Geodesic
Algorithm for restoring the surface of an object from its image
Matematičeskaâ fizika i kompʹûternoe modelirovanie, Tome 24 (2021) no. 1, pp. 16-24.

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This paper describes an algorithm for constructing a surface based on the projection of a triangular mesh applied to this surface. In this case, the angles of the mesh triangles are assumed to be known. This algorithm can be applied to determining the orientation of a three-dimensional object from its snapshot, if the object surface has triangular elements with known angles in advance. In addition to the description of the algorithm, the article gives examples of surface restoration (see figures 3, 4), calculates the calculation error for them and examples of the algorithm application in the problem of determining the orientation of buildings from a photograph. As a result, a spatial triangular mesh was reconstructed from a given flat grid (see figure 2), and the calculation error was 6.21e-05. Measurements of the coordinates of a point in the imagesand calculations using the formulas (2) and (3) gave an error on average of 0.84$^\circ$.
Keywords: surface triangulation, central projection, system of quadratic equations, algorithm for restoring.
Mots-clés : object spatial orientation 
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     author = {A. A. Klyachin and V. A. Klyachin},
     title = {Algorithm for restoring the surface of an object from its image},
     journal = {Matemati\v{c}eska\^a fizika i kompʹ\^uternoe modelirovanie},
     pages = {16--24},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VVGUM_2021_24_1_a1/}
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A. A. Klyachin; V. A. Klyachin. Algorithm for restoring the surface of an object from its image. Matematičeskaâ fizika i kompʹûternoe modelirovanie, Tome 24 (2021) no. 1, pp. 16-24. http://geodesic.mathdoc.fr/item/VVGUM_2021_24_1_a1/