On the Number of Empty Pseudo-Triangles in Point Sets

نویسندگان

  • Marc J. van Kreveld
  • Bettina Speckmann
چکیده

We analyze the minimum and maximum number of empty pseudo-triangles defined by any planar point set. We consider the cases where the three convex vertices are fixed and where they are not fixed. Furthermore, the pseudo-triangles must either be star-shaped or can be arbitrary.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On Decompositions, Partitions, and Coverings with Convex Polygons and Pseudo-Triangles

We propose a novel subdivision of the plane that consists of both convex polygons and pseudo-triangles. This pseudo-convex decomposition is significantly sparser than either convex decompositions or pseudo-triangulations for planar point sets and simple polygons. We also introduce pseudo-convex partitions and coverings. We establish some basic properties and give combinatorial bounds on their c...

متن کامل

Decompositions, Partitions, and Coverings with Convex Polygons and Pseudo-triangles

We propose a novel subdivision of the plane that consists of both convex polygons and pseudo-triangles. This pseudo-convex decomposition is significantly sparser than either convex decompositions or pseudo-triangulations for planar point sets and simple polygons. We also introduce pseudo-convex partitions and coverings. We establish some basic properties and give combinatorial bounds on their c...

متن کامل

Holes or Empty Pseudo-Triangles in Planar Point Sets

Let E(k, l) denote the smallest integer such that any set of at least E(k, l) points in the plane, no three on a line, contains either an empty convex polygon with k vertices or an empty pseudo-triangle with l vertices. The existence of E(k, l) for positive integers k, l ≥ 3, is the consequence of a result proved by Valtr [Discrete and Computational Geometry, Vol. 37, 565–576, 2007]. In this pa...

متن کامل

The Maximum Number of Empty Congruent Triangles Determined by a Point Set

Let be a set of points in the plane and consider a family of (nondegenerate) pairwise congruent triangles whose vertices belong to . While the number of such triangles can grow superlinearly in — as it happens in lattice sections of the integer grid — it has been conjectured by Brass that the number of pairwise congruent empty triangles is only at most linear. We disprove this conjecture by con...

متن کامل

On edge-disjoint empty triangles of point sets

Let P be a set of points in the plane in general position. Any three points x, y, x 2 P determine a triangle (x, y, z) of the plane. We say that (x, y, z) is empty if its interior contains no element of P . In this paper we study the following problems: What is the size of the largest family of edge-disjoint triangles of a point set? How many triangulations of P are needed to cover all the empt...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007