The Multilevel Finite Element Method for Adaptive Mesh Optimization and Visualization of Volume Data
Roberto Grosso
Multilevel representations and mesh reduction techniques have been used for accelerating the processing and the rendering of large datasets representing scalar or vector valued functions defined on complex 2 or 3 dimensional meshes. We present a method based on finite elements and hierarchical bases which combines these two approaches in a new and unique way that is conceptually simple and theoretically sound. Starting with a very coarse triangulation of the functional domain a hierarchy of highly non-uniform tetrahedral (or triangular in 2D) meshes is generated adaptively by local refinement. This process is driven by controlling the local error of the piecewise linear finite element approximation of the function (in the least-squares sense) on each mesh element. Flexibility in choosing the underlying error norm allows for gradient information to be included. A reliable and efficient a posteriori estimate of the global approximation error combined with a preconditioned conjugate gradient solver are the key components of the implementation. Many areas where the proposed method can by applied successfully are envisioned, such as mesh reduction of parameterized grids, visualization of scalar and vector volume data, physically based computer animation of extended bodies and global illumination algorithms. The example application we implemented in order to analyze the properties and advantages of the generated tetrahedral mesh is an iso-surface algorithm which combines the so far separated tasks of extraction acceleration and polygonal decimation in one single processing step. The quality of the iso-surface is measured based on a special geometric norm which does not require the full resolution surface.
Motion Blur Algorithms for Animated Radiosity Environments
Gonzalo Besuievsky
We present two Global Monte Carlo based algorithms to perform accurate illumination simulation of motion blur effects in radiosity scenes. Our first results will be presented
Some Topics in Shooting Random Walk Radiosity
Mateu Sbert
In this talk we will deal with two topics in shooting random walk radiosity. The first is to decide, which of the different estimators we have available is the best. The second question is that, when given different sources, what the optimal probability for a path to begin at a source is.
An Improved Sampling Technique for Monte Carlo Global Illumination
Carlos Urena
We present some results on the analysis of variance of Monte Carlo algorithms, and show how they can be applied to improve two-step algorithms for global illumination.
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