Incremental polygonization of implicit surfaces

This paper describes an incremental polygonization technique for implicit s urfaces built from skeletal elements. Our method is dedicated to fast previ ewing in an interactive modeling system environment, We rely on an octree d ecomposition of space combined with Lipschitz conditions to recursively sub divide cells until a given level of precision is reached and converge to th e implicit surface. We use a trilinear interpolation approximation of the f ield function to create a topologically consistent tessellation characteriz ed by an adjacency graph. Our algorithm aims at updating the mesh locally i n regions of space where changes in the potential field occurred. Therefore , we propose an octree inflating and deflating strategy to preserve the oct ree structure as much as possible and to avoid useless or redundant computa tions. Timings show that our incremental algorithm dramatically speeds up t he overall polygonization process for complex objects. (C) 2000 Academic Pr ess.