An Efficient and Simple Quad Edge Conversion of Polygonal Mainfold Objects

This paper presents an efficient and simple quad edge conversion method of polygonal (manifold) objects. In a wide variety of applications such as scientific visualization, virtual reality and computer aided geometric design, polygonal objects are expected to be visualized and manipulated within a given time constraint. To achieve these expectations, it is necessary to introduce an efficient data structure as well as high performance graphics hardware and real-time processing techniques such as simplification and level of details. The quad edge data structure is very efficient for handling polygonal objects even though it was originally designed to handle the subdivisions of manifold objects such as Delaunay triangulations and Voronoi diagrams. It, however, has not been used widely because there is no efficient algorithm for quad edge conversion of conventional polygonal objects. In this paper, we propose a new incremental quad edge conversion algorithm that processes the triangles one by one. Since quad edge has only the splice as a topological operator, the quad edge conversion of each triangle is done by applying three splice operations, a splice per vertex. As an applicaion for the quad edge, a simplification of conventional polygonal objects is implemented. It includes the removing, moving, replacing, and inserting of vertices and edges.