114views more  SIAMREV 2010»
12 years 6 months ago
From Random Polygon to Ellipse: An Eigenanalysis
Suppose x and y are unit 2-norm n-vectors whose components sum to zero. Let P(x, y) be the polygon obtained by connecting (x1, y1), . . . , (xn, yn), (x1, y1) in order. We say that...
Adam N. Elmachtoub, Charles F. Van Loan
99views more  IJCGA 2010»
12 years 10 months ago
Finding All Door Locations that Make a Room Searchable
—A room is a simple polygon with a prespecified point, called the door, on its boundary. Search may be conducted by two guards on the boundary who keep mutual visibility at all ...
Tsunehiko Kameda, John Z. Zhang
12 years 11 months ago
Decomposing a simple polygon into pseudo-triangles and convex polygons
In this paper we consider the problem of decomposing a simple polygon into subpolygons that exclusively use vertices of the given polygon. We allow two types of subpolygons: pseud...
Stefan Gerdjikov, Alexander Wolff
105views Education» more  CORR 1999»
12 years 11 months ago
Hinged Dissection of Polyominoes and Polyforms
A hinged dissection of a set of polygons S is a collection of polygonal pieces hinged together at vertices that can be rotated into any member of S. We present a hinged dissection...
Erik D. Demaine, Martin L. Demaine, David Eppstein...
118views more  IPL 2002»
12 years 11 months ago
Lower bounds for approximate polygon decomposition and minimum gap
We consider the problem of decomposing polygons (with holes) into various types of simpler polygons. We focus on the problem of partitioning a rectilinear polygon, with holes, int...
Joachim Gudmundsson, Thore Husfeldt, Christos Levc...
172views Solid Modeling» more  SMA 2008»
12 years 11 months ago
Guarding curvilinear art galleries with edge or mobile guards
In this paper we consider the problem of monitoring an art gallery modeled as a polygon, the edges of which are arcs of curves. We consider two types of guards: edge guards (these...
Menelaos I. Karavelas
113views more  JGS 2006»
12 years 11 months ago
Pattern based map comparisons
Map comparison techniques based on a pixel-by-pixel comparison are useful for many purposes, but fail to reveal important aspects of map similarities and differences. In contrast, ...
Roger White
118views more  ARSCOM 2008»
12 years 11 months ago
Proper Partitions of a Polygon and k-Catalan Numbers
Let P be a polygon whose vertices have been colored (labeled) cyclically with the numbers 1, 2, . . . , c. Motivated by conjectures of Propp, we are led to consider partitions of ...
Bruce E. Sagan
13 years 1 months ago
An algorithm for the MaxMin area triangulation of a convex polygon
Given a convex polygon in the plane, we are interested in triangulations of its interior, i.e. maximal sets of nonintersecting diagonals that subdivide the interior of the polygon...
J. Mark Keil, Tzvetalin S. Vassilev
13 years 1 months ago
Partitioning Regular Polygons into Circular Pieces I: Convex Partitions
We explore an instance of the question of partitioning a polygon into pieces, each of which is as “circular” as possible, in the sense of having an aspect ratio close to
Mirela Damian-Iordache, Joseph O'Rourke