1. A Fast Shadow Algorithm for Area Light Sources Using Backprojection George Drettakis Eugene Fiume Department of Computer Science University of Toronto, CANADA

2. A Fast Shadow Algorithm for Area Light Sources Using Backprojection George Drettakis Eugene Fiume Department of Computer Science University of Toronto, CANADA

3. Motivation [IMAGE] Fast calculation of images with analytic radiance values in the penumbraFast calculation of images with analytic radiance values in the penumbra (Images DC D2C2)(Images DC D2C2)

4. Results of the Algorithm Efficient representation of visible part of the sourceEfficient representation of visible part of the source Fast ray-cast rendering of accurate shadowsFast ray-cast rendering of accurate shadows –Analytic radiance values in penumbra Interpolant representation for hardware polygon rendering (interactive walkthroughs) and ray- castingInterpolant representation for hardware polygon rendering (interactive walkthroughs) and ray- casting

5. Previous Work in Shadows Nishita & Nakamae (1983), extremal boundaries, explicit visibility calculationNishita & Nakamae (1983), extremal boundaries, explicit visibility calculation Campbell & Fussell (1990, 1991), Chin & Feiner (1990, 1992), point sources extended to area sources, extremal boundariesCampbell & Fussell (1990, 1991), Chin & Feiner (1990, 1992), point sources extended to area sources, extremal boundaries Lischinski et al. 1992, Heckbert 1992, visibility changes within penumbraLischinski et al. 1992, Heckbert 1992, visibility changes within penumbra

6. Other Related Work Aspect graph calculation in Computer Vision (Gigus & Malik 1990, Gigus et al. 1991)Aspect graph calculation in Computer Vision (Gigus & Malik 1990, Gigus et al. 1991) Full mesh calculation, Stewart & Ghali 1993, 1994Full mesh calculation, Stewart & Ghali 1993, 1994 –Different methodology –2D vs. 3D approach –Heuristics vs. Geometric/Asymptotic Analysis

7. Backprojection [IMAGE] A Backprojection instance at a pointA Backprojection instance at a point (Colour Image of BP)(Colour Image of BP) Backprojection: ordered list of vertices and edges allowing the formation of the backprojection instanceBackprojection: ordered list of vertices and edges allowing the formation of the backprojection instance

8. Discontinuity Mesh Segmentation of input polygons into faces (or cells) having the same backprojectionSegmentation of input polygons into faces (or cells) having the same backprojection The mesh is calculated by casting discontinuity surfaces into the environmentThe mesh is calculated by casting discontinuity surfaces into the environment Four sub-classes of disc. surfaces:Four sub-classes of disc. surfaces: –Emitter EV and EEE (EeEE) –Non-Emitter EV and EEE

9. Algorithm Overview Algorithm:Algorithm: –Cast surfaces, generate mesh –Calculate backprojections –Separate light/shadow regions –Build interpolants (if needed)

10. Algorithm Overview (cont.) Extension of Heckbert 92Extension of Heckbert 92 –treatment of non-emitter surfaces –treatment of EEE –incremental mesh construction Utilisation of typical scene structureUtilisation of typical scene structure –use of spatial subdivision structure (grid)

11. Emitter Surface Casting EV surfacesEV surfaces –2-D visibility on wedge EeEE surfacesEeEE surfaces –identify and connect mesh edges caused by the same edge pair

12. Non Emitter Surfaces [IMAGE] Efficient identification using grid structureEfficient identification using grid structure [IMAGE][IMAGE] Non-emitter EEENon-emitter EEE –visibility sweep across quadric surface

13. Non-Emitter Surface Statistics Small number of non-emitter surfacesSmall number of non-emitter surfaces Number of non-emitter surfaces grows slowlyNumber of non-emitter surfaces grows slowly Efficient identification feasibleEfficient identification feasible

14. Incremental Backprojection Update Start in region of light or umbraStart in region of light or umbra –"backprojection" is the source or null –explicit calculations rarely needed (only for objects entirely in penumbra) Store discontinuity surface info with mesh edgesStore discontinuity surface info with mesh edges –perform small incremental update when crossing each edge

15. Mesh Timing Results Quasi-linear time for mesh calculationQuasi-linear time for mesh calculation Grid effective; 2-D visibility insignificantGrid effective; 2-D visibility insignificant

16. Backprojection Timing Results Incremental vs explicit backprojection calculationIncremental vs explicit backprojection calculation Incremental calculation permits almost- interactive update rate for moving objectsIncremental calculation permits almost- interactive update rate for moving objects

17. Ray-cast Rendering [IMAGE] Ray-casting with analytic radiance values in the penumbraRay-casting with analytic radiance values in the penumbra – stored backprojections, allow cheap shading

18. Hardware Polygon Rendering [IMAGE] Build interpolantsBuild interpolants –structured tensor products for light (DrFi93) –triangular for penumbra

19. Other Applications of the Algorithm [IMAGE] Study of radiance in the penumbra (Dret94a)Study of radiance in the penumbra (Dret94a) –study of monotonicity and other properties –mesh simplification

20. Other Applications of the Algorithm [IMAGE] Mesh simplfication for multiple sourcesMesh simplfication for multiple sources –calculate full mesh only when needed –([Dret94b] published in the 5th EG workshop on Rendering)

21. Future Work Global IlluminationGlobal Illumination –computation of complete mesh locally, only when necessary –Use of backprojections and discontinuity meshing for error bound calculations Incremental modification of the mesh for moving objectsIncremental modification of the mesh for moving objects –modify only the part of the mesh that changes

22. Discussion Only small and moderate size scenes have been tested to dateOnly small and moderate size scenes have been tested to date General EEE implementation not yet completeGeneral EEE implementation not yet complete Robustness an important issueRobustness an important issue –numerical accuracy a problem

23. Conclusion Efficient algorithm for complete discontinuity mesh calculation with backprojectionsEfficient algorithm for complete discontinuity mesh calculation with backprojections Images with analytic radiance values in penumbraImages with analytic radiance values in penumbra Interactive walkthroughsInteractive walkthroughs Almost-interactive updates for object or source motionAlmost-interactive updates for object or source motion

24. Conclusion Efficient algorithm for complete discontinuity mesh calculation with backprojectionsEfficient algorithm for complete discontinuity mesh calculation with backprojections Images with analytic radiance values in penumbraImages with analytic radiance values in penumbra Interactive walkthroughsInteractive walkthroughs Almost-interactive updates for object or source motionAlmost-interactive updates for object or source motion