Convexity of Sub-polygons of Convex Polygons
نویسنده
چکیده
A convex polygon is defined as a sequence (V0, . . . , Vn−1) of points on a plane such that the union of the edges [V0, V1], . . . , [Vn−2, Vn−1], [Vn−1, V0] coincides with the boundary of the convex hull of the set of vertices {V0, . . . , Vn−1}. It is proved that all sub-polygons of any convex polygon with distinct vertices are convex. It is also proved that, if all sub-(n − 1)-gons of an n-gon with n > 5 are convex, then the n-gon is convex. Other related results are given.
منابع مشابه
Measuring Convexity via Convex Polygons
This paper describes a general approach to compute a family of convexity measures. Inspired by the use of geometric primitives (such as circles) which are often fitted to shapes to approximate them, we use convex polygons for this task. Convex polygons can be generated in many ways, and several are demonstrated here. These polygons are scaled and translated to ensure that they fit the input sha...
متن کاملConstant-Time Convexity Problems on Reconfigurable Meshes
The purpose of this paper is to demonstrate that the versatility of the reconngurable mesh can be exploited to devise constant-time algorithms for a number of important computational tasks relevant to robotics, computer graphics, image processing, and computer vision. In all our algorithms, we assume that one or two n-vertex (convex) polygons are pretiled, one vertex per processor, onto a recon...
متن کاملOn the X-Y Convex Hull of a Set of X-Y Polygons
We study the class of rectilinear polygons, called X Y polygons, with horizontal and vertical edges, which are frequently used as building blocks for very large-scale integrated (VLSI) circuit layout and wiring. In the paper we introduce the notion of convexity within the.~class of X Y polygons and present efficient algorithms for computing the X Y convex hulls of an X Y polygon and of a set of...
متن کاملOn k-convex polygons
We introduce a notion of k-convexity and explore polygons in the plane that have this property. Polygons which are k-convex can be triangulated with fast yet simple algorithms. However, recognizing them in general is a 3SUM-hard problem. We give a characterization of 2-convex polygons, a particularly interesting class, and show how to recognize them in O(n log n) time. A description of their sh...
متن کاملFast Triangulation of the Plane with Respect to Simple Polygons
Let P~,..., Pk be pairwise non-intersecting simple polygons with a total of n vertices and s start vertices. A start vertex, in general, is a vertex both of which neighbors have larger x coordinate. We present an algorithm for triangulating P~,..., Pk in time O(n + s log s). s may be viewed as a measure of non-convexity. In particular, s is always bounded by the number of concave angles + 1, an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006