About: Curves and surfaces with rational chord length parameterization

Facets (new session)
Description
Metadata
Settings
- owl:sameAs
- Inference Rule:

About: Curves and surfaces with rational chord length parameterization Goto Sponge NotDistinct Permalink

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
Description	The investigation of rational varieties with chord length parameterization (shortly RCL varieties) was started by Farin (2006) who observed that rational quadratic circles in standard Bézier form are parametrized by chord length. Motivated by this observation, general RCL curves were studied. Later, the RCL property was extended to rational triangular Bézier surfaces of an arbitrary degree for which the distinguishing property is that the ratios of the three distances of a point to the three vertices of an arbitrary triangle inscribed to the reference circle and the ratios of the distances of the parameter point to the three vertices of the corresponding domain triangle are identical. In this paper, after discussing rational tensor-product surfaces with the RCL property, we present a general unifying approach and study the conditions under which a k-dimensional rational variety in d-dimensional Euclidean space possesses the RCL property. We analyze the entire family of RCL varieties, provide their general parameterization and thoroughly investigate their properties. Finally, the previous observations for curves and surfaces are presented as special cases of the introduced unifying approach. The investigation of rational varieties with chord length parameterization (shortly RCL varieties) was started by Farin (2006) who observed that rational quadratic circles in standard Bézier form are parametrized by chord length. Motivated by this observation, general RCL curves were studied. Later, the RCL property was extended to rational triangular Bézier surfaces of an arbitrary degree for which the distinguishing property is that the ratios of the three distances of a point to the three vertices of an arbitrary triangle inscribed to the reference circle and the ratios of the distances of the parameter point to the three vertices of the corresponding domain triangle are identical. In this paper, after discussing rational tensor-product surfaces with the RCL property, we present a general unifying approach and study the conditions under which a k-dimensional rational variety in d-dimensional Euclidean space possesses the RCL property. We analyze the entire family of RCL varieties, provide their general parameterization and thoroughly investigate their properties. Finally, the previous observations for curves and surfaces are presented as special cases of the introduced unifying approach. (en)
Title	Curves and surfaces with rational chord length parameterization Curves and surfaces with rational chord length parameterization (en)
skos:prefLabel	Curves and surfaces with rational chord length parameterization Curves and surfaces with rational chord length parameterization (en)
skos:notation	RIV/49777513:23520/12:43914987!RIV13-MSM-23520___
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM 235200001)
http://linked.open...iv/cisloPeriodika	5
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Bastl, Bohumír Lávička, Miroslav 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	Západočeská univerzita v Plzni / Fakulta aplikovaných věd
http://linked.open...dnocenehoVysledku	129302
http://linked.open...ai/riv/idVysledku	RIV/49777513:23520/12:43914987
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Rational Bézier patches; Chord lengths parameterizations; Rational varieties (en)
http://linked.open.../riv/klicoveSlovo	Rational varieties Chord lengths parameterizations Rational Bézier patches
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[FB1D03281090]
http://linked.open...i/riv/nazevZdroje	COMPUTER AIDED GEOMETRIC DESIGN
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	3 (xsd:int)
http://linked.open...cetTvurcuVysledku	4 (xsd:int)
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	29
http://linked.open...iv/tvurceVysledku	Bastl, Bohumír Lávička, Miroslav Šír, Zbyněk Jüttler, Bert
http://linked.open...n/vavai/riv/zamer	http://linked.opendata.cz/resource/domain/vavai/zamer/MSM%20235200001
issn	0167-8396
number of pages	11 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.cagd.2011.04.003
http://localhost/t...ganizacniJednotka	23520

Faceted Search & Find service v1.16.118 as of Jun 21 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Jun 21 2024, on Linux (x86_64-pc-linux-gnu), Single-Server Edition (126 GB total memory, 48 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software