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On k-enclosing objects in a coloured point set
(2014)
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We introduce the exact coloured
k
-enclosing object
problem: given a set
P
of
n
points in
R
2
, each of
which has an associated colour in
f
1
;:::;t
g
, and a vec-
tor
c
= (
c
1
;:::;c
t
), ...
On the disks with diameters the sides of a convex 5-gon
(Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II (MA2), 2015)
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We prove that for any convex pentagon there are two disks, among the five disks having a side of the pentagon as diameter and the midpoint of the side as its center, that do not intersect. This shows that K5 is never the ...
Matching points with diametral disks
(2017)
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We consider matchings between a set R of red points and a set B of blue points with diametral disks. In other words, for each pair of matched points p ¿ R and q ¿ B, we consider the diametral disk defined by p and q. We ...
New results on stabbing segments with a polygon
(Springer, 2013)
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We consider a natural variation of the concept of stabbing a segment by a simple polygon: a segment is stabbed by a simple polygon P if at least one of its two endpoints is contained in P. A segment set S is stabbed by P ...
Stabbing circles for some sets of Delaunay segments
(2016)
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Let S be a set of n segments in the plane such that, for
every segment, its two endpoints are adjacent in the Delaunay triangulation of the set of endpoints of all segments in S. Our goal is to compute all the combinatorially ...
Implementing data-dependent triangulations with higher order Delaunay triangulations
(Association for Computing Machinery (ACM), 2016)
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The Delaunay triangulation is the standard choice for building triangulated irregular networks (TINs) to represent terrain surfaces. However, the Delaunay triangulation is based only on the 2D coordinates of the data points, ...
A faster algorithm to compute the visibility map of a 1.5D terrain
(2014)
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Given a 1.5D terrain, i.e., an x -monotone polygonal line in R 2 with n vertices, and 1 m n viewpoints placed on some of the terrain vertices, we study the problem of computing the parts of the terrain that are visible ...
Recoloring directed graphs
(Prensas Universitarias de Zaragoza, 2009)
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Let G be a directed graph and k a positive integer. We define the k-color graph of G (Dk(G)
for short) as the directed graph having all k-colorings of G as node set, and where two k-colorings
and ' are joined by a ...
Moving rectangles
(2010)
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Consider a set of n pairwise disjoint axis-parallel rectangles in the plane.
We call this set the source rectangles S. The aim is to move S to a set of (pairwise
disjoint) target rectangles T . A move consists in a ...
Flow computations on imprecise terrains
(Springer Verlag, 2011)
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Text en actes de congrés.
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We study water flow computation on imprecise terrains. We
consider two approaches to modeling flow on a terrain: one where water
flows across the surface of a polyhedral terrain in the direction of steepest
descent, and ...