Draw a sphere: Difference between revisions

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@@ Line 155: / Line 155: @@
              eeeeeeeeeeeee               </lang>
-===Fun with 3D simplex noise texture===
+===Fun with 3D noise texture===
 [[file:sphere-perlin.png]]
 <lang c>#include <stdio.h>
@@ Line 161: / Line 161: @@
 #include <math.h>
+typedef double FLOAT;
-/* see http://www.csee.umbc.edu/~olano/s2002c36/ch02.pdf */
+inline FLOAT
-static int B[] = {0x15, 0x38, 0x32, 0x2c, 0x0d, 0x13, 0x07, 0x2a};
+rnd(int x) { return ((x^0x5555) * 1103515245) / (FLOAT)(1 << 31); }
-inline int bitmix(int i, int j, int k)
+FLOAT nn(int i, int j)
 {
-	inline int b(int i, int j, int k, int n) {
+	return rnd( (i << (j & 10)) - (j << (i & 5)));
+}
-		return B[((i>>n & 1) << 2) | ((j>>n & 1) << 1) | (k>>n & 1)];
-	}
+FLOAT noise2(FLOAT x, FLOAT y)
+{
+	int i, j;
+	FLOAT u, v, r = 0, r1, r2;
+	i = floor(x), j = floor(y);
+	u = x - i, v = y - j;
+#if 1
+	u = u * u * (3 - 2 * u);
+	v = v * v * (3 - 2 * v);
+#else
+	u *= u; u *= (1 - u);
+	v *= v; v *= (1 - v);
+#endif
+	r1 = nn(i, j) * (1 - v) + nn(i, j + 1) * v;
+	r2 = nn(i + 1, j) * (1 - v) + nn(i + 1, j + 1) * v;
+	r = r1 * (1 - u) + r2 * u;
+	return r;
-	return	b(i, j, k, 0) + b(j, k, i, 1) + b(k, i, j, 2) +
-		b(i, j, k, 3) + b(j, k, i, 4) + b(k, i, j, 5) +
-		b(i, j, k, 6) + b(j, k, i, 7);
 }
-float noise(float x, float y, float z)
+FLOAT n3(int i, int j, int k)
 {
+	return rnd( (i << ((j + k) & 10)) - (j << ((k + i) & 5)) + (k << ((i + j) & 15)));
-	float s, u, v, w;
+}
-	int i, j, k, dir[3] = {0}, a, b;
-	float weight(int d) {
-		float s = (dir[0] + dir[1] + dir[2]) / 6.0f;
-		float x = u - dir[0] + s, y = v - dir[1] + s, z = w - dir[2] + s;
-		float t = .6f - (x * x + y * y + z * z);
-		float p, q, r;
-		int m, b01, b2, b3, b4, b5;
+FLOAT noise3(FLOAT x, FLOAT y, FLOAT z)
-		m = bitmix(i + dir[0], j + dir[1], k + dir[2]);
+{
-		dir[d]++;
+	int i, j, k;
+	FLOAT u, v, w, x1, x2, y1, y2;
+	i = floor(x), j = floor(y), k = floor(z);
-		if (t < 0) return 0;
+	u = x - i, v = y - j, w = z - k;
+#if 1
-		b01 = m & 3;
-		b2 = m>>2 & 1, b3 = m>>3 & 1, b4 = m>>4 & 1, b5 = m>>5 & 1;
+	u = u * u * (3 - 2 * u);
+	v = v * v * (3 - 2 * v);
-		switch(b01) {
-		case 1:		p = x, q = y, r = z; break;
+	w = w * w * (3 - 2 * w);
+#else
-		case 2:		p = y, q = z, r = x; break;
-		default:	p = z, q = x, r = y; break;
+	u *= u; u *= (1 - u);
+	v *= v; v *= (1 - v);
-		}
+	w *= w; w *= (1 - w);
+#endif
-		if (b5 == b3) p = -p;
+#define interp(a, b, c) a * (1 - c) + b * c
+	x1 = interp(n3(i, j, k), n3(i + 1, j, k), u);
