We develop algorithms and geometric representations for visualization and light simulation. For light simulation, we take the "geometry and sampling" point of view, and try to find optimum function bases for representing light on objects. We have studied algorithms to minimize the quantization noise power (Lloyd relaxation). We proved that the quantization noise power is a function of class C2, and designed a Newtonbased algorithm with faster speed of convergence [ACM TOG 2009]. The next step is to use these results on sampling theory to dynamically optimize finite elements over a mesh. The figure shows our first results.

This image shows our Discrete Master Element technique applied to Michelangelo's David (dataset courtesy of Stanford Digital Michelangelo Project). Our DME technique makes it possible to run Finite Element methods on fine tesselated models. As can be seen in the picture, indirect lighting effects and color blends are accurately simulated. This work was done in cooperation with JeanClaude Paul.

