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. Does anyone knows other works?
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.