# Mathematics of Rectangles

1/i m looking for all stuff relative to Rectangles Set (specialty rectangles with edges parallel to axes of orthonormal 2d space: lets note it $RS$.

i found this interesting article A new tractable subclass of the rectangle algebra

any one knows other works?

2/ given a set $S$ of rectangles in $RS$ , and a point $P$ in the same space, how can i find the "nearest" rectangle, with given height and width , to the point $P$ such that it do not "overlap" any element of $S$.

• nearest means: in the sense of the distance between the "center" of the rectangle and the point P
• center of rectangle means: the point with coordinate the center of each interval that defines the rectangle.
• overlap: means that the set of points defined by the two rectangles intersect.

regards

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Posted yesterday to m.se, math.stackexchange.com/questions/111205/…. You should have mentioned this! –  Gerry Myerson Feb 21 '12 at 5:06
Despite Gerry's comment, and the not entirely clear presentation of the question, I think the paper that's linked to is doing something non-trivial and of potential interest. However, I think that the question as phrased is just a fishing expedition; the only question is "Here is something, are there other things?" I suggest that the author looks at mathoverflow.net/howtoask and edits his question to try and get a more focused, well-defined question –  Yemon Choi Feb 21 '12 at 5:11
I've also replaced the AG tag with an OC one, since the paper that's linked to seems to be written from and for an OC perspective –  Yemon Choi Feb 21 '12 at 5:12
how can i mention that, i m the same person in both sites? –  hassan Feb 21 '12 at 5:26
@Yemon Choi, there is two questions : the first one is about finding references, so i can try to do stuff with my self; the second one is more optimization: i m also looking for resources: algorithm, math, library, to solve this problem. thank you –  hassan Feb 21 '12 at 5:34