Problem Idea Equidecomposable Polygons

What you are allowed to do:

• Cut a polygon with a line into two polygons
• Glue together polygons

Problem Statement: You are given two polygons P1 and P2. P1 and P2 both have the same area. Give a sequence of cutting and glueing actions which starts with a single polygon P1 and ends up with a single polygon P2.

Fun Fact: Not only is this always possible. It is always possible even if you restrict yourself to "hinged dissections"

Honestly, this sounds like a real "coffin" to program

Without having started writing any code for it (but already knowing a solution that would work) it does seem to me like this would be cumbersome in terms of representing the sequence of actions and verifying a solution. Perhaps the solution verification can be simplified if we restrict vertices of polygons (including intermediate polygons) to integer coordinates.

Actually, maybe that would be too easy.

Actually no, that should be perfectly fine. If we use doubles for coordinates, then those are just rational values, and multiplying by an appropriate power of 2 would make them integers. We can use large integer coordinates.

so if you feel in the great mood to provide generator/checker code for such task yourself - just tell

Speaking of this, I actually have another problem which I wanted to suggest adding, which I already have a solution for but wanted to save it until I had generator/checker ready. How should the generator/checker be formed? As in, what format or style should it follow or what languages am I allowed to use?