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A fast polymesh to level set algorithm

A grid point in a level set contains the distance to the closest point on the surface of all objects. A naive approach to computing this distance is to compare each grid point with every polygonal surface. Additionally, inside/outside checks are required to determine the sign of the distance. [Breen et al. 2001] developed a scanconversion technique that relied on a Voronoi space partition based on the features of the polygonal objects. We developed a scheme that uses a simple bounding box and space partitioning cone. Computation of values within a narrow band around the surface consists of two steps: pre-processing of geometric information and distance splatting. Further, we provide the option to produce completely populated signed distance fields using a high order Fast Marching Method [Sethian 1996]. Our approach is to minimize the number of triangles that are compared with each grid point by building bounding geometries for each triangle in a pre-processing step. Because this is a local approach, it is sensitive to errors in the geometry. Self-intersecting objects and incorrect normals will cause artifacts. However holes can be filled using Volumetric Diffusion [Davis et al. 2002].