Reporting and Counting Intersections Between Two Sets of Line Segments

External-Memory Algorithms for Processing Line Segments in Geographic Information Systems

“…Although a timeoptimal internal-memory algorithm for the general intersection problem exists [10], a number of simpler solutions have been presented for the red-blue problem [8,11,22,26]. Two of these algorithms [11,26] are not plane-sweep algorithms, but both sort segments of the same color in a preprocessing step with a plane-sweep algorithm.…”

Toward spatial joins for polygons

“…This problem is closely related to line segment intersection [7,10,20,12,5] in computational geometry. When there are no intersections among the non-horizontal boundaries of the same trapezoid set, the problem is closely related to the red/blue line segment intersection problem [19,11,24], a variant of line segment intersection. In this section, we show that some in-memory algorithms for these two problems can be extended to detect intersections between non-horizontal boundaries of trapezoids in trapezoid join.…”

“…While many existing algorithms [7,10,20,19,11,12,5,24] can be the candidates for the first component, the second component seems new and unrelated to known problems. Surprisingly, we show that the containment and horizontal boundary intersection conditions on trapezoids can be reduced to a "dynamic" version of the rectangle join problem.…”

“…Specifically, one case is to determine intersections of non-horizontal boundaries of trapezoids. This step is closely related to the line segment intersection problem [7,10,20,19,11,12,5,24]. The other case is to find intersections that are caused by containment or horizontal lines.…”

“…To achieve the efficiency goal, we extend the algorithm by Mairson and Stolfi [19] (for the case of no non-horizontal boundary intersection) and the algorithm by Bentley and Ottmann [7] (for the general case) for Step 1. We show that Step 2 can be done by modifying Step 1.…”