Placing 2D shapes in a rectangle efficiently. How to approach it?
I've been searching far and wide on the seven internets, and have come to no avail. The closest to what I need seems to be The cutting stock problem, only in 2D (which is disappointing since Wikipedia doesn't provide any directions on how to solve that one). Another look-alike problem would be UV unwrapping. There are solutions there, but only those that you get from add-ons on various 3D software.
Cutting the long talk short - what I want is this: given a rectangle of known width and height, I have to find out how many shapes (polygons) of known sizes (which may be rotated at will) may I fit inside that rectangle.
For example, I could choose a T-shaped piece and in the same rectangle I could pack it both in an efficient way, resulting in 4 shapes per rectangle
as well as tiling them based on their bounding boxes, case in which I could only fit 3
But of course, this is only an example... and I don't think it would be much use to solving on this particular case. The only approaches I can think of right now are either like backtracking in their complexity or solve only particular cases of this problem. So... any ideas?
Answer
consider what the other answer said by placing the t's into a square, but instead of just leaving it as a square set the shapes up in a list. Then use True and False to fill the nested list as the shape i.e. [[True,True,True],[False,True,False]] for your T shape. Then use a function to place the shapes on the grid. To optimize the results, create a tracker which will pay attention to how many false in a new shape overlap with trues that are already on the grid from previous shapes. The function will place the shape in the place with the most overlaps. There will have to be modifications to create higher and higher optimizations, but that is the general premise which you are looking for.