Surfaces Modelling Using Isotropic Fractional-Rational Curves

Surfaces Modelling Using Isotropic Fractional-Rational Curves

The problem of building a smooth surface containing given points or curves is actual due to development of industry and computer technology. Previously used for those purposes, shells of zero Gaussian curvature and minimal surfaces based on isotropic analytic curves are restricted in their consumer...

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Main Authors: Igor V. Andrianov, Nataliia M. Ausheva, Yuliia B. Olevska, Viktor I. Olevskyi
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2019/5072676
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spelling doaj-a7e4ad2b09f6412c9575f422218e06602020-11-24T21:36:01ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422019-01-01201910.1155/2019/50726765072676Surfaces Modelling Using Isotropic Fractional-Rational CurvesIgor V. Andrianov0Nataliia M. Ausheva1Yuliia B. Olevska2Viktor I. Olevskyi3Institute of General Mechanics, RWTH Aachen University, Aachen 52056, GermanyDepartment of Design Automation of Energy Processes and Systems, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv 03056, UkraineMathematic Department, National Technical University “Dnipro Polytechnic”, Dnipro 49005, UkraineMathematic Department, Ukrainian State University of Chemical Technology, Dnipro 49005, UkraineThe problem of building a smooth surface containing given points or curves is actual due to development of industry and computer technology. Previously used for those purposes, shells of zero Gaussian curvature and minimal surfaces based on isotropic analytic curves are restricted in their consumer properties. To expand the possibilities regarding the shaping of surfaces we propose the method of constructing surfaces based on isotropic fractional-rational curves. The surfaces are built using flat isothermal and orthogonal grids and on the basis of the Weierstrass method. In the latter case, the surfaces are minimal. Examples of surfaces that were built according to the proposed method are given.http://dx.doi.org/10.1155/2019/5072676
collection DOAJ
language English
format Article
sources DOAJ
author Igor V. Andrianov
Nataliia M. Ausheva
Yuliia B. Olevska
Viktor I. Olevskyi
spellingShingle Igor V. Andrianov
Nataliia M. Ausheva
Yuliia B. Olevska
Viktor I. Olevskyi
Surfaces Modelling Using Isotropic Fractional-Rational Curves
Journal of Applied Mathematics
author_facet Igor V. Andrianov
Nataliia M. Ausheva
Yuliia B. Olevska
Viktor I. Olevskyi
author_sort Igor V. Andrianov
title Surfaces Modelling Using Isotropic Fractional-Rational Curves
title_short Surfaces Modelling Using Isotropic Fractional-Rational Curves
title_full Surfaces Modelling Using Isotropic Fractional-Rational Curves
title_fullStr Surfaces Modelling Using Isotropic Fractional-Rational Curves
title_full_unstemmed Surfaces Modelling Using Isotropic Fractional-Rational Curves
title_sort surfaces modelling using isotropic fractional-rational curves
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2019-01-01
description The problem of building a smooth surface containing given points or curves is actual due to development of industry and computer technology. Previously used for those purposes, shells of zero Gaussian curvature and minimal surfaces based on isotropic analytic curves are restricted in their consumer properties. To expand the possibilities regarding the shaping of surfaces we propose the method of constructing surfaces based on isotropic fractional-rational curves. The surfaces are built using flat isothermal and orthogonal grids and on the basis of the Weierstrass method. In the latter case, the surfaces are minimal. Examples of surfaces that were built according to the proposed method are given.
url http://dx.doi.org/10.1155/2019/5072676
work_keys_str_mv AT igorvandrianov surfacesmodellingusingisotropicfractionalrationalcurves
AT nataliiamausheva surfacesmodellingusingisotropicfractionalrationalcurves
AT yuliiabolevska surfacesmodellingusingisotropicfractionalrationalcurves
AT viktoriolevskyi surfacesmodellingusingisotropicfractionalrationalcurves
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