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Title: Generating strictly non-self-overlapping structured quadrilateral grids
Authors: Lin, Hongwei
Tang, Kai
Joneja, Ajay
Bao, Hujun
Keywords: Structured quadrilateral grid
Four-sided region
Boundary-conforming mapping
Issue Date: Sep-2007
Citation: Computer-Aided Design, v. 39, iss. 9, September 2007, p. 709-718
Abstract: In this paper, we present a BPM (Bézier 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 Bézier 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 Bézier Patch Mapping, 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
Rights: 'Computer-Aided Design © copyright 2007 Elsevier. The Journal's web site is located at
Appears in Collections:MECH Journal/Magazine Articles
ISOM Journal/Magazine Articles

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