Title :
Angle-Preserving Quadrilateral Mesh Parameterization
Author :
Wenyong Gong ; Xiaohua Xie ; Rui Ma ; Tieru Wu
Author_Institution :
Jilin Univ., Jilin, China
Abstract :
In response to their growing use in the real world, this article presents two algorithms for direct parameterization of quadrilateral meshes. The proposed algorithms are angle-preserving mappings, with one mapping a topological disk surface onto a Euclidean plane and one mapping a topological sphere surface onto a unit sphere. Specifically, for topological disk surfaces, the authors devise a discrete conformal energy function to flatten the quadrilateral meshes with a length-preserving boundary condition. For topological sphere surfaces, a derived Tuette energy function is applied to the initialization of parameterization for a mesh, and then the final spherical parametrization result is obtained by minimizing a devised harmonic energy function. Experimental results demonstrate the efficiency of the proposed methods.
Keywords :
conformal mapping; mesh generation; solid modelling; topology; 3D modeling; Euclidean plane; Tuette energy function; angle-preserving mappings; angle-preserving quadrilateral mesh parameterization; direct parameterization; discrete conformal energy function; harmonic energy function; length-preserving boundary condition; spherical parametrization; topological disk surface; topological sphere surface; Boundary conditions; Conformal mapping; Harmonic analysis; Human computer interaction; Laplace equations; Mesh generation; Solid modeling; computer graphics; conformal mapping; parameterization; quadrilateral mesh;
Journal_Title :
Computer Graphics and Applications, IEEE
DOI :
10.1109/MCG.2015.114