Indire c t Diffuse and Glossy Illumination on the GPU

1. Indirect Diffuse and Glossy Illumination on the GPU István LazányiLászló Szirmay-KalosTU Budapest

2. Environment mapping for ideal reflections [Blinn & Newel, 1976] Environment map = Fast approximation of environmental effects

3. Environment mapping for ideal reflections (original) If the environment is very (or infinitely) far…  skybox (enlarged)

4. Environment mapping for ideal reflections If the environment is "close"… re-render environment map from the new reference point performance ?!

5. Environment mapping for ideal reflections Note: (classic) environment mapping cannot deal with "large" objects  storing depth information in the environment map ray-traced [Approximate Ray-Tracing…, Eurographics 2005]

6. Offline convolution:  preconvolved diffuse/specular map Environment mapping for diffuse & glossy reflections - classical Ideal reflection vs. indirect illumination: many sampling raysare necessary! Adding cosine-weighted contributions: = convolution

7. Environment mapping for diffuse & glossy reflections – our proposal • Take an environment map • (with depth info. in the alpha channel) 2. Evaluate the convolution integral on the fly where Δωi (i=1..N) corresponds to the texels of the environment mapωi = ? from a point x

8. Environment mapping for diffuse & glossy reflections – our proposal For the reference point: solid angles Δωican easily be calculated (no information is necessary about the environment! )

9. Environment mapping for diffuse & glossy reflections – our proposal For an arbitrary point x: to calculate solid angle Δωi  distance r’ is known  but cosθ’ is unknown Instead of storing orientation information about the environment, assume that the movement is small  cosine value is approx. the same as in the reference point

10. How about the bunny …? ? Environment mapping for diffuse & glossy reflections – our proposal Thus, localization means multiplying solid angle with a factor for each texel  precalculation of the convolution integral is not possible

11. Environment mapping for diffuse & glossy reflections – our proposal To allow real-time calculation the environment map is downsampled by averaging neighboring texels. (e.g. 128 x 128  4 x 4) ≈ clustering the texels of the environment into larger area lights

12. Results(Diffuse bunny) classical our proposal (75FPS @ 2x2, 20FPS @ 4x4)

13. Results(Glossy bunny, s=10) classical our proposal

14. Implementation //Illumination formula for N,V,L L = L / |L|; float a = kd * max(dot(N,L),0) (or texture lookup) float4 Lin = texCUBE(LREnvMap, I); float r = texCUBE(LREnvMap, I).a; float3 L = r * I – pos ; float r’ = length(L); float dw = dw_texel * r2 / r’2 return Lin * a * dw;

15. Question time!