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