A Fast Polygonization Method for Quasi-Convolutionally Smoothed Polyhedra

Burkhard Wusche, MSc thesis 1996

Abstract

This thesis introduces Triage Polygonization, a new fast polygonization method for quasi-convolutionally smoothed polyhedra. The polygonization method exploits the property that quasi-convolutionally smoothed polyhedra usually have predominantly planar surfaces with only edges and corners rounded. A quasi-convolutionally smoothed polyhedron is represented implicitly as a density field iso-surface. Triage Polygonization subdivides the density field in a BSP-like manner and classifies the resulting cells as inside, outside, or intersected by the iso-surface. 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 iso-surface a more general polygonization is performed. For quasi-convolutionally smoothing scenes with a small 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. Currently research is underway to extend Triage Polygonization to handle truly convolutionally smoothed scenes.

Thesis

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