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Sib. Zh. Ind. Mat., 2020, Volume 23, Number 1, Pages 84–92 (Mi sjim1079)  

A 3D reconstruction algorithm of a surface of revolution from its projection

V. A. Klyachin, E. G. Grigorieva

Volgograd State University, Universitetskii pr. 100, Volgograd 400062, Russia

Abstract: Under consideration is the problem of reconstruction of a surface of revolution from the boundary curves of its projection. Two approaches to this problem are suggested. The first approach reduces the problem to a system of functional-differential equations. We describe in detail how to obtain this system. The second approach bases on geometrical considerations and uses a piecewise-conic approximation of the desired surface. The second method rests on the auxiliary statement on the 3D reconstruction of a straight circular cone. We give a formula for calculating the base radius of the cone. In the general case, the surface of revolution is approximated by the surface of rotation of some polygonal curve.

Keywords: 3D reconstruction, surface of revolution, differential equations, central projection.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-47-340015_р_а


DOI: https://doi.org/10.33048/SIBJIM.2020.23.108

Full text: PDF file (513 kB)
First page: PDF file
References: PDF file   HTML file

UDC: 514.88:004.922
Received: 20.08.2019
Revised: 08.10.2019
Accepted:05.12.2019

Citation: V. A. Klyachin, E. G. Grigorieva, “A 3D reconstruction algorithm of a surface of revolution from its projection”, Sib. Zh. Ind. Mat., 23:1 (2020), 84–92

Citation in format AMSBIB
\Bibitem{KlyGri20}
\by V.~A.~Klyachin, E.~G.~Grigorieva
\paper A 3D reconstruction algorithm of a surface of revolution from its projection
\jour Sib. Zh. Ind. Mat.
\yr 2020
\vol 23
\issue 1
\pages 84--92
\mathnet{http://mi.mathnet.ru/sjim1079}
\crossref{https://doi.org/10.33048/SIBJIM.2020.23.108}


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  • Сибирский журнал индустриальной математики
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