1. Simplifying the Representation of Radiance from Multiple Emitters a George Drettakis iMAGIS/IMAG-INRIA Grenoble, FRANCE

2. MAGISi General Motivation Sampling for multiple sources Sampling for multiple sources –Unnecessary expensive meshing –too many elements IMAGE: full mesh table (marked region)IMAGE: rendered two image Goal: reduce meshing cost; reduce number of interpolants

3. MAGISi Previous Work Shadow Meshing (Campbell & Fussell 90, 91, Chin & Feiner 90, 91) Shadow Meshing (Campbell & Fussell 90, 91, Chin & Feiner 90, 91) –Extremal (umbral/penumbral, penumbral/light) boundary –Constant interpolants Discontinuity Meshing (Lischinski et al. 92, Heckbert 92) Discontinuity Meshing (Lischinski et al. 92, Heckbert 92) –Interior discontinuity surfaces (EV and EEE) –Higher order interpolants

4. MAGISi (Previous Work cont. ) Structured Sampling Drettakis & Fiume 93: unoccluded environments Drettakis & Fiume 93: unoccluded environments Drettakis & Fiume 94: discontinuity meshing Drettakis & Fiume 94: discontinuity meshing IMAGE: Struct Mesh 1 srcIMAGE: Backprojection (SIGRAPH) IMPORTANT: Light mesh is accurate; allows simplification

5. MAGISi (Previous Work cont.) Structured Sampling with Shadows Penumbral groups; tensor products (light), triangular (penumbra) (Drettakis 94) Penumbral groups; tensor products (light), triangular (penumbra) (Drettakis 94) IMAGE: Table 4 (SIGGRAPH)

6. MAGISi Extension to Multiple Sources and Two- Pass Meshing Extension to Multiple Sources and Two- Pass Meshing Simplification Criteria (two sources case) Simplification Criteria (two sources case) First Implementation Results First Implementation Results Multiple Sources and Conclusion Multiple Sources and Conclusion Organisation of Remaining Talk

7. MAGISi Extension to Multiple Sources Multiple meshes Multiple meshes –ray-tracing for image generation Merge the multiple meshes Merge the multiple meshes –light/light –> tensor product interpolant –penumbra/light –> triangular interpolant

8. MAGISi Two-pass Meshing Extremal boundary computation Extremal boundary computation –include minimal EEE –extremal boundary 4 times cheaper than complete mesh

9. MAGISiSimplification Two-sources only case first Two-sources only case first Methodology: use structured light representation Methodology: use structured light representation –Light/Light: compare with simpler interpolant –Penumbra/Light: compare moderate quality interpolant (triangular) to simpler (tensor product) –Penumbra/Penumbra: no simplification Compare using L 2 error computation Compare using L 2 error computation –All integral computations on polynomials

10. MAGISi Light-Light Simplification Simplified interpolant construction Simplified interpolant construction –9-point biquadratic Lagrange interpolant L 2 -norm calculation L 2 -norm calculation –difference of structured interpolant and simplified tensor product –efficient computation (all quadratic polynomials) Enforce C 0 continuity Enforce C 0 continuity

11. MAGISi Light-Light Simplification Unsimplified mesh and image

12. MAGISi Light-Light Simplification Results Simplified mesh and image

13. MAGISi Light-Penumbra Simplification First construct simplified mesh First construct simplified mesh For each source For each source –extremal boundary –structured sampling for light IMAGE: Src1 simplified meshsrc2 complexity of triangles construction does not depend on scene

14. MAGISi Light-Penumbra Simplification For each penumbral group For each penumbral group –Create a mesh containing extremal boundary –Add light faces; calulate appropriate radiance values IMAGE MAXMINOUNDIMAGE LIGHT ADDED

15. MAGISi Light-Penumbra Simplification (cont.) Construct "moderate quality" approximation Construct "moderate quality" approximation Compute L 2 -norm Compute L 2 -norm Perform full meshing only where needed Perform full meshing only where needed IMAGE LIGHT TRISIMAGE: Triangles ADDED

16. MAGISi Estimating Penumbral Radiance For a point known to be in penumbra For a point known to be in penumbra –Find closest point on minimal and maximal boundary –Estimate derivative –Create interpolants –Evaluate interpolant Experimental verification pending Experimental verification pending

17. MAGISi Light-Penumbra Implementation First implementation First implementation –Construct full mesh; apply simplification criteria a-posteriori. Promising first results. IMAGE COMPLETE MESHIMAGE

18. MAGISi Light-Penumbra Results (1) IMAGE MESH (35%) 0.005IMAGE

19. MAGISi Light-Penumbra Results (2) IMAGE MESH (40%) 0.001IMAGE

20. MAGISi Multiple Sources Compute simplified mesh for each source M 1, M 2,... M n Compute simplified mesh for each source M 1, M 2,... M n Merge to M 1, M 2, create M m Merge to M 1, M 2, create M m Subsequently merge each M i into the mesh M m Subsequently merge each M i into the mesh M m Perform complete meshing at the end Perform complete meshing at the end

21. MAGISiDiscussion First results encouraging First results encouraging L 2 -norm insufficient L 2 -norm insufficient –specialised error norms need to be designed Gradation between "simplified" and "complete" Gradation between "simplified" and "complete" Results of complete implementation required to determine savings in computation time Results of complete implementation required to determine savings in computation time

22. MAGISiFuture Complete implementation Complete implementation –partial meshing –simplifcation –complete meshing on demand Application to complex environments Application to complex environments Application to global illumination Application to global illumination

23. MAGISiAcknowledgements The author is an ERCIM fellow, currently hosted by INRIA in Grenoble The author is an ERCIM fellow, currently hosted by INRIA in Grenoble Many ideas in this research originated at the Dynamic Graphics Project (DGP) of the University of Toronto, Canada Many ideas in this research originated at the Dynamic Graphics Project (DGP) of the University of Toronto, Canada Software elements written by researchers at DGP have been used in the implementation Software elements written by researchers at DGP have been used in the implementation