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OpenSimplex 2 Derivative Impl

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This commit is contained in:
Zoe Gidiere 2024-09-23 20:29:41 -06:00
parent 017b4608bc
commit bd73427072
2 changed files with 200 additions and 1 deletions
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2
common/addons/config-noise-function/src/main/java/com/dfsek/terra/addons/noise/samplers/noise/simplex/OpenSimplex2SSampler.java
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@ -479,7 +479,7 @@ public class OpenSimplex2SSampler extends SimplexStyleSampler {
int yNMask = (int) (-0.5 - yi);
int zNMask = (int) (-0.5 - zi);
double[] out = { 0.0f, 0.0f, 0.0f };
double[] out = { 0.0f, 0.0f, 0.0f, 0.0f };
double x0 = xi + xNMask;
double y0 = yi + yNMask;

199
common/addons/config-noise-function/src/main/java/com/dfsek/terra/addons/noise/samplers/noise/simplex/OpenSimplex2Sampler.java
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@ -153,4 +153,203 @@ public class OpenSimplex2Sampler extends SimplexStyleSampler {
return value * 32.69428253173828125;
}
@Override
public boolean isDifferentiable() {
return true;
}
@Override
public double[] getNoiseDerivativeRaw(long sl, double x, double y) {
int seed = (int) sl;
// 2D OpenSimplex2 case uses the same algorithm as ordinary Simplex.
final double G2 = (3 - SQRT3) / 6;
final double F2 = 0.5f * (SQRT3 - 1);
double s = (x + y) * F2;
x += s;
y += s;
int i = (int) Math.floor(x);
int j = (int) Math.floor(y);
double xi = x - i;
double yi = y - j;
double t = (xi + yi) * G2;
double x0 = xi - t;
double y0 = yi - t;
i *= PRIME_X;
j *= PRIME_Y;
double[] out = { 0.0f, 0.0f, 0.0f };
double a = 0.5 - x0 * x0 - y0 * y0;
if(a > 0) {
double aa = a * a, aaa = aa * a, aaaa = aa * aa;
int gi = gradCoordIndex(seed, i, j);
double gx = GRADIENTS_2_D[gi], gy = GRADIENTS_2_D[gi | 1];
double rampValue = gx * x0 + gy * y0;
out[0] += aaaa * rampValue;
out[1] += gx * aaaa - 8 * rampValue * aaa * x0;
out[2] += gy * aaaa - 8 * rampValue * aaa * y0;
}
double c = 2 * (1 - 2 * G2) * (1 / G2 - 2) * t + ((-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a);
if(c > 0) {
double x2 = x0 + (2 * G2 - 1);
double y2 = y0 + (2 * G2 - 1);
double cc = c * c, ccc = cc * c, cccc = cc * cc;
int gi = gradCoordIndex(seed, i + PRIME_X, j + PRIME_Y);
double gx = GRADIENTS_2_D[gi], gy = GRADIENTS_2_D[gi | 1];
double rampValue = gx * x2 + gy * y2;
out[0] += cccc * rampValue;
out[1] += gx * cccc - 8 * rampValue * ccc * x2;
out[2] += gy * cccc - 8 * rampValue * ccc * y2; }
if(y0 > x0) {
double x1 = x0 + G2;
double y1 = y0 + (G2 - 1);
double b = 0.5 - x1 * x1 - y1 * y1;
if(b > 0) {
double bb = b * b, bbb = bb * b, bbbb = bb * bb;
int gi = gradCoordIndex(seed, i, j + PRIME_Y);
double gx = GRADIENTS_2_D[gi], gy = GRADIENTS_2_D[gi | 1];
double rampValue = gx * x1 + gy * y1;
out[0] += bbbb * rampValue;
out[1] += gx * bbbb - 8 * rampValue * bbb * x1;
out[2] += gy * bbbb - 8 * rampValue * bbb * y1; }
} else {
double x1 = x0 + (G2 - 1);
double y1 = y0 + G2;
double b = 0.5 - x1 * x1 - y1 * y1;
if(b > 0) {
double bb = b * b, bbb = bb * b, bbbb = bb * bb;
int gi = gradCoordIndex(seed, i + PRIME_X, j);
double gx = GRADIENTS_2_D[gi], gy = GRADIENTS_2_D[gi | 1];
double rampValue = gx * x1 + gy * y1;
out[0] += bbbb * rampValue;
out[1] += gx * bbbb - 8 * rampValue * bbb * x1;
out[2] += gy * bbbb - 8 * rampValue * bbb * y1; }
}
out[0] *= 99.83685446303647f;
out[1] *= 99.83685446303647f;
out[2] *= 99.83685446303647f;
return out;
}
@Override
public double[] getNoiseDerivativeRaw(long sl, double x, double y, double z) {
int seed = (int) sl;
// 3D OpenSimplex2Sampler case uses two offset rotated cube grids.
