Mapping rational rotation-minimizing frames from polynomial curves on to rational curves

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10423267" target="_blank" >RIV/00216208:11320/20:10423267 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=nQMwE9HF1P" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=nQMwE9HF1P</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cagd.2020.101833" target="_blank" >10.1016/j.cagd.2020.101833</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Mapping rational rotation-minimizing frames from polynomial curves on to rational curves

Popis výsledku v původním jazyce

Given a polynomial space curve that has a rational rotation-minimizing frame (an RRMF curve), a methodology is developed to construct families of rational space curves with the same rotation-minimizing frame as at corresponding points. The construction employs the dual form of a rational space curve, interpreted as the edge of regression of the envelope of a family of osculating planes, having normals in the direction and distances from the origin specified in terms of a rational function as . An explicit characterization of the rational curves generated by a given RRMF curve in this manner is developed, and the problem of matching initial and final points and frames is shown to impose only linear conditions on the coefficients of , obviating the non-linear equations (and existence questions) that arise in addressing this problem with the RRMF curve . Criteria for identifying low-degree instances of the curves are identified, by a cancellation of factors common to their numerators and denominators, and the methodology is illustrated by a number of computed examples.

Název v anglickém jazyce

Mapping rational rotation-minimizing frames from polynomial curves on to rational curves

Popis výsledku anglicky

Given a polynomial space curve that has a rational rotation-minimizing frame (an RRMF curve), a methodology is developed to construct families of rational space curves with the same rotation-minimizing frame as at corresponding points. The construction employs the dual form of a rational space curve, interpreted as the edge of regression of the envelope of a family of osculating planes, having normals in the direction and distances from the origin specified in terms of a rational function as . An explicit characterization of the rational curves generated by a given RRMF curve in this manner is developed, and the problem of matching initial and final points and frames is shown to impose only linear conditions on the coefficients of , obviating the non-linear equations (and existence questions) that arise in addressing this problem with the RRMF curve . Criteria for identifying low-degree instances of the curves are identified, by a cancellation of factors common to their numerators and denominators, and the methodology is illustrated by a number of computed examples.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA20-11473S" target="_blank" >GA20-11473S: Symetrie a invariance v analýze, geometrickém modelování a teorii optimálního řízení</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

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

78

Číslo periodika v rámci svazku

March 2020

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

13

Strana od-do

101833

Kód UT WoS článku

000526979400006

EID výsledku v databázi Scopus

2-s2.0-85082559625