Research On Parameterization Of Surface Triangulations

A parameterization of surface triangulations can be viewed as a one-to-onemapping from a parametric domain to the surface. Parameterization of discretesurfaces is a fundamental and widely-used operation in graphics, required, forinstance, for texture mapping, remeshing or surface fitting. In this paper, theattention is mainly paid to parameterizing meshes to a certain parameter domain.The main achievements are as follows: Several typical parameterization methods were studied. Geometric stretch of these methods was compared. One better method was applied to texture mapping and surface fitting. An algorithm of polygonal region partition of arbitrary triangle mesh was put forward and implemented. The algorithm is highly automatic, effective, robust and suitable for the consequent parameterization. Two parameterizations of triangle mesh based on surface partition were presented. One is based on quadrilateral region partition; the other is based on arbitrary polygonal region partition. The algorithms make parameterization more quickly. And the latter provides a new approach for research on global parameterization of triangle mesh with holes. A new arc-length parameterization algorithm was presented for solving parameterization of boundaries produced by polygonal partition. Parameterization with virtual boundary was studied. And the relationship between the number of virtual layers and geomegic stretch was analyzed.