Surface Quadrangulation Algorithms Based On Skeleton Graphs

Mesh quadrangulation has received increasing attention in the past decade. Because of the complexity and diversity of the three-dimensional mesh, the majority of quadrangular segmentation algorithms focused on the geometry optimization, while ignoring the topological properties; others focused on the topological properties, while ignoring the geometry properties. This paper presents a new quadrangular segmentation algorithm based on skeleton, which get combinatorial optimization in both topology and geometry.Firstly, we review the development of three-dimensional mesh segmentation, and introduce several common quadrangular segmentation algorithms. Secondly, this paper improves the three dimensional model skeletonization algorithm, presents a new voxelization method, which based on solving system of linear equations. Thirdly, By editing and H-type segmentation of skeleton graph, three-dimensional model is splited into the T-shirt type and the Pants type of surface. Finally, we propose a quadrangular segmentation method based on the surface of the T-shirt and Pants type, while meeting the constraint condition of topology, which provides the conditions for the flexibility of geometry optimization. In this paper, numerical experiments of algorithms are done on MFC+OpenGL platform.