Tetrahedral meshes from planar cross-sections

摘要: In biomedicine, many three-dimensional (3D) objects are sampled in terms of slices such as computed tomography (CT), magnetic resonance imaging (MRI), and ultrasound imaging. It is often necessary to construct surface meshes from the cross sections for visualization, thereafter tetrahedra solid bounded by purpose finite element analysis. Ref. [1] (C. Bajaj, E. Coyle K. Lin, Graphical Models Image Processing 58 (6) (1996) 524–543), we provided a solution construction triangular mesh planar -section contours. Here provide an approach tetrahedralize region contours mesh. difficult task because can be high genus (several through holes) well have complicated branching regions. We develop algorithm effectively reduce into prismatoids, prismatoids. Our tetrahedralization similar advancing front technique (AFT) its flexible control quality. The main criticism AFT that remaining interior may badly shaped or even untetrahedralizable. emphasis our prismatoid on characterization prevention untetrahedralizable parts. Ruppert Seidel (J. Ruppert, R. Seidel, On difficulty tetrahedralizing non-convex polyhedra, in: Proceedings 5th Annual ACM Symposium Comput. Geom., 1989, p. 380–392) shown problem deciding whether polyhedron tetrahedralizable without adding Steiner points NP-complete. characterize this under certain constraints, design one rule chance generating shapes. also leads classification two common categories which better processed if they do occur.