Let us say you are given a polygon, and also are given some, but not all, of its angle measures and side lengths. How would one compute the following:
- If there is a finite number (zero inclusive) of polygons described by the givens, then list them.
- If there are an infinite number of polygons, then say so.
I was thinking that you could break the polygon into a triangle for each triplet of points, and start solving them, but I was thinking that this would be inefficient, and may not solve $1$ and $2$.
Is there any literature or algorithms relating to this problem, or am I on my own?
Note: It is a bonus if the algorithm also calculates the area during the calculation, but I know methods to do so if you have all the sides and angles.