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A symbolic-numerical approach to approximate parameterizations of space curves using graphs of critical points

Citace:
BIZZARRI, M., LÁVIČKA, M. A symbolic-numerical approach to approximate parameterizations of space curves using graphs of critical points. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2013, roč. 242, č. April, s. 107-124. ISSN: 0377-0427
Druh: ČLÁNEK
Jazyk publikace: eng
Anglický název: A symbolic-numerical approach to approximate parameterizations of space curves using graphs of critical points
Rok vydání: 2013
Autoři: Mgr. Michal Bizzarri , Doc. RNDr. Miroslav Lávička Ph.D. ,
Abstrakt EN: A simple algorithm for computing an approximate parameterization of real space algebraic curves using their graphs of critical points is designed and studied in this paper. The first step is determining a suitable space graph which contains all critical points of a real algebraic space curve C implicitly defined as the complete intersection of two surfaces. The construction of this graph is based on one projection of C in a general position onto an xy-plane and on an intentional choice of vertices. The second part of the designed method is a computation of a spline curve which replaces the edges of the constructed graph by segments of a chosen free-form curve. This step is formulated as an optimization problem when the objective function approximates the integral of the squared Euclidean distance of the constructed approximate curve to the intersection curve. The presented method, based on combining symbolic and numerical steps to the approximation problem, provides approximate parameterizations of space algebraic curves from a small number of approximating arcs. It may serve as a first step to several problems originating in technical practice where approximation curve parameterizations are needed.
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