-		if (b5 == b4) q = -q;
+	x2 = interp(n3(i, j + 1, k), n3(i + 1, j + 1, k), u);
-		if (b5 ^ (b4 ^ b3)) r = -r;
+	y1 = interp(x1, x2, v);
-		t *= t;
-		return 8 * t * t * (p + (b01 ? b2 ? r : q : q + r));
-	}
-	s = (x + y + z)/3;
+	x1 = interp(n3(i, j, k + 1), n3(i + 1, j, k + 1), u);
-	i = floorf(x + s), j = floorf(y + s), k = floorf(z + s);
+	x2 = interp(n3(i, j + 1, k + 1), n3(i + 1, j + 1, k + 1), u);
+	y2 = interp(x1, x2, v);
+	return interp(y1, y2, w);
-	s = (i + j + k) / 6.0f;
+}
-	u = x - i + s;
-	v = y - j + s;
-	w = z - k + s;
+FLOAT getnoise2(FLOAT x, FLOAT y)
-	a = u>=w ? u>=v ? 0 : 1 : v>=w ? 1 : 2;
+{
-	b = u< w ? u< v ? 0 : 1 : v< w ? 1 : 2;
+	int i;
-	return weight(a) + weight(3 - a - b) + weight(b) + weight(0);
+	FLOAT r = 0, w, s = 0;
+	for (i = 1; i <= 256; i <<= 1) {
+		w = 1./sqrt(i);
+		s += w;
+		r += noise2(x * i, y * i) * w;
+	}
+	return r / s / 2 + .5;
 }
-float getnoise(float *vv)
+FLOAT getnoise(FLOAT x, FLOAT y, FLOAT z)
 {
-	float v[3], r = 0;
 	int i;
-	for (i = 256; i > 8; i >>= 1) {
+	FLOAT r = 0, w, s = 0;
+	for (i = 1; i <= 32; i <<= 1) {
-		v[0] = vv[0] * 256/i;
-		v[1] = vv[1] * 256/i;
+		w = 1./i;
-		v[2] = vv[2] * 256/i;
+		s += w;
-		r += noise(v[0], v[1], v[2]) * i / 256;
+		r += (noise3(x * i, y * i, z * i) * w);
 	}
-	r = fmod(r * 2 + 2, 1);
+	r = fmod((r / s + 1) * 2, 1);
 	if (r < .4) return 0;
+	return r;
-	r *= -vv[0] + vv[1] + vv[2];
-	if (r < 0) r = .1; else r += .1;
-	if (r > 1) r = 1;
-	return sqrt(r);
 }
@@ Line 241: / Line 259: @@
 {
 	unsigned char pix[256 * 256], *p = pix;
-	float fv[256 * 256], *pf = fv;
+	FLOAT fv[256 * 256], *pf = fv;
-	float v[3], x, y, z;
 	int i, j;
+	FLOAT x, y, z, r;
 	FILE *fp;
 	for (i = 0; i < 256 * 256; i++) *pf++ = 0, *p++ = 0;
+	for (i = 0, p = pix; i < 256; i++) {
-	for (p = pix, i = 0; i < 256; i++) {
+		x = (i - 128) / 120.;
-		x = (i - 128) / 125.0;
-		v[0] = (x + 1) / 2;
 		for (j = 0; j < 256; j++, p++) {
-			y = (j - 128) / 125.0;
+			y = (j - 128) / 120.;
-			v[1] = (y + 1) / 2;
+			*p = i * getnoise2(x, y);
-			z = x * x + y * y;
-			if (z > 1) { *p = 0; continue; }
+			z = 1 - x*x - y*y;
-			z = sqrt(1 - z);
+			if (z < 0) { continue; }
-			v[2] = -z;
+			z = sqrt(z);
-			*p = getnoise(v) ? 80 : 0;
-			v[2] = z;
+			r = getnoise(x, y, -z);
-			z = getnoise(v);
+			if (r) *p = 50;
-			if (z > 0) *p = z * 128 + 127;
+			r = getnoise(x, y, z);
+			if (r) {
+				r = (x + y + z) / 2.3 + .5;
+				if (r > 1) r = 1;
+				*p = 180 * r + 70;
+			}
 		}
 	}
@@ Line 272: / Line 292: @@
 	fwrite(pix, 1, 256 * 256, fp);
 	fclose(fp);
 	return 0;
 }</lang>