fractal brownian motion

Author: ssloy

out.jpg

@@ -8,14 +8,52 @@
 #include "geometry.h"
 
 const float sphere_radius   = 1.5;
-const float noise_amplitude = 0.2;
+const float noise_amplitude = 1.0;
+
+template <typename T> inline T lerp(const T &v0, const T &v1, float t) {
+    return v0 + (v1-v0)*std::max(0.f, std::min(1.f, t));
+}
+
+float hash(const float n) {
+    float x = sin(n)*43758.5453f;
+    return x-floor(x);
+}
+
+float noise(const Vec3f &x) {
+    Vec3f p(floor(x.x), floor(x.y), floor(x.z));
+    Vec3f f(x.x-p.x, x.y-p.y, x.z-p.z);
+    f = f*(f*(Vec3f(3.f, 3.f, 3.f)-f*2.f));
+    float n = p*Vec3f(1.f, 57.f, 113.f);
+    return lerp(lerp(
+                     lerp(hash(n +  0.f), hash(n +  1.f), f.x),
+                     lerp(hash(n + 57.f), hash(n + 58.f), f.x), f.y),
+                lerp(
+                    lerp(hash(n + 113.f), hash(n + 114.f), f.x),
+                    lerp(hash(n + 170.f), hash(n + 171.f), f.x), f.y), f.z);
+}
+
+Vec3f rotate(const Vec3f &v) {
+    return Vec3f(Vec3f(0.00,  0.80,  0.60)*v, Vec3f(-0.80,  0.36, -0.48)*v, Vec3f(-0.60, -0.48,  0.64)*v);
+}
+
+float fractal_brownian_motion(const Vec3f &x) {
+    Vec3f p = rotate(x);
+    float f = 0;
+    f += 0.5000*noise(p); p = p*2.32;
+    f += 0.2500*noise(p); p = p*3.03;
+    f += 0.1250*noise(p); p = p*2.61;
+    f += 0.0625*noise(p);
+    return f/0.9375;
+}
 
 float signed_distance(const Vec3f &p) {
-    float displacement = sin(16*p.x)*sin(16*p.y)*sin(16*p.z)*noise_amplitude;
+    float displacement = -fractal_brownian_motion(p*3.4)*noise_amplitude;
     return p.norm() - (sphere_radius + displacement);
 }
 
 bool sphere_trace(const Vec3f &orig, const Vec3f &dir, Vec3f &pos) {
+    if (orig*orig - pow(orig*dir, 2) > pow(sphere_radius, 2)) return false; // early discard
+
     pos = orig;
     for (size_t i=0; i<128; i++) {
         float d = signed_distance(pos);