Recent Advances in Radiosity Philippe Bekaert Department of Computer Science K.U.Leuven

KV 02/10/98 T.U.Wien2 Global Illumination ä Goal: produce images that are perceived indistinguishable from reality.

KV 02/10/98 T.U.Wien3 Global Illumination (2) ä Three steps: ä Modelling: geometry + optical properties ä Illumination computation: stochastic ray tracing, radiosity method, … ä Visualisation of the result (tone mapping,...)

KV 02/10/98 T.U.Wien4 Illumination computation

KV 02/10/98 T.U.Wien5 Radiosity vs. (MC) Ray Tracing Radiosity ä ä view-independent solution (world-space) ä ä diffuse scenes (soft shadows, colour bleeding, …) ä ä approximate solution on BREP model. ä ä time consuming ? ä ä huge storage requirements (only for simple scenes)?Ray-Tracing ä view-dependent solution (pixel-driven) ä general reflection, refraction, emission ä exact solution for CSG models, procedural objects, fractals,... ä low storage requirements (complex scenes) ä reliable

KV 02/10/98 T.U.Wien6 The Radiosity Method ä ä Scene discretised in patches i ä Compute average radiosity B i [W/m 2 ] for each patch by solving... ä The radiosity system of equations: B i = E i +  i  j F ij B j B i = E i +  i  j F ij B j reflectivity form factor

KV 02/10/98 T.U.Wien7 The Radiosity Method(2) ä Four steps: ä Discretisation of the scene into patches ä Form factor F ij computation ä Solution of radiosity system of equations ä Render image using computed radiosities ä In practice: intertwined steps

KV 02/10/98 T.U.Wien8 Step 1: Discretisation ä Quality: ä consistent enumeration of vertices ä well-formed facets ä non intersecting facets (shadow- and light leaks) ä Constant radiosity assumption should be fulfilled (cannot be determined a priori)

KV 02/10/98 T.U.Wien9 Discretisation (2) ä Illustration: washed out shadows, light leaks

KV 02/10/98 T.U.Wien10 Step 2: Form Factors ä F ij = Fraction of power emitted by i and received by j. ä Difficult double integral, numerous techniques: analytic formulae, contour integration, MC integration of deterministic quadrature rules, hemicube, MC simulation... ä Number of FF = square number of patches: storage?

KV 02/10/98 T.U.Wien11 Step 3: Radiosity system solution ä Iterative methods (Jacobi, Gauss-Seidel, Southwell =progressive radiosity) ä Monte Carlo simulation ä Not so problematic.

KV 02/10/98 T.U.Wien12 Step 4: Rendering ä Not so problematic either Using graphics hardware Ray-tracing second pass

KV 02/10/98 T.U.Wien13 Summary of problems: ä Discretisation (meshing) quality ä Need for a priori adaptive meshing ä Form factor storage ä Form factor computation time ä Reliability: numerical errors

KV 02/10/98 T.U.Wien14 Solutions ä Discontinuity meshing ä Hierarchical Refinement ä Clustering ä Implicit instead of explicit form factor computation by MC simulation ä Higher order approximations instead of constant ä View potential driven “focussing” of the computations

KV 02/10/98 T.U.Wien15 Hierarchical Refinement ä Goal: ä automatic adaptive discretisation ä reduction of the number of form factors through multiresolution representation of radiosity. ä Example:

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KV 02/10/98 T.U.Wien18 oracle says: “Refine!” oracle says: “OK!” Recursive refinement in HR.

KV 02/10/98 T.U.Wien19 Hierarchical refinement ä Questions: ä Q1: When to refine? ä Q2: If required, how to carry out refinement? ä Q3: How to keep the multilevel representation consistent? ä Q4: Relation between link error threshold and total error?

KV 02/10/98 T.U.Wien20 Q1: When to refine? ä When form factor too large. ä Based on error estimates: total error = approximation error + propagated error.

KV 02/10/98 T.U.Wien21 Q2: How to refine? ä Which element: receiver or source? ä The largest of the two ä The one contributing the largest error ä How to subdivide the chosen element? ä Regular quad-tree subdivision ä Along discontinuity lines ä Alternative: Increase approximation order.

KV 02/10/98 T.U.Wien22 Q3: Keeping the MRR consistent ä Goal: obtain new consistent representation of total radiosity on all levels? ä push: propagate radiosity top-down ä pull: average radiosity bottom-up.

Elementary push-pull

KV 02/10/98 T.U.Wien24 Q4: link error versus total error? ä Link error threshold can be computed in order to give same total error everywhere. ä Experiment: measured (total) error versus desired accuracy:

KV 02/10/98 T.U.Wien25 Remaining problems: ä Storage requirements: still several 100 bytes per element. ä Computational error on form factors and error estimates. ä Solution: avoid explicit form factor computation and storage!!!

KV 02/10/98 T.U.Wien26 Monte Carlo Radiosity ä Simulate path of photons through environment. Score yields radiosity. ä Form factors do not need to be computed explcitely.

Which is best?? ä Breadth first versus depth first ä Local versus global lines. ä Continuous versus discrete: ä discrete = warp particle to new position on hit patch. ä Influence of random number generator (MC versus QMC) ???

28 1) Breadth-first versus depth-first Depth-first (particle tracing) Breadth-first (WDRS)

Initial power distribution Initial ray set new power distribution Breadth-first RW (1)

Breadth-first RW (2) modified power distribution extra rays (same ray power) new power distribution

Breath-first RW (3) extra rays (same ray power as before)

Breath-first RW (4) extra rays (same ray power as before)

Depth-first RW (1)

Halton Random Breadth-first vs depth-first ä It doesn‘t really matter.

2) Local versus Global Lines Global lines (Sbert’93) Local lines ä Global lines are cheaper per intersection, but local lines allow better sample distribution.

Local versus Global Lines: global local Halton random

3) Continuous versus discrete Discrete Halton ContinuousHalton Keller

KV 02/10/98 T.U.Wien38 Problems of MC Radiosity ä lack of automatic adaptive meshing ä noise/aliasing effects ä Solution: hierarchical refinement!!

Hierarchical Monte Carlo Radiosity ä Random walk algorithms avoiding explicit form factor computation and storage ä Per sample decision what level of detail is appropriate for light transport. ä Combination of wavelets and Monte Carlo.

KV 02/10/98 T.U.Wien40 Recursive refinement in HMC. form factor sample line oracle says: “Refine!” oracle says: “OK!”

Results: ä Surprisingly fast first complete solutions. ä Gradually improved by reducing noise ä Low storage requirements (no form factor storage) ä Reliable (no difficult element pairwise form factor integration)

KV 02/10/98 T.U.Wien42 5min.9min. 10min.

Conclusion ä We´ve come a long way. ä The way ahead is also long: ä more efficient refinement + better approximations ä general light transport (not only diffuse) ä participating media ä dynamic scenes ä... ä DEMO TIME!!!