So, I am playing with problems related to perspective images produces by a simple pinhole camera.
I came up with the following problem. Suppose you have a triangle of known side lengths, that is drawn on a piece of flat paper, and this paper is lying on the floor. You take an image of the triangle using a pinhole camera having an arbitrary position and orientation. The image produced is given to you, and from it, you would like to determine the position and orientation of the camera, as well as the coordinates of the three vertices of the triangle.
To make determining the coordinates possible, we attach a coordinate system to the triangle, with its origin located at the first vertex, and its $x$ axis extending from the first to the second vertex, where the vertices are ordered in counter clockwise direction.
It is assumed that the camera focal length is known. Using the camera model and the side lengths of the triangle, and the fact that the triangle lies in the $xy$ plane, one should be able to write three equations that can be solved numerically for the unknowns.
This problem is closely related to this problem. In both problems the side lengths of the triangle are known, and also the focal length is known. In this problem, the coordinates are known, and we want to find the location and orientation of the camera, while in the other problem, the location and orientation of the camera is given and it is required to determine the coordinates of the vertices.