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.

http://futur.upc.edu/CGA

Enviaments recents

  • Compatible Paths on Labelled Point Sets 

    Arseneva, Elena; Bahoo, Yeganeh; Biniaz, Ahmad; Cano Vila, María del Pilar; Chanchary, Farah; Iacono, John; Jain, Kshitij; Lubiw, Anna; Mondal, Debajyoti; Sheikhan, Khadijeh; D. Thót, Csaba (2019)
    Text en actes de congrés
    Accés obert
    Let 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 

    Arseneva, Elena; Bose, Prosenjit; Cano Vila, María del Pilar; D'Angelo, Anthony; Dujmovic, Vida; Frati, Fabrizio; Langerman, Stefan; Tappini, Alessandra
    Text en actes de congrés
    Accés restringit per política de l'editorial
    We 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 

    Bose, Prosenjit; Cano Vila, María del Pilar; Silveira, Rodrigo Ignacio (2018)
    Text en actes de congrés
    Accés obert
    We 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 

    Garijo Royo, Delia; Marquez Pérez, Alberto; Rodríguez, Natalia; Silveira, Rodrigo Ignacio (2018)
    Text en actes de congrés
    Accés obert
    We 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 

    Garijo Royo, Delia; Marquez Pérez, Alberto; Rodríguez, Natalia; Silveira, Rodrigo Ignacio (2018)
    Text en actes de congrés
    Accés obert
    We 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 

    Lozano Bojados, Antoni; Mora Giné, Mercè; Seara Ojea, Carlos (2019-04-15)
    Article
    Accés restringit per política de l'editorial
    A 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 

    Cardinal, Jean; Sacristán Adinolfi, Vera; Silveira, Rodrigo Ignacio (Chapman & Hall/CRC, 2018-11-09)
    Article
    Accés obert
    Rectangulations 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 

    Huemer, Clemens; Pilz, Alexander; Silveira, Rodrigo Ignacio (2018)
    Comunicació de congrés
    Accés restringit per política de l'editorial
    We 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 

    Silveira, Rodrigo Ignacio; Speckmann, Bettina; Verbeek, Kevin (Springer, 2018)
    Text en actes de congrés
    Accés restringit per política de l'editorial
    A 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 

    Korman, Matias; Löffler, Maarten; Silveira, Rodrigo Ignacio; Strash, Darren (2018-06)
    Article
    Accés restringit per política de l'editorial
    In 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 

    Fabila Monroy, Ruy; Garcia Olaverri, Alfredo Martin; Hurtado Díaz, Fernando Alfredo; Jaume, Rafel; Pérez Lantero, Pablo; Saumell, Maria; Silveira, Rodrigo Ignacio; Tejel Altarriba, Francisco Javier; Urrutia Galicia, Jorge (2018-05)
    Article
    Accés restringit per política de l'editorial
    We 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 

    Esteban Pascual, Guillermo; Huemer, Clemens; Silveira, Rodrigo Ignacio (2018-07-01)
    Article
    Accés restringit per política de l'editorial
    We 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 ...

Mostra'n més