An Efficient Paving Method of Pure Quad Mesh Generation

Abstract

Triangle mesh and quadrilateral mesh are the most common representations in many applications such as geometric modelling, computer graphics and mechanical engineering. Although triangle mesh are much more popular in applications such as computer graphics, the quadrilateral mesh – which is made only by pure quadrilateral elements – is superior to triangular mesh for finite element method are also well discovered[1] in geometric modelling and simulation applications. The quadrilateral mesh generation can be classified into two categories: direct method and indirect method. The indirect method is relying on ground triangle mesh [2]. The main idea of this method is to form quadrilateral mesh by merging and recombining triangle mesh[3-4]. The direct method constructs quadrilateral using quadrilateral trees or advancing front method[5-6].The former one may often produce many low-quality quadrilateral elements around the boundaries of surface. The advancing front method for quad mesh generation is considered to be nonrobust and computationally expensive. The method to pure quad mesh generation presented in this paper is a direct approach based on paving method. There are some differences between the traditional paving method, the method has two clear advantages: (i) An alternating digital tree (ADT) structure[7] are applied to reduce the cost of intersection check of segments. (ii) Some parallelograms are formed to overcome the disvantage of nonrobust. The robustness of this method is demonstrated and verified on many complex surfaces.