Rational Pythagorean-hodograph space curves

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10104794" target="_blank" >RIV/00216208:11320/11:10104794 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.sciencedirect.com/science/article/pii/S0167839611000033" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0167839611000033</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cagd.2011.01.002" target="_blank" >10.1016/j.cagd.2011.01.002</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Rational Pythagorean-hodograph space curves

Popis výsledku v původním jazyce

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 geometri

Název v anglickém jazyce

Rational Pythagorean-hodograph space curves

Popis výsledku anglicky

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 geometri

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

—

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2011

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Computer Aided Geometric Design

ISSN

0167-8396

e-ISSN

—

Svazek periodika

28

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

14

Strana od-do

75-88

Kód UT WoS článku

000287430400001

EID výsledku v databázi Scopus

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