C2 Hermitovská interpolace Pythagorejskými křivkami

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F07%3A00005642" target="_blank" >RIV/00216208:11320/07:00005642 - isvavai.cz</a>

Výsledek na webu

—

DOI - Digital Object Identifier

—

Jazyk výsledku

angličtina

Název v původním jazyce

C2 Hermite interpolation by Pythagorean hodograph space curves

Popis výsledku v původním jazyce

We solve the problem of C2 Hermite interpolation by Pythagorean Hodograph (PH) space curves. More precisely, for any set of C2 space boundary data (two points with associated Żrst and second derivatives) we construct a four{dimensional family of PH interpolants of degree 9 and introduce a symetrically invariant parameterization of this family. This parameterization is used to identify a particular solution, which has the following properties. Firstly, it preserves planarity, i.e., the interpolant to planar data is a planar PH curve. Secondly, it has the best possible approximation order 6. Thirdly, it is symmetric in the sense that the interpolant of the reversed' set of boundary data is simply the reversed' original interpolant. This particular PH interpolant is exploited for designing algorithms for converting (possibly piecewise) analytical curves into a piecewise PH curve of degree 9 which is globally C2.

Název v anglickém jazyce

C2 Hermite interpolation by Pythagorean hodograph space curves

Popis výsledku anglicky

We solve the problem of C2 Hermite interpolation by Pythagorean Hodograph (PH) space curves. More precisely, for any set of C2 space boundary data (two points with associated Żrst and second derivatives) we construct a four{dimensional family of PH interpolants of degree 9 and introduce a symetrically invariant parameterization of this family. This parameterization is used to identify a particular solution, which has the following properties. Firstly, it preserves planarity, i.e., the interpolant to planar data is a planar PH curve. Secondly, it has the best possible approximation order 6. Thirdly, it is symmetric in the sense that the interpolant of the reversed' set of boundary data is simply the reversed' original interpolant. This particular PH interpolant is exploited for designing algorithms for converting (possibly piecewise) analytical curves into a piecewise PH curve of degree 9 which is globally C2.

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

2007

Kód důvěrnosti údajů

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

Název periodika

Mathematics of Computation

ISSN

0025-5718

e-ISSN

—

Svazek periodika

2007

Číslo periodika v rámci svazku

76

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

19

Strana od-do

1373-1391

Kód UT WoS článku

—

EID výsledku v databázi Scopus

—