Open AccessNovel method of boundary-free mesh parameterization
Author(s) -
Liming Duan,
Xiao Luo,
Lang Ruan,
Minghui Gu
Publication year - 2019
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0217537
Subject(s) - boundary (topology) , distortion (music) , metric (unit) , curvature , polygon mesh , parametric statistics , conformal map , mathematics , tensor (intrinsic definition) , mesh generation , surface (topology) , mathematical analysis , geometry , algorithm , computer science , topology (electrical circuits) , physics , finite element method , amplifier , computer network , operations management , statistics , bandwidth (computing) , combinatorics , economics , thermodynamics
Unless the targeted mesh is developable, metric distortion is inevitable during the process of surface mesh parameterization, thus one important objective of all involved parametric studies is to reduce the metric distortion. In order to further reduce area and angle distortion, a novel method of boundary-free mesh parameterization is presented in the paper. Firstly, the initial boundary-fixed conformal parameterization from 3D surface mesh patch to a plane is performed in the method. Then, based on the initial parameterization, the iterations of boundary-free quasi-harmonic parameterization are developed, where the tensor field is updated in each iterative step and the principal curvature direction is utilized to terminate the iteration. The solution of the novel method is convenient to calculate since it involves a series of linear systems. In our novel parameterization method, lower metric distortion and considerable efficiency have been obtained in experiments.