best search algorithm

My preference is a sort-and-sweep algorithm. Create axis-aligned bounding boxes for the edges. Sort phase: Project the boxes onto the x-axis and sort the points, but remembering which are the "begin" and "end" points for the intervals of projection. Sweep phase: Traverse the sorted points and maintain an "active" set of boxes--those for which you have visited the "begin" point, but not the "end" point. Each time you add a box to the active set, all boxes in that set overlap in x. You test pairs of these boxes for overlap in the y-direction. For those pairs that do overlap, you then finally do an edge-edge intersection test. Whenever you read an "end" point for a box, that box is removed from the active set. The expectation is that the active set has a very small number of boxes at any one time, so the dominant part of the algorithm is the sort phase, which is O(n log n) for n edges.

i'll look into that then, thanks!