Solving polynomial systems using no-root elimination blending schemes
Type
ArticleAuthors
Barton, Michael
KAUST Department
Visual Computing Center (VCC)Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2011-12Permanent link to this record
http://hdl.handle.net/10754/561938
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Show full item recordAbstract
Searching for the roots of (piecewise) polynomial systems of equations is a crucial problem in computer-aided design (CAD), and an efficient solution is in strong demand. Subdivision solvers are frequently used to achieve this goal; however, the subdivision process is expensive, and a vast number of subdivisions is to be expected, especially for higher-dimensional systems. Two blending schemes that efficiently reveal domains that cannot contribute by any root, and therefore significantly reduce the number of subdivisions, are proposed. Using a simple linear blend of functions of the given polynomial system, a function is sought after to be no-root contributing, with all control points of its BernsteinBézier representation of the same sign. If such a function exists, the domain is purged away from the subdivision process. The applicability is demonstrated on several CAD benchmark problems, namely surfacesurfacesurface intersection (SSSI) and surfacecurve intersection (SCI) problems, computation of the Hausdorff distance of two planar curves, or some kinematic-inspired tasks. © 2011 Elsevier Ltd. All rights reserved.Citation
Bartoň, M. (2011). Solving polynomial systems using no-root elimination blending schemes. Computer-Aided Design, 43(12), 1870–1878. doi:10.1016/j.cad.2011.09.011Sponsors
This research was partly supported by the New York Metropolitan Research Fund, Technion.Publisher
Elsevier BVJournal
Computer-Aided Designae974a485f413a2113503eed53cd6c53
10.1016/j.cad.2011.09.011