Convex contouring of volumetric data

Abstract

In this paper, we present a fast, table-driven isosurface extraction technique on volumetric data. Unlike Marching Cubes or other cell-based algorithms, the proposed polygonization generates convex negative space inside individual cells, enabling fast collision detection on the triangulated isosurface. In our implementation, we are able to perform over 2 million point classifications per second. The algorithm is driven by an automatically constructed lookup table that stores compact decision trees by sign configurations. The decision trees determine triangulations dynamically by values at cell corners. Using the same technique, we can perform fast, crack-free multiresolution contouring on nested grids of volumetric data. The method can also be extended to extract isosurfaces on arbitrary convex, space-filling polyhedra.