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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F11%3A10104794%21RIV12-MSM-11320___
rdf:type
skos:Concept n11:Vysledek
rdfs:seeAlso
http://www.sciencedirect.com/science/article/pii/S0167839611000033
dcterms: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.
dcterms:title
Rational Pythagorean-hodograph space curves Rational Pythagorean-hodograph space curves
skos:prefLabel
Rational Pythagorean-hodograph space curves Rational Pythagorean-hodograph space curves
skos:notation
RIV/00216208:11320/11:10104794!RIV12-MSM-11320___
n11:predkladatel
n12:orjk%3A11320
n4:aktivita
n10:Z
n4:aktivity
Z(MSM0021620839)
n4:cisloPeriodika
2
n4:dodaniDat
n15:2012
n4:domaciTvurceVysledku
n19:4296133
n4:druhVysledku
n21:J
n4:duvernostUdaju
n9:S
n4:entitaPredkladatele
n18:predkladatel
n4:idSjednocenehoVysledku
225737
n4:idVysledku
RIV/00216208:11320/11:10104794
n4:jazykVysledku
n20:eng
n4:klicovaSlova
Pythagorean-hodograph curves; Rational
n4:klicoveSlovo
n7:Rational n7:Pythagorean-hodograph%20curves
n4:kodStatuVydavatele
NL - Nizozemsko
n4:kontrolniKodProRIV
[11433C5FE5BF]
n4:nazevZdroje
Computer Aided Geometric Design
n4:obor
n5:BA
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
2
n4:rokUplatneniVysledku
n15:2011
n4:svazekPeriodika
28
n4:tvurceVysledku
Šír, Zbyněk Farouki, Rida
n4:wos
000287430400001
n4:zamer
n16:MSM0021620839
s:issn
0167-8396
s:numberOfPages
14
n14:doi
10.1016/j.cagd.2011.01.002
n6:organizacniJednotka
11320