CGA -Computational Geometry and Applications
The research group on Computational Geometry and Applications (CGA) is devoted to carrying out research on computational geometry with a strong emphasis in applications. Computational geometry is an active field in the interface between applied mathematics and computer science that studies algorithmic problems involving discrete geometric objects. The field has applications in robotics, computer graphics, CAD/CAM, integrated circuit design, computer vision, and geographic information science.
The CGA group has the goal of working not only on the design of efficient algorithms, but also on their application to different domains. In particular, we will concentrate on making progress on core geometric problems, and on their applications to two concrete domains: robotics and geographic information science.
Collections
Recent Submissions
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Compatible Paths on Labelled Point Sets
(2019)
Conference report
Open AccessLet P and Q be finite point sets of the same cardinality in R 2 , each labelled from 1 to n. Two noncrossing geometric graphs GP and GQ spanning P and Q, respectively, are called compatible if for every face f in GP , there ... -
Pole Dancing: 3D Morphs for Tree Drawings
Conference report
Restricted access - publisher's policyWe study the question whether a crossing-free 3D morph between two straight-line drawings of an n-vertex tree can be constructed consisting of a small number of linear morphing steps. We look both at the case in which the ... -
Sequences of spanning trees for L-infinity Delaunay triangulations
(2018)
Conference report
Open AccessWe extend a known result about L2-Delaunay triangulations to L∞-Delaunay. Let TS be the set of all non-crossing spanning trees of a planar n-point set S. We prove that for each element T of TS, there exists a length-decreasing ... -
Computing optimal shortcuts for networks
(2018)
Conference report
Open AccessWe augment a plane Euclidean network with a segment or shortcut to minimize the largest distance between any two points along the edges of the resulting network. In this continuous setting, the problem of computing distances ... -
Computing optimal shortcuts for networks
(2018)
Conference report
Open AccessWe study augmenting a plane Euclidean network with a segment, called shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Questions of this type have received considerable ... -
Antimagic labelings of caterpillars
(2019-04-15)
Article
Restricted access - publisher's policyA k-antimagic labeling of a graph G is an injection from E(G) to {1,2, ..., |E(G)|+k} such that all vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of the labels assigned to edges incident ... -
A note on flips in diagonal rectangulations
(Chapman & Hall/CRC, 2018-11-09)
Article
Open AccessRectangulations are partitions of a square into axis-aligned rectangles. A number of results provide bijections between combinatorial equivalence classes of rectangulations and families of pattern-avoiding permutations. ... -
A new lower bound on the maximum number of plane graphs using production matrices
(2018)
Conference lecture
Restricted access - publisher's policyWe use the concept of production matrices to show that there exist sets of n points in the plane that admit ¿(41.77n) crossing-free geometric graphs. This improves the previously best known bound of ¿(41.18n) by Aichholzer ... -
Non-crossing paths with geographic constraints
(Springer, 2018)
Conference report
Restricted access - publisher's policyA geographic network is a graph whose vertices are restricted to lie in a prescribed region in the plane. In this paper we begin to study the following fundamental problem for geographic networks: can a given geographic ... -
On the complexity of barrier resilience for fat regions and bounded ply
(2018-06)
Article
Restricted access - publisher's policyIn the barrier resilience problem (introduced by Kumar et al., Wireless Networks 2007), we are given a collection of regions of the plane, acting as obstacles, and we would like to remove the minimum number of regions so ... -
Colored ray configurations
(2018-05)
Article
Restricted access - publisher's policyWe study the cyclic color sequences induced at infinity by colored rays with apices being a given balanced finite bichromatic point set. We first study the case in which the rays are required to be pairwise disjoint. We ... -
New results on production matrices for geometric graphs
(2018-07-01)
Article
Restricted access - publisher's policyWe present novel production matrices for non-crossing partitions, connected geometric graphs, and k-angulations, which provide another way of counting the number of such objects. For instance, a formula for the number of ...
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