On the eigenvalue distribution of a class of preconditioning methods
Numerische Mathematik
On vectorizing incomplete factorization and SSOR preconditioners
SIAM Journal on Scientific and Statistical Computing - Telecommunication Programs at U.S. Universities
Visual simulation of lightning
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Applied numerical linear algebra
Applied numerical linear algebra
Visual Simulation of Lightning Taking into Account Cloud Growth
CGI '01 Computer Graphics International 2001
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
PG '01 Proceedings of the 9th Pacific Conference on Computer Graphics and Applications
Simulating water and smoke with an octree data structure
ACM SIGGRAPH 2004 Papers
Physically Based Animation and Rendering of Lightning
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
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We present a fast method for simulating, animating, and rendering lightning using adaptive grids. The "dielectric breakdown model” is an elegant algorithm for electrical pattern formation that we extend to enable animation of lightning. The simulation can be slow, particularly in 3D, because it involves solving a large Poisson problem. Losasso et al. recently proposed an octree data structure for simulating water and smoke, and we show that this discretization can be applied to the problem of lightning simulation as well. However, implementing the incomplete Cholesky conjugate gradient (ICCG) solver for this problem can be daunting, so we provide an extensive discussion of implementation issues. ICCG solvers can usually be accelerated using "Eisenstat's trick,” but the trick cannot be directly applied to the adaptive case. Fortunately, we show that an "almost incomplete Cholesky” factorization can be computed so that Eisenstat's trick can still be used. We then present a fast rendering method based on convolution that is competitive with Monte Carlo ray tracing but orders of magnitude faster, and we also show how to further improve the visual results using jittering.