Mesh parameterization using elastic FEM with negative Poisson's ratio material and triangle shape transformation. (July 2023) - Kong, Haijiao; Zhang, Zhibing; Liu, Yuqi; Wang, Zhen; Wei, Yang; Li, Qiaomin
Abstract: Linear mesh parameterization method with a free boundary is an attractive technology and a ubiquitous tool that is widely used in computer graphics and geometry processing. The existing methods always have the shortcoming of element flipping. In this study, a novel linear mesh parameterization method with a free boundary is proposed based on the linear elastic finite element model of a material with negative Poisson's ratio. With appropriate parameter settings, the method can flatten a 3D mesh without element flipping to the most extent. The proposed method is divided into two steps: (1) each element of the 3D mesh is compressed to the origin point; (2) the degenerated mesh is gradually expanded in a plane under the two forces of equal magnitude and opposite directions based on a finite element model of an elastic membrane material with negative Poisson's ratio. Subsequently, the causes of element flipping are analyzed at internal nodes and boundary nodes. The triangle shape transformation (TST) method is proposed to solve the problem of internal element flipping, and the stiffness enhancement method is presented to overcome the boundary element flipping caused by the severe mutual extrusion of the internal elements near the boundary. Finally, typical examples are tested to verify the effectiveness of the proposed mesh parameterization method. Highlights: New linear mesh parameterization method to obtain flattened mesh. A 3D mesh is compressed to origin point, then degenerated mesh expands in a plane. Finite element method is used in mesh parameterization. Flattened mesh without element flipping is obtained.