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Efficiente Radiositeitsberekening met de Stochastische Jacobi Iteratieve Methode

Efficiente Radiositeitsberekening met de Stochastische Jacobi Iteratieve Methode. Philippe Bekaert Departement Computerwetenschappen K.U.Leuven. The Radiosity Method. Reflectivity. Self-emitted radiosity. Total radiosity. Form factor radiative exchange factor. 4 Steps, 2 Problematic.

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Efficiente Radiositeitsberekening met de Stochastische Jacobi Iteratieve Methode

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  1. Efficiente Radiositeitsberekening met de Stochastische Jacobi Iteratieve Methode Philippe Bekaert Departement Computerwetenschappen K.U.Leuven

  2. The Radiosity Method Reflectivity Self-emitted radiosity Total radiosity Form factor radiative exchange factor Nederlands Mathematisch Congres

  3. 4 Steps, 2 Problematic • Discretise the input scene Problem: discretisation artifacts • Compute form factors Problem: huge number of non-trivial integrals: 95% of the computing time, very large storage requirements, computational error. • Solve radiosity system • Tone mapping and display In practice intertwined! Nederlands Mathematisch Congres

  4. Discretisation Artifacts Constant Approximation “true” solution Quadratic Approximation Nederlands Mathematisch Congres

  5. Form Factor Singularities and Discontinuities Nederlands Mathematisch Congres

  6. Jacobi Iterative Method • Power equations: • Deterministic Jacobi Algorithm: (quadratic cost) Nederlands Mathematisch Congres

  7. Stochastic Jacobi iterations 1) Select patch j: (Neumann et al.) 2) Select i conditional on j: 3) Score (form factor cancels!!) VARIANCE: (log-linear cost) Nederlands Mathematisch Congres

  8. Form Factor Sampling • Form factors Fij for fixed patch i form a probability distribution that can be sampled efficiently by tracing rays: Local Lines Global Lines (Sbert) Nederlands Mathematisch Congres

  9. Results (30000patches) 2 min. 32 min. 8 min 2h 8h Nederlands Mathematisch Congres

  10. Variance Reduction • Importance Sampling • View-importance driven Stochastic Jacobi Radiosity (with L&A Neumann, J.Prikryl) • Control Variates • Compute difference w.r.t. well-chosen constant radiosity (with L. Neumann) • Combining estimators • Bi-directional energy transfers (with M. Sbert) • Weighted Importance Sampling • Low-discrepancy Sampling • Sequential Monte Carlo (with M. Sbert) Nederlands Mathematisch Congres

  11. View-Importance Driven Stochastic Jacobi Iterations • Goal: focus computations on small part of a complex scene • Important parts? • Compute Importance of each patch: • Use importance to sample more rays starting from/directed to important parts • Clever merging heuristic Nederlands Mathematisch Congres

  12. View Importance Importance A A B B Nederlands Mathematisch Congres

  13. 1 iteration (no importance) 3 iterations (no importance) A B Nederlands Mathematisch Congres

  14. 2 importance-driven iteration for VP A 2 more importance-driven iteration for VP B A B Nederlands Mathematisch Congres

  15. Discretisation artifacts • Monte Carlo algorithms for higher order radiosity approximations • Incorporation of hierarchical refinement • automatic, adaptive meshing • multi-resolution radiosity representation • related with wavelet preconditioning of linear systems. Nederlands Mathematisch Congres

  16. 5min. 9min. 10min. Nederlands Mathematisch Congres

  17. Conclusions • More reliable, user-friendly, rapid, simple to implement & lower storage cost than deterministic algorithms • Discretisation remains a difficult problem • Future work: • related problems: dynamic environments, non-diffuse reflection&refraction, • problems not in graphics Nederlands Mathematisch Congres

  18. More Information • Http://www.cs.kuleuven.ac.be/ • Research • Computer Graphics Nederlands Mathematisch Congres

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