Convexifying Monotone Polygons
نویسندگان
چکیده
This paper considers reconngurations of polygons, where each polygon edge is a rigid link, no two of which can cross during the motion. We prove that one can reconngure any monotone polygon into a convex polygon; a polygon is monotone if any vertical line intersects the interior at a (possibly empty) interval. Our algorithm computes in O(n 2) time a sequence of O(n 2) moves, each of which rotates just four joints at once.
منابع مشابه
Convexifying Monotone Polygons while Maintaining Internal Visibility
Let P be a simple polygon on the plane. Two vertices of P are visible if the open line segment joining them is contained in the interior of P . In this paper we study the following questions posed in [5, 6]: (1) Is it true that every non-convex simple polygon has a vertex that can be continuously moved such that during the process no vertex-vertex visibility is lost and some vertex-vertex visib...
متن کاملOptimal Algorithms for Stabbing Polygons by Monotone Chains
In this paper we present optimal algorithms to compute monotone stabbers for convex polygons. More precisely, given a set of m convex polygons with n vertices in total we want to stab the polygons with an x-monotone polygonal chain such that each polygon is entered at its leftmost point and departed at its rightmost point. Since such a stabber does not exist in general, we study two related pro...
متن کاملModem illumination of monotone polygons
We study a generalization of the classical problem of illumination of polygons. Instead of modeling a light source we model a wireless device whose radio signal can penetrate a given number k of walls. We call these objects k-modems and study the minimum number of k-modems necessary to illuminate monotone and monotone orthogonal polygons. We show that every monotone polygon on n vertices can be...
متن کامل