Algorithm for restoring the surface of an object from its image

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$^\circ$.