Stabbing information of a simple polygon

Stabbing Information of a Simple Polygon

Stabbing Convex Polygons with a Segment or a Polygon

Let O = {O1, . . . , Om} be a set of m convex polygons in R 2 with a total of n vertices, and let B be another convex k-gon. A placement of B, any congruent copy of B (without reflection), is called free if B does not intersect the interior of any polygon in O at this placement. A placement z of B is called critical if B forms three “distinct” contacts with O at z. Let φ(B,O) be the number of f...

New Results on Stabbing Segments with a Polygon

We consider a natural variation of the concept of stabbing a set of segments with a simple polygon: a segment s is stabbed by a simple polygon P if at least one endpoint of s is contained in P, and a segment set S is stabbed by P if P stabs every element of S. Given a segment set S, we study the problem of finding a simple polygon P stabbing S in a way that some measure of P (such as area or pe...

Zero-Parity Stabbing Information

Everett et al. [EHN96, EHN97] introduced several varieties of stabbing information for the lines determined by pairs of vertices of a simple polygon P , and established their relationships to vertex visibility and other combinatorial data. In the same spirit, we define the “zero-parity (ZP) stabbing information” to be a natural weakening of their “weak stabbing information,” retaining only the ...

A Simple Polygon Triangulation Algorithm

In this Paper we propose an easily implementable polygon triangulation algorithm using Shortest Paths. The algorithm runs in O(nlogk) deterministic time with k < n 3 . Our algorithm runs in linear time for a large class of polygons. The biggest advantage of the algorithm is that it uses very simple data structures and it computes the triangulation just by scanning the boundary of the polygon. W...