Order Types and Visibility Types of Conngurations of Disjoint Convex Plane Sets Order Types and Visibility Types of Conngurations of Disjoint Convex Plane Sets Extended Abstract
نویسندگان
چکیده
We introduce the notions of order type (or: dual arrangement) and visibility type (or: tangent visibility graph) for conngurations of disjoint convex sets in the plane. We develop optimal algorithms for computing and sweeping the order type, and also give a worst case optimal algorithm for computing the tangent visibility graph. The methods are based on a relation, introduced in this paper, between conngurations of disjoint convex sets and arrangements of pseudolines. Finally we give enumeration results for the number of distinct order and visibility types.
منابع مشابه
A convex combinatorial property of compact sets in the plane and its roots in lattice theory
K. Adaricheva and M. Bolat have recently proved that if $,mathcal U_0$ and $,mathcal U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $jin {0,1,2}$ and $kin{0,1}$ such that $,mathcal U_{1-k}$ is included in the convex hull of $,mathcal U_kcup({A_0,A_1, A_2}setminus{A_j})$. One could say disks instead of circles.Here we prove the existence of such a $j$ and $k$ ...
متن کاملThree-dimensional strong convexity and visibility
We define the notions of strong convexity and strong visibility. These notions generalize standard convexity and visibility, as well as several types of nontraditional convexity, such as iso-oriented rectangles and C-oriented polygons. We explore the properties of strong convexity and strong visibility in two and three dimensions. In particular, we establish analogs of the following properties ...
متن کاملOn Order Types of Systems of Segments in the Plane
Let r(n) denote the largest integer such that every family C of n pairwise disjoint segments in the plane in general position has r(n) members whose order type can be represented by points. Pach and Tóth gave a construction that shows r(n) < n 8/ log 9 [11]. They also stated that one can apply the Erdős-Szekeres theorem for convex sets in [10] to obtain r(n) > log16 n. In this note, we will sho...
متن کاملFamilies of convex sets not representable by points
Let (A,B,C) be a triple of disjoint closed convex sets in the plane such that each of them contributes at least one point to the boundary ∂ of the convex hull of their union. If there are three points a ∈ A, b ∈ B, c ∈ C that belong to ∂ and follow each other in clockwise (counterclockwise) order, we say that the orientation of the triple (A,B,C) is clockwise (counterclockwise). We construct fa...
متن کاملThe Hadwiger transversal theorem for pseudolines
We generalize the Hadwiger theorem on line transversals to collections of compact convex sets in the plane to the case where the sets are connected and the transversals form an arrangement of pseudolines. The proof uses the embeddability of pseudoline arrangements in topological affine planes. In 1940 Santaló showed [8], by an example, that Vincensini’s proof [9] of an extension of Helly’s theo...
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 1994