__constant double earth_radius = $earth_radius; __constant double atmos_height = $atmos_height; __constant double3 rayleigh_beta = (double3)$rayleigh_beta; __constant double3 mie_beta = (double3)$mie_beta; __constant double mie_g = $mie_g; __constant int ray_samples = $ray_samples; __constant int light_samples = $light_samples; __constant double exposure = $exposure; bool insideAtmosphere(double3 pos) { return length(pos) < earth_radius + atmos_height; } double altitude(double3 pos) { return length(pos) - earth_radius; } /// Solve x^2 + px + q bool solvePolynomialOfDegreeTwo(double p, double q, double* x1, double* x2) { const double pHalf = 0.5*p; const double inner = pHalf*pHalf - q; if (inner >= 0.0) { *x1 = -pHalf + sqrt(inner); *x2 = -pHalf - sqrt(inner); return true; } else { return false; } } /// Interection of origin + d*dir and a sphere of radius r for normalized dir bool solveRaySphereIntersection(double3 origin, double3 dir, double r, double* d0, double* d1) { const double p = 2 * dot(dir,origin); const double q = dot(origin,origin) - r*r; if (solvePolynomialOfDegreeTwo(p, q, d0, d1)) { if (*d0 > *d1) { double tmp = *d1; *d1 = *d0; *d0 = tmp; } return true; } else { return false; } } /// Map {0,...,screenX}x{0,...,screenY} to [-1,1]^2 double2 getNormalizedScreenPos(double x, double y) { return (double2)( 2.0 * (0.5 - x / $size_x) * $size_x.0 / $size_y.0, 2.0 * (0.5 - y / $size_y) ); } /// Pinhole camera double3 getEyeRayDir(double2 screen_pos, double3 eye_pos, double3 eye_target) { const double3 forward = normalize(eye_target - eye_pos); const double3 right = normalize(cross((double3)(0.0, 0.0, -1.0), forward)); const double3 up = normalize(cross(forward, right)); return normalize(screen_pos.x*right + screen_pos.y*up + $zoom*forward); } /// Fisheye camera bool inFishEyeView(double2 screen_pos) { return length(screen_pos) <= 1.0; } double3 getFishEyeRayDir(double2 screen_pos) { const double phi = atan2(screen_pos.y, screen_pos.x); const double theta = acos(1.0 - (screen_pos.x*screen_pos.x + screen_pos.y*screen_pos.y)); return (double3)(sin(theta)*cos(phi), sin(theta)*sin(phi), cos(theta)); } /// Return true iff earth is hit by rays along dir bool isVisible(double3 origin, double3 dir) { double e0, e1; return !solveRaySphereIntersection(origin, dir, earth_radius, &e0, &e1) || (e0 < 0 && e1 < 0); } /// Return distance between entering and exiting the atmosphere double lengthOfRayInAtmosphere(double3 origin, double3 dir) { double d0, d1; solveRaySphereIntersection(origin, dir, earth_radius + atmos_height, &d0, &d1); return d1 - d0; } /// Return light depths of secondary rays double2 lightDepth(double3 curr, double3 sun) { const double h = lengthOfRayInAtmosphere(curr, sun) / light_samples; double2 depth = 0.0; for (unsigned i = 0; i < light_samples; ++i) { const double height = altitude(curr + (i+0.5)*h*sun); depth += exp(-height / (double2)($rayleigh_atmos_height, $mie_atmos_height)) * h; } return depth; } /// Calculate color of light along ray double3 scatter(double3 origin, double3 dir, double dist, double3 sun) { double3 rayleigh_sum = 0.0; double3 mie_sum = 0.0; double rayleigh_depth = 0.0; double mie_depth = 0.0; const double h = dist / ray_samples; for (unsigned i = 0; i < ray_samples; ++i) { double3 curr = origin + (i+0.5)*h*dir; if (isVisible(curr, sun)) { const double height = altitude(curr); const double rayleigh_h = exp(-height / $rayleigh_atmos_height) * h; const double mie_h = exp(-height / $mie_atmos_height) * h; rayleigh_depth += rayleigh_h; mie_depth += mie_h; const double2 light_depth = lightDepth(curr, sun); const double3 tau = rayleigh_beta * (rayleigh_depth + light_depth.x) + mie_beta * (mie_depth + light_depth.y); const double3 attenuation = exp(-tau); rayleigh_sum += attenuation * rayleigh_h; mie_sum += attenuation * mie_h; } } const double mu = dot(dir,sun); const double rayleigh_phase = 0.75 * (1.0 + mu*mu); const double mie_phase = 0.5*(1-mie_g*mie_g)/pow(1+mie_g*mie_g-2*mie_g*mu,1.5); return rayleigh_sum*rayleigh_beta*rayleigh_phase + mie_sum*mie_beta*mie_phase; } void setColor(__global double* result, unsigned x, unsigned y, double3 color) { result[3*$size_x*y + 3*x + 0] = color.x; result[3*$size_x*y + 3*x + 1] = color.y; result[3*$size_x*y + 3*x + 2] = color.z; } void render(__global double* result, unsigned x, unsigned y, double3 origin, double3 ray_dir, double3 sun) { double d0, d1; if (!solveRaySphereIntersection(origin, ray_dir, earth_radius + atmos_height, &d0, &d1)) { setColor(result, x, y, 0.0); return; } double min_dist = d0; double max_dist = d1; if (insideAtmosphere(origin)) { min_dist = 0.0; if (solveRaySphereIntersection(origin, ray_dir, earth_radius, &d0, &d1) && d1 > 0) { max_dist = max(0.0, d0); } } else { if (solveRaySphereIntersection(origin, ray_dir, earth_radius, &d0, &d1)) { max_dist = d0; } } const double3 ray_origin = origin + min_dist*ray_dir; const double ray_length = max_dist - min_dist; double3 color = scatter(ray_origin, ray_dir, ray_length, normalize(sun)); color = 1.0 - exp(-exposure * color); setColor(result, x, y, color); } __kernel void render_fisheye(__global double* result, double3 eye_pos, double3 eye_dir, double3 sun) { const unsigned x = get_global_id(0); const unsigned y = get_global_id(1); const double2 screen_pos = getNormalizedScreenPos(x, y); if (!inFishEyeView(screen_pos)) { setColor(result, x, y, 1.0); return; } const double3 ray_dir = getFishEyeRayDir(screen_pos); render(result, x, y, eye_pos, ray_dir, sun); } __kernel void render_pinhole(__global double* result, double3 eye_pos, double3 eye_dir, double3 sun) { const unsigned x = get_global_id(0); const unsigned y = get_global_id(1); const double2 screen_pos = getNormalizedScreenPos(x, y); const double3 ray_dir = getEyeRayDir(screen_pos, eye_pos, eye_pos + eye_dir); render(result, x, y, eye_pos, ray_dir, sun); }