Development of vector-parametric fifth-degree B-spline with control points incident the surface

Authors

  • Александр Михайлович Ковтун Danube Institute of National University «Odessa Maritime Academy», 9, Fanagoriyskaja Str., Izmail, Odessa Region, 68600, Ukraine https://orcid.org/0000-0002-6531-2561

DOI:

https://doi.org/10.15587/2312-8372.2016.72032

Keywords:

vector-parametric spline, B-spline, spline with control points incident the curve, smoothness

Abstract

Studies in the field of geometric modeling are aimed at the development of the already existing ways of describing spline surfaces, because to be a bit inconvenient to construct smooth contours of the existing methods. A method in which the control points belong to the curve is proposed.

Based on previous research the method of B-spline construction is proposed. B-spline is a vector-parametric surface with control points incident (belonging to) the curve based on the fifth-degree splines in compliance with the smoothness of the first to the second order. To do this, the resulting vector-parametric spline r = r(u) will «stretch» to v, in a direction different from the u, which gives an opportunity to build a relevant «portions» of the surface. Further, to obtain a B-spline with full smoothness order it is necessary to ensure the «gluing» of the respective portions of the surface providing the appropriate smoothness by «gluing» line, i. e. ensure equality of the corresponding (first and second) derivatives. However, to achieve full smoothness of second order (i. e., ensure continuity of the second fundamental form across the surface), it is necessary to provide equal mixed derivatives through «gluing» line. Test examples of bicubic splines are given.

Author Biography

Александр Михайлович Ковтун, Danube Institute of National University «Odessa Maritime Academy», 9, Fanagoriyskaja Str., Izmail, Odessa Region, 68600

Candidate of Technical Sciences, Associate Professor

Department of General Technical Subjects 

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Published

2016-05-26

How to Cite

Ковтун, А. М. (2016). Development of vector-parametric fifth-degree B-spline with control points incident the surface. Technology Audit and Production Reserves, 3(1(29), 17–21. https://doi.org/10.15587/2312-8372.2016.72032

Issue

Vol. 3 No. 1(29) (2016): Mathematical modeling. Mechanical engineering and machine building. Information technologies

Section

Mathematical Modeling: Original Research

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Copyright (c) 2016 Александр Михайлович Ковтун

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