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fresnel.c
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#include "svpng.inc"
#include <math.h> // fabsf(), fminf(), fmaxf(), sinf(), cosf(), sqrt()
#include <stdlib.h> // rand(), RAND_MAX
#define TWO_PI 6.28318530718f
#define W 512
#define H 512
#define N 256
#define MAX_STEP 64
#define MAX_DISTANCE 5.0f
#define EPSILON 1e-6f
#define BIAS 1e-4f
#define MAX_DEPTH 3
typedef struct { float sd, emissive, reflectivity, eta; } Result;
unsigned char img[W * H * 3];
float circleSDF(float x, float y, float cx, float cy, float r) {
float ux = x - cx, uy = y - cy;
return sqrtf(ux * ux + uy * uy) - r;
}
float boxSDF(float x, float y, float cx, float cy, float theta, float sx, float sy) {
float costheta = cosf(theta), sintheta = sinf(theta);
float dx = fabs((x - cx) * costheta + (y - cy) * sintheta) - sx;
float dy = fabs((y - cy) * costheta - (x - cx) * sintheta) - sy;
float ax = fmaxf(dx, 0.0f), ay = fmaxf(dy, 0.0f);
return fminf(fmaxf(dx, dy), 0.0f) + sqrtf(ax * ax + ay * ay);
}
float planeSDF(float x, float y, float px, float py, float nx, float ny) {
return (x - px) * nx + (y - py) * ny;
}
Result unionOp(Result a, Result b) {
return a.sd < b.sd ? a : b;
}
Result intersectOp(Result a, Result b) {
return a.sd > b.sd ? a : b;
}
Result subtractOp(Result a, Result b) {
Result r = a;
r.sd = (a.sd > -b.sd) ? a.sd : -b.sd;
return r;
}
Result scene(float x, float y) {
Result a = { circleSDF(x, y, -0.2f, -0.2f, 0.1f), 10.0f, 0.0f, 0.0f };
Result b = { boxSDF(x, y, 0.5f, 0.5f, 0.0f, 0.3, 0.2f), 0.0f, 0.2f, 1.5f };
Result c = { circleSDF(x, y, 0.5f, -0.5f, 0.05f), 20.0f, 0.0f, 0.0f };
Result d = { circleSDF(x, y, 0.5f, 0.2f, 0.35f), 0.0f, 0.2f, 1.5f };
Result e = { circleSDF(x, y, 0.5f, 0.8f, 0.35f), 0.0f, 0.2f, 1.5f };
Result f = { boxSDF(x, y, 0.5f, 0.5f, 0.0f, 0.2, 0.1f), 0.0f, 0.2f, 1.5f };
Result g = { circleSDF(x, y, 0.5f, 0.12f, 0.35f), 0.0f, 0.2f, 1.5f };
Result h = { circleSDF(x, y, 0.5f, 0.87f, 0.35f), 0.0f, 0.2f, 1.5f };
Result i = { circleSDF(x, y, 0.5f, 0.5f, 0.2f), 0.0f, 0.2f, 1.5f };
Result j = { planeSDF(x, y, 0.5f, 0.5f, 0.0f, -1.0f), 0.0f, 0.2f, 1.5f };
return unionOp(a, b);
// return unionOp(c, intersectOp(d, e));
// return unionOp(c, subtractOp(f, unionOp(g, h)));
// return unionOp(c, intersectOp(i, j));
}
void gradient(float x, float y, float* nx, float* ny) {
*nx = (scene(x + EPSILON, y).sd - scene(x - EPSILON, y).sd) * (0.5f / EPSILON);
*ny = (scene(x, y + EPSILON).sd - scene(x, y - EPSILON).sd) * (0.5f / EPSILON);
}
void reflect(float ix, float iy, float nx, float ny, float* rx, float* ry) {
float idotn2 = (ix * nx + iy * ny) * 2.0f;
*rx = ix - idotn2 * nx;
*ry = iy - idotn2 * ny;
}
int refract(float ix, float iy, float nx, float ny, float eta, float* rx, float* ry) {
float idotn = ix * nx + iy * ny;
float k = 1.0f - eta * eta * (1.0f - idotn * idotn);
if (k < 0.0f)
return 0; // Total internal reflection
float a = eta * idotn + sqrtf(k);
