I want to find the number of rectangles that there are in a region, that do not include any of a given set of points, but do include another specific point. Below is an example, where the blue point is the point that must be included, and the red points cannot be included in any of the rectangles. Is there any formula, or summation, that I could use to find this number out? I know of this problem, which is similar to mine, except that I have more conditions, and I cannot find out how to apply this formula with my restrictions.
In the example, the green dot must be in all rectangles, red dots cannot be in any rectangles, the blue rectangle is an example of a valid rectangle, and purple rectangle is example of invalid rectangle. The rectangles can extend all the way up to the black boundaries, which are also given.
