CONVEX TRAVERSAL IN POLYGON WITH SEGMENT STABBING

Given a set S of disjoint simple polygons on a bounded 2D - Plane, we studied the problem of finding a set of polygon P, such that stabbing S by segment stabbing region in optimal way. We present a novel approach for solvi ng the convex traversing method in PTIME. Convex traversing is a mechanism of layering continues convex hull extracted from points P. Whenever adding a point in the convex traversing plane, it is necessary to compute the whole convexation again, which cont radict the better runtime. We introduce the new notion of dynamic algorithm to reduce the runtime of this problem into LOG - SPACE bounded. Hence output produced at every dynamic modification results only a LOG - SPACE bounded reconstruction.