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Simplifying the Representation of Radiance from Multiple Emitters

a. Simplifying the Representation of Radiance from Multiple Emitters. George Drettakis. iMAGIS/IMAG-INRIA Grenoble, FRANCE. General Motivation. Sampling for multiple sources Unnecessary expensive meshing too many elements. IMAGE: full mesh table (marked region) IMAGE: rendered two image.

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Simplifying the Representation of Radiance from Multiple Emitters

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

  2. General Motivation • 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. Previous Work • 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) • Interior discontinuity surfaces (EV and EEE) • Higher order interpolants

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

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

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

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

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

  9. Simplification • Two-sources only case first • 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 L2 error computation • All integral computations on polynomials

  10. Light-Light Simplification • Simplified interpolant construction • 9-point biquadratic Lagrange interpolant • L2-norm calculation • difference of structured interpolant and simplified tensor product • efficient computation (all quadratic polynomials) • Enforce C0continuity

  11. Light-Light Simplification Unsimplified mesh and image

  12. Light-Light Simplification Results Simplified mesh and image

  13. Light-Penumbra Simplification • First construct simplified mesh • For each source • extremal boundary • structured sampling for light IMAGE: Src1 simplified mesh src2 complexity of triangles construction does not depend on scene

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

  15. Light-Penumbra Simplification (cont.) • Construct "moderate quality" approximation • Compute L2-norm • Perform full meshing only where needed IMAGE LIGHT TRIS IMAGE: Triangles ADDED

  16. Estimating Penumbral Radiance • 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

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

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

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

  20. Multiple Sources • Compute simplified mesh for each source M1, M2, ... Mn • Merge to M1,M2, create Mm • Subsequently merge each Miinto the mesh Mm • Perform complete meshing at the end

  21. Discussion • First results encouraging • L2-norm insufficient • specialised error norms need to be designed • Gradation between "simplified" and "complete" • Results of complete implementation required to determine savings in computation time

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

  23. Acknowledgements • 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 • Software elements written by researchers at DGP have been used in the implementation

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