Surface and 3 D Triangular Meshes from Planar Cross

This paper presents two unstructured mesh generation algorithms with a discussion of their implementation. One algorithm is for the generation of a surface triangular mesh from a parallel stack of planar cross-sections (polygons). The other algorithm is for the construction of a 3D triangular (tetrahedral) mesh of the solid region (polyhedron) bounded by the surface mesh and the planar cross-sections. Construction of a surface triangular mesh from planar contours is diicult because of \correspondence", \tiling" and \branching" problems. We provide a simultaneous solution to all three of these problems. This is accomplished by imposing a set of three constraints on the constructed surface mesh and then by deriving precise correspondence and tiling rules from these constraints. The constraints ensure that the regions tiled by these rules obey physical constructs and have a natural appearance. Regions which cannot be tiled by these rules without breaking one or more constraints are tiled with their medial axis (edge Voronoi diagram). Construction of the tetrahedral mesh of the solid region bounded by planar contours and the surface mesh is diicult because the solid can be of high genus (several tunnels and holes) as well as have internal voids. We present a new algorithm to tetrahedralize the prismatoid bounded by two slices and the reconstructed tiling surfaces. Surface and tetrahedral meshing results are obtained with both synthetic and actual medical data.

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