Separating and intersecting spherical polygons

摘要: We consider the computation of an optimal workpiece orientation allowing maximal number surfaces to be machined in a single setup on three-, four-, or five-axis numerically controlled machine. Assuming use ball-end cutter, we establish conditions under which surface is machinable by cutter aligned certain direction, without cutter's being obstructed portions same surface. The set such directions represented sphere as convex region, called visibility map By using Gaussian maps and component, can formulate problems geometric sphere. These related include finding densest hemisphere that contains largest subset given spherical polygons, determining great circle separates computing bisects intersects smallest polygons. show how all possible ways intersecting n polygons with v total vertices computed O(vn log n) time partition. making this representation, present efficient algorithms for solving five