final double R3 = (2.0 / 3.0);
double r = (x + y + z) * R3; // Rotation, not skew
x = r - x;
y = r - y;
z = r - z;
int i = (int) Math.round(x);
int j = (int) Math.round(y);
int k = (int) Math.round(z);
double x0 = x - i;
double y0 = y - j;
double z0 = z - k;
int xNSign = (int) (-1.0 - x0) | 1;
int yNSign = (int) (-1.0 - y0) | 1;
int zNSign = (int) (-1.0 - z0) | 1;
double ax0 = xNSign * -x0;
double ay0 = yNSign * -y0;
double az0 = zNSign * -z0;
i *= PRIME_X;
j *= PRIME_Y;
k *= PRIME_Z;
double[] out = { 0.0f, 0.0f, 0.0f, 0.0f };
double a = (0.6f - x0 * x0) - (y0 * y0 + z0 * z0);
for(int l = 0; ; l++) {
if(a > 0) {
double aa = a * a, aaa = aa * a, aaaa = aa * aa;
int gi = gradCoordIndex(seed, i, j, k);
double gx = GRADIENTS_3D[gi], gy = GRADIENTS_3D[gi | 1], gz = GRADIENTS_3D[gi | 2];
double rampValue = gx * x0 + gy * y0 + gz * z0;
out[0] += aaaa * rampValue;
out[1] += gx * aaaa - 8 * rampValue * aaa * x0;
out[1] += gy * aaaa - 8 * rampValue * aaa * y0;
out[2] += gz * aaaa - 8 * rampValue * aaa * z0;
}
if(ax0 >= ay0 && ax0 >= az0) {
double b = a + ax0 + ax0;
if(b > 1) {
b -= 1;
double bb = b * b, bbb = bb * b, bbbb = bb * bb;
int gi = gradCoordIndex(seed, i - xNSign * PRIME_X, j, k);
double gx = GRADIENTS_3D[gi], gy = GRADIENTS_3D[gi | 1], gz = GRADIENTS_3D[gi | 2];
double rampValue = gx * (x0 + xNSign) + gy * y0 + gz * z0;
out[0] += bbbb * rampValue;
out[1] += gx * bbbb - 8 * rampValue * bbb * (x0 + xNSign);
out[1] += gy * bbbb - 8 * rampValue * bbb * y0;
out[2] += gz * bbbb - 8 * rampValue * bbb * z0;
}
} else if(ay0 > ax0 && ay0 >= az0) {
double b = a + ay0 + ay0;
if(b > 1) {
b -= 1;
double bb = b * b, bbb = bb * b, bbbb = bb * bb;
int gi = gradCoordIndex(seed, i, j - yNSign * PRIME_Y, k);
double gx = GRADIENTS_3D[gi], gy = GRADIENTS_3D[gi | 1], gz = GRADIENTS_3D[gi | 2];
double rampValue = gx * x0 + gy * (y0 + yNSign) + gz * z0;
out[0] += bbbb * rampValue;
out[1] += gx * bbbb - 8 * rampValue * bbb * x0;
out[1] += gy * bbbb - 8 * rampValue * bbb * (y0 + yNSign);
out[2] += gz * bbbb - 8 * rampValue * bbb * z0; }
} else {
double b = a + az0 + az0;
if(b > 1) {
b -= 1;
double bb = b * b, bbb = bb * b, bbbb = bb * bb;
int gi = gradCoordIndex(seed, i, j, k - zNSign * PRIME_Z);
double gx = GRADIENTS_3D[gi], gy = GRADIENTS_3D[gi | 1], gz = GRADIENTS_3D[gi | 2];
double rampValue = gx * x0 + gy * y0 + gz * (z0 + zNSign);
out[0] += bbbb * rampValue;
out[1] += gx * bbbb - 8 * rampValue * bbb * x0;
out[1] += gy * bbbb - 8 * rampValue * bbb * y0;
out[2] += gz * bbbb - 8 * rampValue * bbb * (z0 + zNSign); }
}
if(l == 1) break;
ax0 = 0.5 - ax0;
ay0 = 0.5 - ay0;
az0 = 0.5 - az0;
x0 = xNSign * ax0;
y0 = yNSign * ay0;
z0 = zNSign * az0;
a += (0.75 - ax0) - (ay0 + az0);
i += (xNSign >> 1) & PRIME_X;
j += (yNSign >> 1) & PRIME_Y;
k += (zNSign >> 1) & PRIME_Z;
xNSign = -xNSign;
yNSign = -yNSign;
zNSign = -zNSign;
seed = ~seed;
}
out[0] *= 32.69428253173828125;
out[1] *= 32.69428253173828125;
out[2] *= 32.69428253173828125;
out[3] *= 32.69428253173828125;
return out;
}
}