Linear computational approach to interpolations with polynomial Minkowski Pythagorean hodograph curves

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F19%3A43955088" target="_blank" >RIV/49777513:23520/19:43955088 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0377042719302262?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0377042719302262?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cam.2019.04.029" target="_blank" >10.1016/j.cam.2019.04.029</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Linear computational approach to interpolations with polynomial Minkowski Pythagorean hodograph curves

Popis výsledku v původním jazyce

Methods using Pythagorean hodographs both in Euclidean plane and Minkowski space are often used in geometric modelling when necessary to solve the problem of rationality of offsets of planar domains. A main justification for studying and formulating approximation and interpolation algorithms based on the called Minkowski Pythagorean hodograph (MPH) curves is the fact that they make the trimming procedure of inner offsets considerably simpler. This is why one can find many existing techniques in literature. In this paper a simple computational approach to parametric/geometric Hermite interpolation problem by polynomial MPH curves in R 2,1 is presented and an algorithm to construct such interpolants is described. The main idea is to construct first not a tangent but a normal vector space satisfying the prescribed MPH property that matches the given first order conditions, and then to compute a curve possessing this constructed normal vector space and satisfying all the remaining interpolation conditions. Compared to other methods using special formalisms (e.g. Clifford algebra), the presented approach is based only on solving systems of linear equations. The results are confirmed by number of examples.

Název v anglickém jazyce

Linear computational approach to interpolations with polynomial Minkowski Pythagorean hodograph curves

Popis výsledku anglicky

Methods using Pythagorean hodographs both in Euclidean plane and Minkowski space are often used in geometric modelling when necessary to solve the problem of rationality of offsets of planar domains. A main justification for studying and formulating approximation and interpolation algorithms based on the called Minkowski Pythagorean hodograph (MPH) curves is the fact that they make the trimming procedure of inner offsets considerably simpler. This is why one can find many existing techniques in literature. In this paper a simple computational approach to parametric/geometric Hermite interpolation problem by polynomial MPH curves in R 2,1 is presented and an algorithm to construct such interpolants is described. The main idea is to construct first not a tangent but a normal vector space satisfying the prescribed MPH property that matches the given first order conditions, and then to compute a curve possessing this constructed normal vector space and satisfying all the remaining interpolation conditions. Compared to other methods using special formalisms (e.g. Clifford algebra), the presented approach is based only on solving systems of linear equations. The results are confirmed by number of examples.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/LO1506" target="_blank" >LO1506: Podpora udržitelnosti centra NTIS - Nové technologie pro informační společnost</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

ISSN

0377-0427

e-ISSN

—

Svazek periodika

361

Číslo periodika v rámci svazku

1 December

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

12

Strana od-do

283-294

Kód UT WoS článku

000474316500018

EID výsledku v databázi Scopus

2-s2.0-85065620605