#include<graphics.h>#include<conio.h>#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); }
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; 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); sum += (1.0f - refl) * trace(x - nx * BIAS, y - ny * BIAS, rx, ry, depth + 1); } else refl = 1.0f; } 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 0int main() { float nx = -1.0f, ny = 0.0f, eta1 = 1.0f, eta2 = 1.5f; 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)); } 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)); }}#elseint main() { initgraph(W,H); 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)); putpixel(x,y,RGB(p[0],p[1],p[2])); } } _getch();}#endif
