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.
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; J. Appl. Industr. Math., 14:1 (2020), 85–91
\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}
\transl
\jour J. Appl. Industr. Math.
\yr 2020
\vol 14
\issue 1
\pages 85--91
\crossref{https://doi.org/10.1134/S1990478920010093}
Linking options:
https://www.mathnet.ru/eng/sjim1079
https://www.mathnet.ru/eng/sjim/v23/i1/p84
This publication is cited in the following 6 articles:
Vladimir A. Klyachin, Elena G. Grigorieva, Lecture Notes in Networks and Systems, 1120, Artificial Intelligence Algorithm Design for Systems, 2024, 229
Vladimir Klyachin, Aleksei Klyachin, Lecture Notes in Networks and Systems, 597, Data Science and Algorithms in Systems, 2023, 374
A. A. Klyachin, V. A. Klyachin, “Teoremy edinstvennosti vosstanovleniya proobraza pri vyrozhdennykh preobrazovaniyakh”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 22:1 (2022), 15–27
Vladimir A. Klyachin, Elena G. Grigorieva, Lecture Notes in Networks and Systems, 502, Artificial Intelligence Trends in Systems, 2022, 295
Aleksey A. Klyachin, Vladimir A. Klyachin, Lecture Notes in Networks and Systems, 359, Proceedings of the Future Technologies Conference (FTC) 2021, Volume 2, 2022, 210
E.V. Konopatskiy, S.I. Rotkov, M.V. Lagunova, Proceedings of the 32nd International Conference on Computer Graphics and Vision, 2022, 956
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