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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Computing optimal shortcuts for networks
(Elsevier, 2019-11-16)
Article
Restricted access - publisher's policyWe study augmenting a plane Euclidean network with a segment, called a shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Problems of this type have received ... -
Capturing points with a rotating polygon (and a 3D extension)
(2019-04)
Article
Restricted access - publisher's policyWe study the problem of rotating a simple polygon to contain the maximum number of elements from a given point set in the plane. We consider variations of this problem where the rotation center is a given point or lies on ... -
Region-based approximation of probability distributions (for visibility between imprecise points among obstacles)
(2019-07)
Article
Open AccessLet p and q be two imprecise points, given as probability density functions on R2 , and let O be a set of disjoint polygonal obstacles in R2 . We study the problem of approximating the probability that p and q can see each ... -
Metric dimension of maximal outerplanar graphs
(2019-03-28)
External research report
Open Access -
Trees whose even-degree vertices induce a path are antimagic
(2019-05-16)
External research report
Open AccessAn antimagic labeling of a connected graph G is a bijection from the set of edges E(G) to {1, 2, . . . , |E(G)|} such that all vertex sums are pairwise distinct, where the vertex sum at vertex v is the sum of the labels ... -
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. ...
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