how to find order of rectangles sorted by the overlapping (python)

Question

taking as input an image, such as the example one, I want to order the colored rectangles that compose it by their overlap.

I'll explain: from the image I can get the rectangles for each point in the format (x, y)

example :

{("blue"): [(5, 5), (6, 5), (7, 5), (8, 5), (9, 5), (10, 5), (11, 5), (12, 5), (13, 5), (14, 5), (15, 5), (16, 5), (17, 5), (18, 5), (19, 5), (20 , 5), (21, 5), (22, 5), (23, 5), (24, 5), (25, 5), (26, 5), (27, 5), (5, 6 ), (27, 6), (5, 7), (27, 7), (5, 8), (27, 8), (5, 9), (27, 9), (5, 10), (27, 10), (5, 11), (27, 11), (5, 12), (27, 12), (5, 13), (27, 13), (5, 14), (27 , 14), (5, 15), (27, 15), (5, 16), (27, 16), (5, 17), (27, 17), (5, 18), (27, 18 ), (5, 19), (27, 19), (5, 20), (5, 21), (27, 21), (5, 22), (27, 22), (5, 23), (27, 23), (5, 24), (5, 25), (27, 25), (5, 26), (27, 26), (5, 27), (6, 27), (7 , 27), (8, 27), (9, 27), (10, 27), (11, 27), (12, 27), (13, 27), (14, 27), (15, 27 ), (16, 27), (17, 27), (18, 27), (19, 27), (21, 27), (22, 27), (23, 27), (25, 27), (26, 27), (27, 27)]

represents a dictionary whose key is the color of the rectangle and as values ​​a list of each single pixel that forms it, through its x and y coordinates in space

I can therefore obtain for each rectangle also its spatial coordinates ((5,5), (27,27)) which represent the upper left corner and the lower right corner.

however, I can't find a way to sort the rectangles in the order they should be drawn.

example from the image: the order of the rectangles will be blue, green and yellow because I will have to draw them to regain the image in this order so as to maintain the correct sequence of intersections.

ps I would like to make it without using libraries, like openCV ecc..

EDIT.

I take a png image as input. i create a list of list of tuple where i have every single pixel of the image represented like a RGB tuple (ex. (0, 0, 255))

i want every rectangles to be encoded as a pixel which represents the color of the rectangle. : encoded rectangles

the coded image therefore allows you to know that the blue rectangle will be drawn first, then the green one and finally the yellow one.

this is what I mean by overlapping order: if from the encoded image i draw in order the rectangles i obtain the same overlapping of the original image.

Answer 1

Though the question is pretty unclear, I seem to understand that you

• have raw lists of colored pixels which are the result of drawing overlapping rectangles edges;

• are able to figure out the rectangles they originate from.

If this is the case, then traverse the edges of the rectangles and every time you meet a pixel of a different color (say green instead of blue), note it as a relation "green overlaps blue"). Then apply a topological sort to the partial order so obtained.

There can be harder cases such as multiple overlaps or several rectangles of the same color.