A spatial region, such as a geographic region, may be represented by a series of vectors in a binary tree or other binary representation. The binary tree may be generated by successively dividing a region into smaller rectangles or vectors, until either a vector is completely within the region or reaches a size limit. The vectors may be ordered, allowing a linear comparison between two binary trees to determine if one space overlaps the other. Because the comparison between two ordered binary trees results in an ordered binary tree, subsequent comparisons may also be performed linearly.