beerlambert.c

#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, absorption; } 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);
}

Result unionOp(Result a, Result b) {
    return a.sd < b.sd ? a : b;
}

Result scene(float x, float y) {
    Result a = { circleSDF(x, y, -0.2f, -0.2f, 0.1f), 10.0f, 0.0f, 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, 4.0f };
    return unionOp(a, b);
}

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 beerLambert(float a, float d) {
    return expf(-a * d);
}

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);
                        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 * beerLambert(r.absorption, t);
        }
        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;
}

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("beerlambert.png", "wb"), W, H, img, 0);
}