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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

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_ð_à

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

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UDC: 514.88:004.922
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}