Segmentation and parametrization of arbitrary polygon meshes

Polygon meshes are ubiquitous in geometric model representation. Segmentation and parametrization of arbitrary polygon meshes are closely related and crucial in many applications. The primary aim of this paper is to find an efficient and practical way to segment and resample geometric models. We automatically generate a triangular patch network by a simplification algorithm. A simple and cheap algorithm is put forward for calculating the approximate shortest path between two points on triangle mesh, which serves for patch boundary of the segmentation. A set of interactive tools provides users with more freedom to control the final segmentation. The mesh parametrization algorithm in this paper can efficiently map a disk topology mesh surface to an isomorphic planar mesh without fixing boundary points. Ways are also provided to map the planar mesh with natural boundary to specific parameter domain, e.g. square or circular domain. The proposed method can be used in diverse applications, such as patchwise freeform surfaces fitting, multi-resolution analysis, texture mapping, remeshing of arbitrary polygon mesh and blank design of sheet metal forming. Examples are included to demonstrate the efficiency and quality of our method.