WELCOME! TODAYS TOPICS: SOFT SHADOWS GLASS GP1 – Ray Tracing Recap In 3D, light falls Angle also plays a role: off with distance: 2 Iin = IL / r Iin *= dot(L,N) And finally, material color. GP1 – Ray Tracing Homework GP1 – Ray Tracing GP1 – Ray Tracing Caustic(?) Dielectric(?) Shadow Sphere Plane N Quadratic falloff Reflection B T P∙T - O∙T = fx u . scale P∙B - O∙B = fy v . shift P = O + fx * T + fy * B . modulo GP1 – Ray Tracing Dielectrics: reflect and transmit 1. Reflection: RR = Reflect( D, N ); 2. Transmittance: RT = ? 3. Ratio between the two: return ? * Trace(RR) + ? * Trace(RT) nt = index/1, nnt = 1 / index, ddn = D∙N cos2t = 1 – nnt2 * (1 – ddn2) cos2t <= 0 ? TIR Snell 2 RT = normalize( D * nnt – N * (ddn * nnt * sqrt( cos t )) ); v = (nt - 1)2/(nt + 1)2 Fresnel 5 WT = v + (1 - v) * (1 + ddn) , WR = 1 – WT Schlick N GP1 – Ray Tracing Christopher Schlick Willebrord Snel Augustin-Jean Fresnel GP1 – Ray Tracing SO SHA FT DOW GP1 – Ray Tracing GP1 – Ray Tracing 25% 33.3% GP1 – Ray Tracing GP1 – Ray Tracing GP1 – Ray Tracing GP1 – Ray Tracing Soft shadows: . Approximated using N random rays . That means we get noise . More rays, less noise . Reduce variance: stratification . Reduce variance: converging GP1 – Ray Tracing Other applications of randomness: Anti-aliasing: send rays to random position on pixel fx = x / SCRWIDTH fx = (x + rand()) / SCRWIDTH Depth of field: send rays from random position on lens O += float3( rand() – 0.5f, rand() – 0.5f, rand() – 0.5f ) Motion blur: send rays to object at random time t = frameTime + rand() Dispersion: randomly pick wavelength for primary ray λ = rand() Use a high-quality random generator to prevent patterns: MERSENNE TWISTER GP1 – Ray Tracing Other applications of randomness: Homework Implement glass 1. Make sure your reflections are working 2. Make sure you have N dot L and 1/r^2 shading 3. Modify Renderer::Trace Next week: DEPTH OF FIELD ACCELERATION STRUCTURE.