A 3D Surface Meshing Algorithm Using Riemann Calculations with 2D Delaunay in Parametric Space.

Numerical Grid Generation in Computational Field Simulations, The International Society of Grid Generation, pp.729-742, September 2000

MESHING
RESEARCH
CORNER

Abstract

Solid models generated from today's CAD packages routinely contain complex 3D trimmed parametric surfaces. An efficient and robust procedure to mesh these surfaces for finite elements has been sought from their inception. One problem in meshing these surfaces is that the surface's parametric evaluators themselves can create a large computational overhead. The distortions in the surface's parametric mapping can cause great difficulty in finding solutions to the problem of projecting a 3D-point location onto the surface. In the past a preferred way of attacking this problem had been the 3D advancing front method. This method's performance can be directly linked to the solution of the normal projeciton problem. An algorithm of meshing the surfaces in the paramatric space that would pass by these problems is discussed in this paper. This method uses the Riemann calculations to approximate 3D distances, find orthogonal vectors, and locate the 3D midpoints between two 2D parametric locations. The implementation of the method first maps the edges into the 2D parametric space taking into account seams, areas of high curvature, and surface degeneracy. An advancing front algorithm in parametric space, not in 3D-model space, is implemented to check for edge proximity and is used for internal node placement. The internal element generation is then performed in the 2D parametric space with a Delaunay triangulation algorithm. The 2D elements are then mapped back to 3D space and a refinement loop is initiated to ensure acceptable element quality. This approach produces high quality element meshes with substantial time saving over the advancing front algorithm.