Triangular PN patches subject to surface-area constraints

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F17%3A43932526" target="_blank" >RIV/49777513:23520/17:43932526 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Triangular PN patches subject to surface-area constraints
Original language description
This paper is devoted to the construction of polynomial surfaces with Pythagorean normals (PN surfaces) interpolating given data subject to prescribed constraints on the surface area of the patch. This is a problem analogous to the interpolation with Pythagorean hodograph (PH) curves satisfying the condition on the arc length. The special structure of PN surfaces allows the surface-area condition to be expressed as algebraic constraints on the surfaces coefficients. We employ these shapes for solving the $G^1$ Hermite interpolation problem by triangular PN patches with prescribed surface area. The presented technique is based on interpolating points on the unit sphere and consequently on solving a system of several linear and one quadratic equations. We show that for generic input data there exist at most two quartic PN patches depending on the particular value of the prescribed surface area.
Czech name
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Czech description
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Project
<a href="/en/project/LO1506" target="_blank" >LO1506: Sustainability support of the centre NTIS - New Technologies for the Information Society</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Proceedings of the 17th International Conference on Mathematical Methods in Science and Engineering
ISBN
978-84-617-8694-7
ISSN
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e-ISSN
neuvedeno
Number of pages
9
Pages from-to
333-341
Publisher name
CMMSE
Place of publication
Costa Ballena, Rota, Cádiz (Spain)
Event location
Costa ballena (Rota), Cádiz
Event date
Jul 4, 2017
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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