Perlin Noise或者更新的Simplex Noise非常适合于地形生成。
如果我正确理解算法,它是通过将不同频率的噪声梯度(随机点之间的线性插值)相加而工作的。我还找到了一个更详细的解释。
我在Google Code上找到了一个Simplex Noise库,
以及实现:
namespace SimplexNoise
{
public class Noise
{
public static float Generate(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;
t0 *= t0;
n0 = t0 * t0 * grad(perm[i0 & 0xff], x0);
float t1 = 1.0f - x1*x1;
t1 *= t1;
n1 = t1 * t1 * grad(perm[i1 & 0xff], x1);
return 0.395f * (n0 + n1);
}
public static float Generate(float x, float y)
{
const float F2 = 0.366025403f;
const float G2 = 0.211324865f;
float n0, n1, n2;
float s = (x+y)*F2;
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;
float Y0 = j-t;
float x0 = x-X0;
float y0 = y-Y0;
int i1, j1;
if(x0>y0) {i1=1; j1=0;}
else {i1=0; j1=1;}
float x1 = x0 - i1 + G2;
float y1 = y0 - j1 + G2;
float x2 = x0 - 1.0f + 2.0f * G2;
float y2 = y0 - 1.0f + 2.0f * G2;
int ii = i % 256;
int jj = j % 256;
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);
}
return 40.0f * (n0 + n1 + n2);
}
public static float Generate(float x, float y, float z)
{
const float F3 = 0.333333333f;
const float G3 = 0.166666667f;
float n0, n1, n2, n3;
float s = (x+y+z)*F3;
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;
float Y0 = j-t;
float Z0 = k-t;
float x0 = x-X0;
float y0 = y-Y0;
float z0 = z-Z0;
int i1, j1, k1;
int i2, j2, k2;
if(x0>=y0) {
if(y0>=z0)
{ i1=1; j1=0; k1=0; i2=1; j2=1; k2=0; }
else if(x0>=z0) { i1=1; j1=0; k1=0; i2=1; j2=0; k2=1; }
else { i1=0; j1=0; k1=1; i2=1; j2=0; k2=1; }
}
else {
if(y0<z0) { i1=0; j1=0; k1=1; i2=0; j2=1; k2=1; }
else if(x0<z0) { i1=0; j1=1; k1=0; i2=0; j2=1; k2=1; }
else { i1=0; j1=1; k1=0; i2=1; j2=1; k2=0; }
}
float x1 = x0 - i1 + G3;
float y1 = y0 - j1 + G3;
float z1 = z0 - k1 + G3;
float x2 = x0 - i2 + 2.0f*G3;
float y2 = y0 - j2 + 2.0f*G3;
float z2 = z0 - k2 + 2.0f*G3;
float x3 = x0 - 1.0f + 3.0f*G3;
float y3 = y0 - 1.0f + 3.0f*G3;
float z3 = z0 - 1.0f + 3.0f*G3;
int ii = i % 256;
int jj = j % 256;
int kk = k % 256;
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);
}
return 32.0f * (n0 + n1 + n2 + n3);
}
private static byte[] perm = new byte[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
};
private static int FastFloor(float x)
{
return (x > 0) ? ((int)x) : (((int)x) - 1);
}
private static float grad( int hash, float x )
{
int h = hash & 15;
float grad = 1.0f + (h & 7);
if ((h & 8) != 0) grad = -grad;
return ( grad * x );
}
private static float grad( int hash, float x, float y )
{
int h = hash & 7;
float u = h<4 ? x : y;
float v = h<4 ? y : x;
return ((h&1) != 0 ? -u : u) + ((h&2) != 0 ? -2.0f*v : 2.0f*v);
}
private static float grad( int hash, float x, float y , float z ) {
int h = hash & 15;
float u = h<8 ? x : y;
float v = h<4 ? y : h==12||h==14 ? x : z;
return ((h&1) != 0 ? -u : u) + ((h&2) != 0 ? -v : v);
}
private static float grad( int hash, float x, float y, float z, float t ) {
int h = hash & 31;
float u = h<24 ? x : y;
float v = h<16 ? y : z;
float w = h<8 ? z : t;
return ((h&1) != 0 ? -u : u) + ((h&2) != 0 ? -v : v) + ((h&4) != 0 ? -w : w);
}
}
}