Polygonization of Quasi-Convolutionally Smoothed Polyhedra

Abstract

The smoothing of a polyhedral model is an important task in Computer Graphics. Richard Lobb [Lobb96] introduced quasi-convolutional smoothing, a fast rounding scheme approximating convolutional smoothing. For a fast interactive display of the model its surface must be polygonized. We introduce here Triage Polygonization, a new fast polygonization method for quasi-convolutionally smoothed polyhedral. The polygonization method exploits the property that quasi-convolutionally smoothed polyhedral usually have predominantly planar surfaces with only edges and corners rounded. A quasi-convolutionally smoothed polyhedron is represented implicitly as a density field isosurface. Triage Polygonization subdivides the density field in a BSP-like manner and classifies the resulting cells as inside, outside, or intersected by the isosurface. Planar surface areas usually lie on the boundary of cells and are extracted directly from the subdivided density field with minimal fragmentation. For cells intersected by the isosurface a more general polygonization is rounding radius Triage Polygonization is 20-30 times faster and outputs only 1-2% of the polygons of the marching Cubes algorithm without compromising the approximation. The approach taken for Triage Polygonization can be extended to related problems.