About: Rational Pythagorean-hodograph space curves

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://www.sciencedirect.com/science/article/pii/S0167839611000033
Description	A method for constructing rational Pythagorean-hoclograph (PH) curves in R(3) is proposed, based on prescribing a field of rational unit tangent vectors. This tangent field, together with its first derivative, defines the orientation of the curve osculating planes. Augmenting this orientation information with a rational support function, that specifies the distance of each osculating plane from the origin, then completely defines a one-parameter family of oscillating planes, whose envelope is a developable ruled surface. The rational PH space curve is identified as the edge of regression (or cuspidal edge) of this developable surface. Such curves have rational parametric speed, and also rational adapted frames that satisfy the same conditions as polynomial PH curves in order to be rotation-minimizing with respect to the tangent. The key properties of such rational PH space curves are derived and illustrated by examples, and simple algorithms for their practical construction by geometric Hermite interpolation are also proposed. A method for constructing rational Pythagorean-hoclograph (PH) curves in R(3) is proposed, based on prescribing a field of rational unit tangent vectors. This tangent field, together with its first derivative, defines the orientation of the curve osculating planes. Augmenting this orientation information with a rational support function, that specifies the distance of each osculating plane from the origin, then completely defines a one-parameter family of oscillating planes, whose envelope is a developable ruled surface. The rational PH space curve is identified as the edge of regression (or cuspidal edge) of this developable surface. Such curves have rational parametric speed, and also rational adapted frames that satisfy the same conditions as polynomial PH curves in order to be rotation-minimizing with respect to the tangent. The key properties of such rational PH space curves are derived and illustrated by examples, and simple algorithms for their practical construction by geometric Hermite interpolation are also proposed. (en)
Title	Rational Pythagorean-hodograph space curves Rational Pythagorean-hodograph space curves (en)
skos:prefLabel	Rational Pythagorean-hodograph space curves Rational Pythagorean-hodograph space curves (en)
skos:notation	RIV/00216208:11320/11:10104794!RIV12-MSM-11320___
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Šír, Zbyněk
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	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	225737
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/11:10104794
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Pythagorean-hodograph curves; Rational (en)
http://linked.open.../riv/klicoveSlovo	Pythagorean-hodograph curves Rational
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[11433C5FE5BF]
http://linked.open...i/riv/nazevZdroje	Computer Aided Geometric Design
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	28
http://linked.open...iv/tvurceVysledku	Šír, Zbyněk Farouki, Rida
http://linked.open...ain/vavai/riv/wos	000287430400001
http://linked.open...n/vavai/riv/zamer	Metody moderní matematiky a jejich aplikace
issn	0167-8396
number of pages	14 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.cagd.2011.01.002
http://localhost/t...ganizacniJednotka	11320

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