Hi!
I have problem of packing 2 arbitrary polygons. I.e. we have 2 arbitrary polygons. We are to find such placement of this polygons (we could make rotations and movements), when rectangle, which circumscribes this polygons has minimal area.
I know, that this is a NP-complete problem. I want to choose an efficient algorithm for solving this problem. I' looking for No-Fit-Polygon approach. But I could't find anywhere the simple and clear algorithm for finding the NFP of two arbitrary polygons.
If its NP-complete then you need heuristics, not algorithms. I'd try putting each possible pair of sides together and then sliding one against the other to minimise area, constrained by possible overlap if they are concave of course.
The parameter space does not seem too big and testing it is not too bad either. If you fix one polygon, the other ploygon can be shifted along x-axis by X, and shifted along y-axis by Y and rotated by r.
The interesting region for X and Y can be determined by finding some bounding box for for the polygons. r of course is between and 360 degrees.
So how about you tried a set of a set of equally spaced intervals in the interesting range for X,Y and r. Perhaps, once you found the interesting points in these dimensions, you can do more finer grained search.