1. 1 Shadows (2) ©Anthony Steed 2002

2. 2 Overview n Shadows – Umbra Recap n Penumbra Analytical v. Sampling n Analytical Aspect graphs Discontinuity meshing n Sampling Accumulation buffer Convolution

3. 3 Shadows

4. 4 Analytical v. Sampling n Analytical Find all boundaries within the penumbra. Done almost exclusively for polygonal light sources n Sampling Approximate solution that treat the light source as a set of points. Any shape source is possible.

5. 5 Extremal Shadow Boundaries n What is the potential area of the penumbra and umbra? n For penumbra: Bounded by planes define by a pair of source vertex and occluder edge where the source is in the front space and the occluder on the back n For umbra: Similarly defined planes, but where source and occluder are in the back space

6. 6 Extremal Shadow Boundaries

7. 7 Shading Using Extremal Planes n If you write these planes into object space n We can use a scan-conversion as we have before At each pixel we must estimate the proportion of the light source that can be seen Usually done with SVBSP tree(s)

8. 8 More Analysis n Borrowing aspect graphs from computer vision n Define critical surfaces where visual events occur EV surfaces: planes defined by edge and vertex EEE surfaces: quadratic surfaces defined by three non-adjacent edges. n Penumbra volumes so far have used EV only

9. 9 EV and EEE Surfaces

10. 10 Discontinuity Meshing n Discontinuities of the illumination of a polygon occur at the places where EV and EEE surfaces intersect the polygon n Discontinuities occur at different degrees n Discontinuities are written into the geometry of the scene as before

11. 11 Shadows and Discontinuities

12. 12 Storing the Discontinuity Mesh n DM-Tree which uses both 2D BSP tree and winged edge data structure

13. 13 George Drettakis

14. 14 George Drettakis

15. 15 David Hedley

16. 16 David Hedley

17. 17 Sampling Methods n Model an area light source by multiple n point light sources n At rendering time render n times moving the light each time n Compose the image into an accumulation buffer

18. 18 Accumulation Buffer n Yet another set of hardware buffers n Can be cleared (like the colour buffer) n You repeatedly copy the colour buffer to it, using a 1/N scale each time n After N iterations, the A-buffer holds the average of the N frames n Obviously requires precision! (Spend more $$) http://www.sgi.com/software/opengl/advanced96/programs.html

19. 19 Example

20. 20 Recap n Penumbra is difficult to render correctly Boundaries are formed by very complex shapes n Discontinuity meshing is an analytical solution Difficult to implement n Sampling is obviously less accurate Potentially fast enough (soon) to do in real- time