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

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About: A symbolic-numerical approach to approximate parameterizations of space curves using graphs of critical points Goto Sponge NotDistinct Permalink

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	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. 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. (en)
Title	A symbolic-numerical approach to approximate parameterizations of space curves using graphs of critical points A symbolic-numerical approach to approximate parameterizations of space curves using graphs of critical points (en)
skos:prefLabel	A symbolic-numerical approach to approximate parameterizations of space curves using graphs of critical points A symbolic-numerical approach to approximate parameterizations of space curves using graphs of critical points (en)
skos:notation	RIV/49777513:23520/13:43916221!RIV14-MSM-23520___
http://linked.open...avai/predkladatel	Fakulta aplikovaných věd
http://linked.open...avai/riv/aktivita	P S
http://linked.open...avai/riv/aktivity	P(ED1.1.00/02.0090), S
http://linked.open...iv/cisloPeriodika	April
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Lávička, Miroslav Bizzarri, Michal
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Západočeská univerzita v Plzni / Fakulta aplikovaných věd
http://linked.open...dnocenehoVysledku	59130
http://linked.open...ai/riv/idVysledku	RIV/49777513:23520/13:43916221
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Self-intersection; Ferguson?s cubic; Approximate parameterization; Graph of critical points; Space algebraic curve (en)
http://linked.open.../riv/klicoveSlovo	Ferguson?s cubic Graph of critical points Self-intersection Space algebraic curve Approximate parameterization
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[F479EF36FDCE]
http://linked.open...i/riv/nazevZdroje	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	NTIS - New Technologies for Information Society
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	242
http://linked.open...iv/tvurceVysledku	Bizzarri, Michal Lávička, Miroslav
issn	0377-0427
number of pages	18 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.cam.2012.10.015
http://localhost/t...ganizacniJednotka	23520

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