How to compute the union polygon of two (or more) rectangles

Question

For example we have two rectangles and they overlap. I want to get the exact range of the union of them. What is a good way to compute this?

These are the two overlappi

Answer 1

For a relatively simple and reliable way, you can work as follows:

• sort all abscissas (of the vertical sides) and ordinates (of the horizontal sides) independently, and discard any duplicate.

• this establishes mappings between the coordinates and integer indexes.

• create a binary image of size NxN, filled with black.

• for every rectangle, fill the image in white between the corresponding indexes.

• then scan the image to find the corners, by contour tracing, and revert to the original coordinates.

This process isn't efficient as it takes time proportional to N² plus the sum of the (logical) areas of the rectangles, but it can be useful for a moderate amount of rectangles. It easily deals with coincidences.

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In the case of two rectangles, there aren't so many different configurations possible and you can precompute all vertex sequences for the possible configuration (a small subset of the 2^9 possible images).

There is no need to explicitly create the image, just associate vertex sequences to the possible permutations of the input X and Y.