On Quality Triangulation in Three-Dimensional Space

삼차원 공간상에서의 질적인 삼각화에 관한 연구

This paper deals with the problem of generating a uniform tetrahedral mesh which fills a 3-D space with the tetrahedra which are close to the equilateral tetrahedra as possible. This problem is particularly interesting in finite element modeling where a fat triangulation minimizes the error of an analysis. Fat triangulation is defined as a scheme for generating an equilateral triangulation as possible in a given dimension. In finite element modeling, there are many algorithms for generating a mesh in 2-D and 3-D. One of the difficulties in generating a mesh in 3-D is that a 3-D object can not be filled with uniform equilateral tetrahedra only regardless of the shape of the boundary. Fat triangulation in 3-D has been proved to be the one which fills a 3-D space with the tetrahedra which are close to the equilateral as possible. Topological and geometrical properties of the fat triangulation and its application to meshing algorithm are investigated.