度音阶，其大小在1和largestFeature之间，我发现这很有用，但1是最小的大小并没有什么特别之处，你可以修改它。它的输出介于-1和1之间，根据需要进行缩放。
用法
使用这个类的一个主要方法示例如下
public static void main(String args[]){
SimplexNoise simplexNoise=new SimplexNoise(100,0.1,5000);
double xStart=0;
double XEnd=500;
double yStart=0;
double yEnd=500;
int xResolution=200;
int yResolution=200;
double[][] result=new double[xResolution][yResolution];
for(int i=0;i<xResolution;i++){
for(int j=0;j<yResolution;j++){
int x=(int)(xStart+i*((XEnd-xStart)/xResolution));
int y=(int)(yStart+j*((yEnd-yStart)/yResolution));
result[i][j]=0.5*(1+simplexNoise.getNoise(x,y));
}
}
ImageWriter.greyWriteImage(result);
}
这个方法使用我自己的ImageWriter类来将输出呈现到文件
import java.awt.Color;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
import javax.imageio.ImageIO;
public class ImageWriter {
//just convinence methods for debug
public static void greyWriteImage(double[][] data){
//this takes and array of doubles between 0 and 1 and generates a grey scale image from them
BufferedImage image = new BufferedImage(data.length,data[0].length, BufferedImage.TYPE_INT_RGB);
for (int y = 0; y < data[0].length; y++)
{
for (int x = 0; x < data.length; x++)
{
if (data[x][y]>1){
data[x][y]=1;
}
if (data[x][y]<0){
data[x][y]=0;
}
Color col=new Color((float)data[x][y],(float)data[x][y],(float)data[x][y]);
image.setRGB(x, y, col.getRGB());
}
}
try {
// retrieve image
File outputfile = new File("saved.png");
outputfile.createNewFile();
ImageIO.write(image, "png", outputfile);
} catch (IOException e) {
//o no! Blank catches are bad
throw new RuntimeException("I didn't handle this very well");
}
}
}