Solving polynomial systems using no-root elimination blending schemes

Handle URI:
http://hdl.handle.net/10754/561938
Title:
Solving polynomial systems using no-root elimination blending schemes
Authors:
Barton, Michael ( 0000-0002-1843-251X )
Abstract:
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.
KAUST Department:
Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Elsevier BV
Journal:
Computer-Aided Design
Issue Date:
Dec-2011
DOI:
10.1016/j.cad.2011.09.011
Type:
Article
ISSN:
00104485
Sponsors:
This research was partly supported by the New York Metropolitan Research Fund, Technion.
Appears in Collections:
Articles; Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBarton, Michaelen
dc.date.accessioned2015-08-03T09:34:32Zen
dc.date.available2015-08-03T09:34:32Zen
dc.date.issued2011-12en
dc.identifier.issn00104485en
dc.identifier.doi10.1016/j.cad.2011.09.011en
dc.identifier.urihttp://hdl.handle.net/10754/561938en
dc.description.abstractSearching 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.en
dc.description.sponsorshipThis research was partly supported by the New York Metropolitan Research Fund, Technion.en
dc.publisherElsevier BVen
dc.subjectLinear blenden
dc.subjectNo-root criterionen
dc.subjectPolynomial systemsen
dc.subjectSurfacesurfacesurface intersectionen
dc.titleSolving polynomial systems using no-root elimination blending schemesen
dc.typeArticleen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalComputer-Aided Designen
kaust.authorBarton, Michaelen
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