Volume discretization into tetrahedra-I. Verification and orientation of boundary surfaces

Abstract

Three-dimensional triangulation of an arbitrary volume is a time-consuming process, and the boundary surfaces of the object have to be checked very carefully to ensure no error is made. The data verification and preparation work for a general 3D mesh generation problem is best done more or less automatically by another program which not only detects any error in the data but also generates from the given triangular facets all the boundary surfaces with the correct orientations for the next step of volume discretization into tetrahedra, using the advancing front approach. This paper describes such a boundary data pre-processor for discretization of arbitrary objects into tetrahedron elements. In this data-checking and preparation process, first the size and quality of the given randomly numbered triangular facets will be examined, then the closure and orientability of the surfaces that can be constructed from the triangular elements will be verified. Each valid closed surfaces will be given a correct orientation according to its type (interior or exterior surface). The volumes so defined by these surfaces are identified and labelled for 3D mesh generation. © 1991.