1. Volume radiosity Michal Roušal University of West Bohemia, Plzeň Czech republic

2. Index n Introduction to the radiosity method –Lightning model –Form factors –Radiosity equation n Radiosity for the volume and its specifics –Lightning model for volume absorbing and scatering

3. Introduction to radiosity method n Global visualisation method, presented about “1985” n Based on finite element method n Using physical based lightning model n Subdividing scene into small patches (border representation) n Scene should be”closed” for energy

4. General rendering equation n Radiance of patch P is: n Radiance at point x for non transparent patches

5. Lightning model n Represented by BRDF function: f( ,x,  ’) n Reciprocity: n Energy conservation: x  ’’ nxnx

6. Most used lightning models n Diffuse model: n Modified Phong model: –  h halfway vector between  and  ‘.

7. Form factors n Geometric characteristic of the patches visibility in the scene. n Analytical/geometrical approach n Generally we can define:

8. Analytical approach n Probability definition: –We define F ij as probability that random particle shot from patch i will hit path j. (particle tracing) n Monte Carlo integration methods n Global Lines –Fast but less accurate

9. Geometrical approach n Nusselt‘s analog (projection on disk) –high computation complexity n Projection on hemicube –can be used hardware n Projection on tetrahedra –can be used hardware –less faces

10. Radiosity equation (1) n Works not with the point x but with the patch i n Only for diffuse reflectance and uniform emittance we can write. –E i is self-emitted constant radiance of patch i

11. Radiosity equation (2) n We define the radiance of the path B as: n For all patches we can write:

12. Solving radiosity equation n Easy to solve by numerical algorithms (gathering radiosity) –Gauss O(N 3 ) –Gauss-Seidel iteration O(N 2 ) per step –Time and memory consuming n Progressive refinement (shooting radiosity) –Solving equation by columns with highest B j –O(N 2 ) complexity but not so much memory needed

13. Some radiosity improvements n Hierarchical radiosity –Adaptive subdivision of the patches due to error n Clustering –Using clusters of patches to reduce complexity of scene. n Combination of radiosity with other global visualisation algorithms n etc.

14. Volume radiosity n More complex scenes n Usually combination of volume and surface elements n Lightning model for participating media –Not only reflectance but also volume absorption and scattering n Visualisation of volume objects/scenes

15. Lightning model (1) n We define: –  a (x) – coefficient of absorption –  s (x) – scattering coefficient –  e (x) – extinction coefficient –  - scattering albedo

16. Lightning model (2) n Integral equation –transmittance

17. Solving volume radiosity equation n Zonal method –More-less similar to classic approach using Gauss-Seidel iteration n Progressive refinement + Hierarchical radiosity n Finite element method approach n Random (Monte Carlo) based methods

18. My interest n Combination of volume and surface elements n Multiple and not only diffuse scattering n Clustering of patches based on initial scene geometry (probably no adaptive clustering during computation or hierarchical subdivision – orientation on volume) n Parallel and maybe distributed implementation for applications with dynamic environment

19. Possible application n Simulation of visibility from a car with headlights in fog/dense rain or other volume/participating media based environment

20. Our approach (theory) n Main aim is to create fast algorithm with decent accuracy n Progressive refinement with randomized approach (Monte Carlo method) for shooting strategy n Clustering: –Some clusters we can get from the scene model –Analyze the geometry of scene and create clusters of voxels

21. Clustering n Some clusters we can get from the scene model n Analyze the geometry of scene and create clusters of voxels

22. Parallelization n Divide the scene by planes n Each part of the scene can be computed by different processor/thread