Reconstruction of a triangle on a plane by three projections

In this paper, we consider the following problem. On the plane, a triangle $\triangle ABC$ and three straight lines $l_{1}$, $l_{2}$, and $l_{3}$ in the general position are given; the locations of the straight lines are unknown. The problem consists of the reconstruction of the triangle $\triangle ABC$ by the known lengths of the sides of the triangles $\triangle A_{1}B_{1}C_{1}$, $\triangle A_{2}B_{2}C_{2}$, and $\triangle A_{3}B_{3}C_{3}$, which are the projections of the triangle $\triangle ABC$ onto the lines $l_{1}$, $l_{2}$, and $l_{3}$. Similar problems and their multidimensional generalizations are of interest in the theory of computer images.