Splat representation of parametric surfaces

Abstract

Point-based geometry representations and their splat-based generalizations have become a suitable technique both for modeling and rendering complex 3D shapes. So, it seems interesting to convert other kind of models to a point or splat-based representations.

In this work, we present an approach to convert a parametric surface to an elliptical splat-based representation. Although this conversion supposes a loss of information going from an analytical to an approximate model, it will allow to locally modify zones with complex features, to mix surface and splat-based models and to take advantage of the existing point-based rendering methods.

The presented approach works in the parametric space and performs an adaptive sampling based on the surface curvature and a given error tolerance. The goal is to obtain an optimized set of elliptical splats that completely covers the surface. Two strategies are presented, one based on a quadrangular subdivision of the parametric space and the other on power Voronoi diagrams. Finally, some open problems are enumerated.