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An Efficient Progressive Refinement Strategy for Hierarchical Radiosity Nicolas Holzschuch, François Sillion and George Drettakis iMAGIS/IMAG, Grenoble — France A joint research project of IMAG and INRIA

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MAGISiMotivation Hierarchical radiosity is a significant step in radiosity algorithms Hierarchical radiosity is a significant step in radiosity algorithms –creates links between patches and refines them –linear in the number of elements created Proceeds top-down: Proceeds top-down: –First establish links between input surfaces –Then refine these links where needed

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MAGISi Motivation (2) “Initial linking” step quadratic in the number of polygons “Initial linking” step quadratic in the number of polygons Many top-level links will never carry significant energy Many top-level links will never carry significant energy Subdivision is often too high Subdivision is often too high

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MAGISi Proposed improvements Delaying initial linking of input surfaces Delaying initial linking of input surfaces Reducing the number of links Reducing the number of links

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MAGISi Our test scenes

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MAGISi Initial Linking Proportion of top-level links with BF < Proportion of top-level links with BF <

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MAGISiSubdivision

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MAGISi Previous work Hierarchical radiosity: (Hanrahan, 90- 91) Hierarchical radiosity: (Hanrahan, 90- 91) –Link refinement based on radiance and form-factor –proceed from top to bottom –multigridding Importance-driven hierarchical radiosity: (Smits, Arvo & Salesin, 92) Importance-driven hierarchical radiosity: (Smits, Arvo & Salesin, 92) –Links refined using importance and influence on the final image

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MAGISi Previous work (2) Hierarchical radiosity and discontinuity meshing: (Lischinski, Tampieri & Greenberg 93) Hierarchical radiosity and discontinuity meshing: (Lischinski, Tampieri & Greenberg 93) –First refine patches using a discontinuity mesh, then re- refine using radiosity and form-factor Structured sampling: (Drettakis & Fiume 93) Structured sampling: (Drettakis & Fiume 93) –Adapt mesh to illumination structure

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MAGISi Delaying initial linking Delay top-level linking between input surfaces until strictly necessary Delay top-level linking between input surfaces until strictly necessary First iteration results achieved more rapidly First iteration results achieved more rapidly Spread computation over several iterations Spread computation over several iterations Avoid part of initial linking computation; gain on total computation time Avoid part of initial linking computation; gain on total computation time

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MAGISi Classification of pairs Initially, all pairs of polygons are un-classified Initially, all pairs of polygons are un-classified “Important” pairs progressively become classified. “Important” pairs progressively become classified. Un-classified VisiblePartial Un-classified Invisible We compute visibility tests only for classified pairs. We compute visibility tests only for classified pairs. Classified

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MAGISi Linking algorithm First record all polygon pairs as un-classified. First record all polygon pairs as un-classified. As soon as a pair qualifies for linking (B*F > ), compute visibility and link it accordingly. As soon as a pair qualifies for linking (B*F > ), compute visibility and link it accordingly. The remainder of the algorithm is not modified. The remainder of the algorithm is not modified.

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MAGISi Energy Balance Partially linked polygons do not emit all their energy Partially linked polygons do not emit all their energy Un-radiated energy affects the energy balance Un-radiated energy affects the energy balance –quantify the importance of this lost energy – compare it with the overall precision of the algorithm. Unit sum of form-factors allows estimation of lost energy Unit sum of form-factors allows estimation of lost energy

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MAGISi Energy Balance

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MAGISi Reducing the number of links Perform an a posteriori test to determine whether refinement was required: Perform an a posteriori test to determine whether refinement was required:

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MAGISi Reducing the number of links We cancel the refinement if the following four expressions are true: We cancel the refinement if the following four expressions are true:

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MAGISi Results: first iteration

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MAGISi Results: ten iterations

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MAGISiSubdivision

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MAGISiConclusion Delaying top-level linking between input surfaces Delaying top-level linking between input surfaces –storage costs are reduced –we obtain first results earlier –still quadratic in the number of input surfaces Reducing the number of links Reducing the number of links –improved subdivision criterion –limits un-necessary subdivisions Future work: Future work: –Simplify already subdivided meshes

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02/18/05© 2005 University of Wisconsin Last Time Radiosity –Converting the LTE into the radiosity equation –Solving with Gauss-Seidel relaxation –Form.

02/18/05© 2005 University of Wisconsin Last Time Radiosity –Converting the LTE into the radiosity equation –Solving with Gauss-Seidel relaxation –Form.

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