Surface and 3D triangular meshes from planar cross sections

Kwun-Nan Kevin Lin, Purdue University

Abstract

In biomedical fields, many 3D objects are sampled in terms of slices by computed tomography (CT), magnetic resonance imaging (MRI) and ultrasound imaging. It is often required to construct surface meshes from the cross sections for visualization purposes, and thereafter construct tetrahedra from the solid bounded by the surface meshes for the purpose of finite element analysis. Construction of a surface triangular mesh from planar contours is difficult 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 a solid bounded by planar contours and the surface mesh is difficult because the solid can be of high genus (several through holes) and have branching regions. We develop an algorithm to decompose the solid into prismatoids, and then to tetrahedralize the prismatoids. Our prismatoid tetrahedralization approach is similar to the advancing front technique (AFT). The advantage of AFT is flexible control of element quality. However, its main criticism is that it may generate irregularly shaped or even untetrahedralizable remaining parts. The emphasis of our prismatoid tetrahedralization approach is on the characterization, prevention, and postprocessing of untetrahedralizable parts.

Degree

Ph.D.

Advisors

Bajaj, Purdue University.

Subject Area

Computer science|Electrical engineering

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