Test if point is in some rectangle

Question

I have a large collection of rectangles, all of the same size. I am generating random points that should not fall in these rectangles, so what I wish to do is test if the ge

Answer 1

Why not try this. It seems rather light on both computation and memory.

Consider the projections of all the rectangles onto the base line of your space. Denote that set of line intervals as

 {[Rl1, Rr1], [Rl2, Rr2],..., [Rln, Rrn]}, ordered by increasing left coordinates. 

Now suppose your point is (x, y), start a search at the left of this set until you reach a line interval that contains the point x.

If none does, your point (x,y) is outside all rectangles.

If some do, say [Rlk, Rrk], ..., [Rlh, Rrh], (k <= h) then just check whether y is within the vertical extent of any of these rectangles.

Done.

Good luck.

John Doner