*rx = eta * ix - a * nx;
*ry = eta * iy - a * ny;
return 1;
}
float fresnel(float cosi, float cost, float etai, float etat) {
float rs = (etat * cosi - etai * cost) / (etat * cosi + etai * cost);
float rp = (etai * cosi - etat * cost) / (etai * cosi + etat * cost);
return (rs * rs + rp * rp) * 0.5f;
}
float schlick(float cosi, float cost, float etai, float etat) {
float r0 = (etai - etat) / (etai + etat);
r0 *= r0;
float a = 1.0f - (etai < etat ? cosi : cost);
float aa = a * a;
return r0 + (1.0f - r0) * aa * aa * a;
}
float trace(float ox, float oy, float dx, float dy, int depth) {
float t = 1e-3f;
float sign = scene(ox, oy).sd > 0.0f ? 1.0f : -1.0f;
for (int i = 0; i < MAX_STEP && t < MAX_DISTANCE; i++) {
float x = ox + dx * t, y = oy + dy * t;
Result r = scene(x, y);
if (r.sd * sign < EPSILON) {
float sum = r.emissive;
if (depth < MAX_DEPTH && (r.reflectivity > 0.0f || r.eta > 0.0f)) {
float nx, ny, rx, ry, refl = r.reflectivity;
gradient(x, y, &nx, &ny);
float s = 1.0f / (nx * nx + ny * ny);
nx *= sign * s;
ny *= sign * s;
if (r.eta > 0.0f) {
if (refract(dx, dy, nx, ny, sign < 0.0f ? r.eta : 1.0f / r.eta, &rx, &ry)) {
float cosi = -(dx * nx + dy * ny);
float cost = -(rx * nx + ry * ny);
refl = sign < 0.0f ? fresnel(cosi, cost, r.eta, 1.0f) : fresnel(cosi, cost, 1.0f, r.eta);
// refl = sign < 0.0f ? schlick(cosi, cost, r.eta, 1.0f) : schlick(cosi, cost, 1.0f, r.eta);
sum += (1.0f - refl) * trace(x - nx * BIAS, y - ny * BIAS, rx, ry, depth + 1);
}
else
refl = 1.0f; // Total internal reflection
}
if (refl > 0.0f) {
reflect(dx, dy, nx, ny, &rx, &ry);
sum += refl * trace(x + nx * BIAS, y + ny * BIAS, rx, ry, depth + 1);
}
}
return sum;
}
t += r.sd * sign;
}
return 0.0f;
}
float sample(float x, float y) {
float sum = 0.0f;
for (int i = 0; i < N; i++) {
float a = TWO_PI * (i + (float)rand() / RAND_MAX) / N;
sum += trace(x, y, cosf(a), sinf(a), 0);
}
return sum / N;
}
#if 0
int main() {
float nx = -1.0f, ny = 0.0f, eta1 = 1.0f, eta2 = 1.5f;
// Air to denser medium
for (int i = 0; i <= 90; i++) {
float t = i * TWO_PI / 360.0f, ix = cosf(t), iy = sinf(t), rx, ry;
refract(ix, iy, nx, ny, eta1 / eta2, &rx, &ry);
float cosi = -(ix * nx + iy * ny);
float cost = -(rx * nx + ry * ny);
printf("%d,%f,%f\n", i,
fresnel(cosi, cost, eta1, eta2),
schlick(cosi, cost, eta1, eta2));
}
// Denser medium to air
for (int i = 0; i <= 90; i++) {
float t = i * TWO_PI / 360.0f, ix = cosf(t), iy = sinf(t), rx, ry;
int tir = !refract(ix, iy, nx, ny, eta2 / eta1, &rx, &ry);
float cosi = -(ix * nx + iy * ny);
float cost = -(rx * nx + ry * ny);
printf("%d,%f,%f\n", i,
tir ? 1.0f : fresnel(cosi, cost, eta2, eta1),
tir ? 1.0f : schlick(cosi, cost, eta2, eta1));
}
}
#else
int main() {
unsigned char* p = img;
for (int y = 0; y < H; y++)
for (int x = 0; x < W; x++, p += 3)
p[0] = p[1] = p[2] = (int)(fminf(sample((float)x / W, (float)y / H) * 255.0f, 255.0f));
svpng(fopen("fresnel.png", "wb"), W, H, img, 0);
}
#endif