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Simplifying the Representation of Radiance from Multiple Emitters

This presentation explores techniques to simplify the representation of radiance from multiple light sources while reducing meshing costs and the number of interpolants. By employing structured sampling, we aim to minimize the use of expensive meshing, allowing for more efficient rendering in complex environments. The study builds upon previous work in shadow meshing and discontinuity meshing, introducing a two-pass meshing method that merges multiple meshes and uses tensor product interpolants. Preliminary implementation results demonstrate the feasibility and potential for significant computational savings in image generation.

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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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