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Concept

Point (geometry)

Related publications (27)

Order Types of Convex Bodies

We prove a Hadwiger transversal-type result, characterizing convex position on a family of non-crossing convex bodies in the plane. This theorem suggests a definition for the order type of a family of convex bodies, generalizing the usual definition of ord ...

2011

Orthogeodesic Point-Set Embedding of Trees

Radoslav Fulek, Fabrizio Frati

Let S be a set of N grid points in the plane, no two of which lie on the same horizontal or vertical line, and let G be a graph with n vertices (n

Elsevier Science Bv2011

Coloring axis-parallel rectangles

János Pach

For every k and r, we construct a finite family of axis-parallel rectangles in the plane such that no matter how we color them with k colors, there exists a point covered by precisely r members of the family, all of which have the same color. For r = 2, th ...

2010

Indecomposable Coverings with Concave Polygons

Doemoetoer Palvoelgyi

We show that for any concave polygon that has no parallel sides and for any k, there is a k-fold covering of some point set by the translates of this polygon that cannot be decomposed into two coverings. Moreover, we give a complete classification of open ...

Springer-Verlag2010

Delaunay Graphs of Point Sets in the Plane With Respect to Axis-Parallel Rectangles

János Pach

Given a point set P in the plane, the Delaunay graph with respect to axis-parallel rectangles is a graph defined on the vertex set P, whose two points p, q is an element of P are connected by an edge if and only if there is a rectangle parallel to the coor ...

Wiley-Blackwell2009

Points surrounding the origin

János Pach

Suppose d > 2, n > d+1, and we have a set P of n points in d-dimensional Euclidean space. Then P contains a subset Q of d points such that for any p ∈ P, the convex hull of Q∪{p} does not contain the origin in its interior. We also show that for non-emp ...

Springer-Verlag2008

On the estimation of geodesic paths on sampled manifolds under random projections

Pierre Vandergheynst, Matteo Sorci

In this paper, we focus on the use of random projections as a dimensionality reduction tool for sampled manifolds in high-dimensional Euclidean spaces. We show that geodesic paths approximations from nearest neighbors Euclidean distances are well-preserved ...

2008

Related publications (27)

Order Types of Convex Bodies

2011

Orthogeodesic Point-Set Embedding of Trees

Radoslav Fulek, Fabrizio Frati

Let S be a set of N grid points in the plane, no two of which lie on the same horizontal or vertical line, and let G be a graph with n vertices (n

Elsevier Science Bv2011