Geodesic
A 3D reconstruction algorithm of a surface of revolution from its projection
Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 1, pp. 84-92

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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.
Mots-clés : 3D reconstruction
Keywords: surface of revolution, differential equations, central projection. 
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     author = {V. A. Klyachin and E. G. Grigorieva},
     title = {A {3D} reconstruction algorithm of a surface of revolution from its projection},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
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     url = {http://geodesic.mathdoc.fr/item/SJIM_2020_23_1_a7/}
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V. A. Klyachin; E. G. Grigorieva. A 3D reconstruction algorithm of a surface of revolution from its projection. Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 1, pp. 84-92. http://geodesic.mathdoc.fr/item/SJIM_2020_23_1_a7/