Please use this identifier to cite or link to this item: http://hdl.handle.net/1783.1/3559

Generating strictly non-self-overlapping structured quadrilateral grids

Authors Lin, Hongwei
Tang, Kai
Joneja, Ajay
Bao, Hujun
Issue Date 2007
Source Computer-aided design, v. 39, (9), 2007, SEP, p. 709-718
Summary In this paper, we present a BPM (Bezier patch mapping) algorithm which generates a strictly non-self-overlapping structured quadrilateral grid in a given four-sided planar region. Given four pieces of polynomial curves which enclose a simple region in the plane, the algorithm first constructs a Bezier patch which interpolates the four curves (as its four boundary curves), while the inner control points of its control grid remain unknown. In this paper, we show that. for the bijective condition to be satisfied, it is sufficient that the interior points satisfy a set of quadratic inequality equations. Exploiting this key result, we formulate the mapping algorithm as an optimization problem where the constraints are the bijective condition of the Bezier patch mapping (BPM), and the objective is to find out the best from all of the non-self-overlapping grids. Thus, commercial optimization solvers can be used to find the bijective mapping. If a solution to the optimization problems exists, then so does a solution to the mapping problem. and vice-versa. The BPM method is simple and intuitive, and some examples presented in this paper demonstrate its effectiveness. (C) 2007 Elsevier Ltd. All rights reserved.
Subjects
ISSN 0010-4485
Rights 'Computer-Aided Design © copyright 2007 Elsevier. The Journal's web site is located at http://www.sciencedirect.com/
Language English
Format Article
Access View full-text via DOI
View full-text via Web of Science
View full-text via Scopus
Find@HKUST
Files in this item:
File Description Size Format
lin_tang_joneja_bao_cad_v39n91.pdf 522.04 kB Adobe PDF