1. Virtual Light Field Group vlfproject@cs.ucl.ac.uk University College London GR/R13685/01 Research funded by: Propagating the VLF – Problems and Solutions I Pankaj Khanna p.khanna@cs.ucl.ac.uk

2. VLF Project Introduction Current state of the VLF – Area Emitters only – Specular and Diffuse planar polygons – Energy conserving (all equations balance) – Does all L(S|D)* paths – No diffuse texture maps Easy to add though

3. VLF Project Implementing the VLF Murphy’s Laws: – Nature always sides with the hidden flaw The hidden flaw never stays hidden for long. – Murphy’s Law of thermodynamics: Things get worse under pressure. – If anything can go wrong, it will. – Every solution breeds new problems. – If anything simply cannot go wrong, it will anyway. – If everything seems to be going well, you have obviously overlooked something

4. VLF Project Evolution of the VLF

5. VLF Project Outline of this section Discretisation artefacts – Discretisation of directions Accounting for variance Propagating with discretised directions – Discretisation of surfaces Visibility issues Diffuse transfer of radiance – Validity of transfer – Mechanism of transfer Continued in Section II by Insu

6. VLF Project Discretisation of directions What constitutes an “ideal” discretisation? – Unfortunately an ideal discretisation does not exist Recursive subdivision of tetrahedron produces variance in solid-angle size and shape – Results in non-uniform distribution – Aliasing and sampling problems

7. VLF Project Using discrete directions Discrete directions have different significance depending on the nature of transport being performed – Radiance to/from Diffuse surface A single direction (PSF) actually corresponds to the set of directions contained in that direction’s solid-angle – Radiance to Specular surfaces A specular surface has direction-dependent propagation and viewing attributes and can not be generalised over the solid angle – Has error proportional to the number of discretised directions – Specular  Diffuse transfer can however be taken to be over the solid-angle

8. VLF Project Normalising solid-angle area variance Radiance sent along a PSF direction should be proportional to the area of the solid-angle associated to that discretised direction – Normalise energy transfer per PSF direction by factor based on corresponding solid- angle For Level 5, 2049 directions, SA MIN =0.0016, SA MAX =0.005 Energy conservation still required Normalisation= SA PSF /  (SA PSF ) Without normalisation Normalised   Please note that illustrative images here and henceforth may have several inaccuracies as they were taken at various stages of the development of the VLF

9. VLF Project “Holes” due to discretised directions Energy is only propagated along discretised directions (PSFs) Error multiplies on successive iterations

10. VLF Project “Holes” Problem is more severe with fewer directions and smaller emitters 513 directions2049 directions Iteration 1 Iteration 2

11. VLF Project Filling the holes Discretised directions actually represent solid-angles for diffuse surfaces Need to sample the solid angles during radiance transfer – How to sample? – How do we combine the samples? – Where do we put the sampled results?

12. VLF Project Filling holes with a jittered transfer Send energy along original and a few additional sampled directions within the solid-angle – Random or stratified sampling Select samples over the solid-angle and rotate all directions by the corresponding angle to obtain a jittered set of discretised directions – Use largest solid-angle & assume symmetry

13. VLF Project Jittered transfer only Jittered transfer is only used for transfer to diffuse surfaces – Specular surfaces receive radiance only during Jitter 0 Combining samples from jittered transfer – Use a Gaussian Kernel Small  to prevent blurring out of details Need to manage filtering at edges of map Needs to be energy conserving Results of transfer stored in Diffuse Maps as described earlier – More details later…

14. VLF Project Constant time direction-lookup artefacts Lookup involves referring to an OpenGL rasterised image – Map needs to be of sufficiently high resolution to avoid aliasing 512x5121024x10242048x2048

15. VLF Project Discretisation and the constant  Irradiance  Radiance conversion requires division by  Discretisation of directions & points into patch areas lead –  is replaced by a constant obtained by summing projected area of a cell along all PSF directions Level 3, 129 directions, discretised ‘  ’= 0.8291 Level 4, 513 directions, discretised ‘  ’= 5.2369 Level 5, 2049 directions, discretised ‘  ’= 20.9565

16. VLF Project Visibility Visibility in tiles is at low resolution – need more detail for radiance transfer – Analytical computation – OpenGL visibility (P­ buffers) Super-sampled exchange (visibility) buffers No super-samplingSuper-sampled visibility

17. VLF Project Visibility for jittered transfer Visibility (face-lists) stored in tiles is no longer valid – Produces incorrect list of polygons to rasterise for visibility exchange buffer More severe with fewer directions 3 possible options – Recomputing visibility by OpenGL rasterisation is expensive but also most accurate Visibility from Original PSF Visibility from Nearest PSF Recomputed Visibility (OpenGL)

18. VLF Project Transfer to Diffuse surfaces Transfer of irradiance between 2 diffuse surfaces can be described by: – (CosA  CosB)/  r 2 In words this is: – (CosA  CosB) : product of projected areas –  : total projected area of source cell – r 2 : term expressing angular spread with distance

19. VLF Project Validity of diffuse transfer in the VLF All parts of the previous equation are represented in the radiant transfer between two diffuse surfaces – Actual projected areas are used in determining mapping of radiance – A constant equivalent to “  ” is obtained and used for the given discretisation – The r 2 -term that represents the spread of the propagating solid-angle with distance is explicitly represented in the VLF approach of propagation along discretised directions

20. VLF Project Transfer along a PSF Tile Transfer of radiance from a sender to a receiver takes place in the PSF direction via a temporary radiance tile – All senders push radiance into the temp tile – Temp tile pushes radiance into receiver

21. VLF Project Mapping radiance Radiance maps need to be sampled for each Tile- cell (per PSF) The mapping is not one-to-one

22. VLF Project Radiance sampling strategies Point-sampling Sampling by determining cell overlaps – Discrete  Continuous  Resample  Discrete – Uses (slow) Liang-Barsky clipping Currently the main bottleneck but high accuracy Point-sampledArea-overlap

23. VLF Project Jittered diffuse transfer (an overview) for (each Jitter) { if (Jitter>0) jitter the VLF for (each PSF, Tile) { if (Jitter>0) compute polygons in this tile for (each diffuse receiver R) { compute visibility exchange buffer for R for (each sender S) { Map radiance (URM) from sender S to temp radiance tile } // S Map temp radiance tile onto receiver’s DM N } // R } // PSF, Tile } // Jitter divide radiance in DM N s by NumJitters to normalise transfer apply gaussian filter to diffuse DM N s and add to DM T

24. VLF Project Diffuse – bringing it all together