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2007
Springer

Generating strictly non-self-overlapping structured quadrilateral grids

9 years 3 months ago
Generating strictly non-self-overlapping structured quadrilateral grids
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, th...
Hongwei Lin, Kai Tang, Ajay Joneja, Hujun Bao
Added 12 Dec 2010
Updated 12 Dec 2010
Type Journal
Year 2007
Where CAD
Authors Hongwei Lin, Kai Tang, Ajay Joneja, Hujun Bao
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