Interpolation of Hermite data by clamped Minkowski Pythagorean hodograph B-spline curves

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F21%3A43961320" target="_blank" >RIV/49777513:23520/21:43961320 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0377042721000881" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0377042721000881</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cam.2021.113469" target="_blank" >10.1016/j.cam.2021.113469</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Interpolation of Hermite data by clamped Minkowski Pythagorean hodograph B-spline curves

Popis výsledku v původním jazyce

In this paper, the problem of Hermite interpolation by clamped Minkowski Pythagorean hodograph (MPH) B-spline curves is considered. Using the properties of B-splines, our intention is to use the MPH curves of degrees lower than in algorithms designed before. Special attention is devoted to C1/C2 Hermite interpolation by MPH B-spline cubics/quintics. The resulting interpolants are obtained by exploiting properties of B-spline basis functions and via solving special quadratic and linear equations in Clifford algebra Cℓ2,1. All the presented algorithms are purely symbolic. The results are confirmed by several applications, in particular we use them to generate an approximate conversion of a given analytic curve to MPH B-spline curve with a high order of approximation, then to an efficient approximation of the medial axis transform of a planar domain leading to NURBS representation of the (trimmed) offsets of the domain boundaries, and to skinning of systems of circles in plane.

Název v anglickém jazyce

Interpolation of Hermite data by clamped Minkowski Pythagorean hodograph B-spline curves

Popis výsledku anglicky

In this paper, the problem of Hermite interpolation by clamped Minkowski Pythagorean hodograph (MPH) B-spline curves is considered. Using the properties of B-splines, our intention is to use the MPH curves of degrees lower than in algorithms designed before. Special attention is devoted to C1/C2 Hermite interpolation by MPH B-spline cubics/quintics. The resulting interpolants are obtained by exploiting properties of B-spline basis functions and via solving special quadratic and linear equations in Clifford algebra Cℓ2,1. All the presented algorithms are purely symbolic. The results are confirmed by several applications, in particular we use them to generate an approximate conversion of a given analytic curve to MPH B-spline curve with a high order of approximation, then to an efficient approximation of the medial axis transform of a planar domain leading to NURBS representation of the (trimmed) offsets of the domain boundaries, and to skinning of systems of circles in plane.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied 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

2021

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

392

Číslo periodika v rámci svazku

15 August 2021

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

17

Strana od-do

—

Kód UT WoS článku

000634783600021

EID výsledku v databázi Scopus

2-s2.0-85101636957