The quick measure of a NURBS surface curvature for accurate triangular meshing

Abstract

NURBS surfaces are the most widely used surfaces for three-dimensional models in CAD/CAE programs. When a model for FEM calculation is prepared with a CAD program it is inevitable to mesh it finally. There are many algorithms for meshing planar regions. Some of them may be used for meshing surfaces but it is necessary to take the curvature of the surface under consideration to avoid poor quality mesh. The mesh must be denser in the curved regions of the surface. In this paper, instead of analysing a surface curvature, the method to assess how close is a mesh triangle to the surface to which its vertices belong, is presented. The distance between a mesh triangle and a parallel tangent plane through a point on a surface is the measure of the triangle quality. Finding the surface point whose projection is located inside the mesh triangle and which is the tangency point to the plane parallel to this triangle is an optimization problem. Mathematical description of the problem and the algorithm to find its solution are also presented in the paper.