About: Low Degree Euclidean and Minkowski Pythagorean Hodograph Curves

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In our contribution we study cubic and quintic Pythagorean Hodograph (PH) curves in the Euclidean and Minkowski planes. We analyze their control polygons and give necessary and sufficient conditions for cubic and quintic curves to be PH. In the case of Euclidean cubics the conditions are known and we provide a new proof. For the case of Minkowski cubics we formulate and prove a new simple geometrical condition. We also give conditions for the control polygons of quintics in both types of planes. Moreover, we introduce the new notion of the preimage of a transformation, which is closely connected to the so-called preimage of a PH curve. We determine which transformations of the preimage curves produce similarities of PH curves in both Euclidean and Minkowski plane. In our contribution we study cubic and quintic Pythagorean Hodograph (PH) curves in the Euclidean and Minkowski planes. We analyze their control polygons and give necessary and sufficient conditions for cubic and quintic curves to be PH. In the case of Euclidean cubics the conditions are known and we provide a new proof. For the case of Minkowski cubics we formulate and prove a new simple geometrical condition. We also give conditions for the control polygons of quintics in both types of planes. Moreover, we introduce the new notion of the preimage of a transformation, which is closely connected to the so-called preimage of a PH curve. We determine which transformations of the preimage curves produce similarities of PH curves in both Euclidean and Minkowski plane. (en)
Title	Low Degree Euclidean and Minkowski Pythagorean Hodograph Curves Low Degree Euclidean and Minkowski Pythagorean Hodograph Curves (en)
skos:prefLabel	Low Degree Euclidean and Minkowski Pythagorean Hodograph Curves Low Degree Euclidean and Minkowski Pythagorean Hodograph Curves (en)
skos:notation	RIV/00216208:11320/10:10052006!RIV11-GA0-11320___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/08/0486), Z(MSM0021620839)
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Šír, Zbyněk
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
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	268951
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/10:10052006
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Pythagorean Hodograph Curves (en)
http://linked.open.../riv/klicoveSlovo	Pythagorean Hodograph Curves
http://linked.open...ontrolniKodProRIV	[59D891915EAB]
http://linked.open...v/mistoKonaniAkce	Tonsberg, Norsko
http://linked.open...i/riv/mistoVydani	BERLIN
http://linked.open...i/riv/nazevZdroje	MATHEMATICAL METHODS FOR CURVES AND SURFACES
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...vavai/riv/projekt	Statistical analysis of functional random variable and its applications
http://linked.open...UplatneniVysledku	2010
http://linked.open...iv/tvurceVysledku	Kosinka, Jiří Šír, Zbyněk
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open...ain/vavai/riv/wos	000279393600026
http://linked.open.../riv/zahajeniAkce	2008-06-26 (xsd:date)
http://linked.open...n/vavai/riv/zamer	Metody moderní matematiky a jejich aplikace
issn	0302-9743
number of pages	25 (xsd:int)
http://purl.org/ne...btex#hasPublisher	SPRINGER-VERLAG BERLIN
https://schema.org/isbn	978-3-642-11619-3
http://localhost/t...ganizacniJednotka	11320

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