David P. Dobkin and Diane L. Souvaine. Detecting the intersection of convex objects in the plane. Technical Report No. 89-9, DIMACS, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... this, we have developed and implemented a novel algorithm that determines sightlines through rectangles [13] Briefly, the algorithm operates in a dual space in which the problem reduces to performing a linear number of convex polygon polygon intersections, each requiring logarithmic time [7]. The algorithm finds a stabbing line through oriented, axis aligned rectangles, or determines that no such stabbing line exists, in 2 4 time. ....

David P. Dobkin and Diane L. Souvaine. Detecting the intersection of convex objects in the plane. Technical Report No. 89-9, DIMACS, 1989.

....with good asymptotic bounds, however their practical utility is not clear since many of them are not implemented in a realistic environment. Many algorithms are known for intersection between curved objects represented as algebraic surfaces or piecewise spline models in geometric modeling [14, 25, 33, 24, 37]. However, they are targeted towards robust computations of the intersection curve between such models for CSG operations and boundary computations. They are usually specialized to static environments and are relatively slow for the kind of performance desired in computer simulated environments ....

D. P. Dobkin and D. L. Souvaine. Detecting the intersection of convex objects in the plane. Comput. Aided Geom. Design, 8:181--200, 1991.

.... this, we have developed and implemented a novel algorithm that determines sightlines through rectangles [13] Briefly, the algorithm operates in a dual space in which the problem reduces to performing a linear number of convex polygon polygon intersections, each requiring logarithmic time [7]. The algorithm finds a stabbing line through n oriented, axis aligned rectangles, or determines that no such stabbing line exists, in O(n lg n) time. ##### ##### ##### ##### ##### ##### ##### ##### ######## ######## ######## ######## ######## ######## ########## ########## ########## ########## ....

David P. Dobkin and Diane L. Souvaine. Detecting the intersection of convex objects in the plane. Technical Report No. 89-9, DIMACS, 1989.

.... has been exploited in a series of subsequent papers dealing with separation of polytopes [11] generalized extremal queries and applications [16] intersection of convex and non convex polyhedra [21] intersection of convex bodies with curved edges and faces i.e. splinegons and splinehedra [12,13,25], parallel algorithms for manipulation of polytopes [6,7] applications in computer graphics [8] on line maintenance of polygons [1] and construction of polyhedral intersections [3] Of particular significance in the background of the present paper is the result of Chazelle and Dobkin [4,5] that ....

Dobkin, D. and Souvaine, D., Detecting the intersection of convex objects in the plane, Princeton University Technical Report CS-TR-231-89, October, 1989.

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D. P. Dobkin and D. L. Souvaine. Detecting the intersection of convex objects in the plane. Comput. Aided Geom. Design, 8:181200, 1991.

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