Hermite interpolation by piecewise polynomial surfaces with polynomial area element

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F17%3A43931520" target="_blank" >RIV/49777513:23520/17:43931520 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/17:10370823

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.cagd.2017.02.003" target="_blank" >http://dx.doi.org/10.1016/j.cagd.2017.02.003</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cagd.2017.02.003" target="_blank" >10.1016/j.cagd.2017.02.003</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Hermite interpolation by piecewise polynomial surfaces with polynomial area element

Popis výsledku v původním jazyce

This paper is devoted to the construction of polynomial 2-surfaces which possess a polynomial area element. In particular we study these surfaces in the Euclidean space R^3 (where they are equivalent to the PN surfaces) and in the Minkowski space R^{3,1} (where they provide the MOS surfaces). We show generally in real vector spaces of any dimension equipped with a symmetric bilinear form that the Gram determinant of a parametric set of subspaces is a perfect square if and only if the Gram determinant of its orthogonal complement is a perfect square. Consequently the polynomial surfaces of a given degree with polynomial area element can be constructed from the prescribed normal fields solving a system of linear equations. The degree of the constructed surface depending on the degree and the properties of the prescribed normal field is investigated and discussed. We use the presented approach to interpolate a network of points and associated normals with piecewise polynomial surfaces with polynomial area element and demonstrate our method on a number of examples (constructions of quadrilateral as well as triangular patches).

Název v anglickém jazyce

Hermite interpolation by piecewise polynomial surfaces with polynomial area element

Popis výsledku anglicky

This paper is devoted to the construction of polynomial 2-surfaces which possess a polynomial area element. In particular we study these surfaces in the Euclidean space R^3 (where they are equivalent to the PN surfaces) and in the Minkowski space R^{3,1} (where they provide the MOS surfaces). We show generally in real vector spaces of any dimension equipped with a symmetric bilinear form that the Gram determinant of a parametric set of subspaces is a perfect square if and only if the Gram determinant of its orthogonal complement is a perfect square. Consequently the polynomial surfaces of a given degree with polynomial area element can be constructed from the prescribed normal fields solving a system of linear equations. The degree of the constructed surface depending on the degree and the properties of the prescribed normal field is investigated and discussed. We use the presented approach to interpolate a network of points and associated normals with piecewise polynomial surfaces with polynomial area element and demonstrate our method on a number of examples (constructions of quadrilateral as well as triangular patches).

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)

Rok uplatnění

2017

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

51

Číslo periodika v rámci svazku

February

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

18

Strana od-do

30-47

Kód UT WoS článku

000398755900003

EID výsledku v databázi Scopus

2-s2.0-85014455183