La geometria computacional, àrea primordial d'actuació del grup, és una disciplina a cavall entre les matemàtiques i la informàtica teòrica. El seu objectiu principal és el disseny i l'anàlisi d'algorismes per a la solució eficient de problemes geomètrics. En conseqüència, una tasca fonamental és la identificació de conceptes, propietats i tècniques que ajudin a la descoberta i implementació d'algorismes eficients. Això comporta l'estudi d'estructures de dades geomètriques, la complexitat d'algorismes, la representació i manipulació de figures i d'objectes, la construcció de llocs geomètrics i, més en general, el desenvolupament de la fonamentació geomètrica. En particular, els problemes estudiats inclouen la cerca i el recompte geomètrics, la convexitat i els processos afins, la proximitat, la intersecció, la triangulació, l'aproximació de formes i la visibilitat. Les àrees principals d'aplicació són la informàtica gràfica, el disseny i la fabricació assistits per ordinador, el reconeixement de formes, la morfologia geomètrica, el disseny VLSI, la visió per computador, els sistemes d'informació geogràfica i la robòtica.

http://futur.upc.edu/DCCG

Computational geometry, which is the main area of activity of the group, is a discipline that lies between mathematics and theoretical computer science. The group?s main objective is the design and analysis of algorithms for efficiently solving geometric problems. As a consequence, a fundamental task is to identify concepts, properties and techniques that will help to find and implement efficient geometric algorithms. This involves the study of geometric data structures, algorithm complexity, the representation and manipulation of figures and objects, geometric loci construction and, in general, the development of geometric principles. The problems studied include geometric search and enumeration, convexity and affine processes, proximity, intersection, triangulation, shape approximation and visibility. The main areas of application are computer graphics, computer-aided design and manufacturing, pattern recognition, computational morphology, VLSI design, computer vision, geographical information systems and robotics.

http://futur.upc.edu/DCCG

Computational geometry, which is the main area of activity of the group, is a discipline that lies between mathematics and theoretical computer science. The group?s main objective is the design and analysis of algorithms for efficiently solving geometric problems. As a consequence, a fundamental task is to identify concepts, properties and techniques that will help to find and implement efficient geometric algorithms. This involves the study of geometric data structures, algorithm complexity, the representation and manipulation of figures and objects, geometric loci construction and, in general, the development of geometric principles. The problems studied include geometric search and enumeration, convexity and affine processes, proximity, intersection, triangulation, shape approximation and visibility. The main areas of application are computer graphics, computer-aided design and manufacturing, pattern recognition, computational morphology, VLSI design, computer vision, geographical information systems and robotics.

http://futur.upc.edu/DCCG

Enviaments recents

  • Implementing data-dependent triangulations with higher order delaunay triangulations 

    Rodríguez, Natalia; Silveira, Rodrigo Ignacio (Multidisciplinary Digital Publishing Institute (MDPI), 2017-12-01)
    Article
    Accés restringit per política de l'editorial
    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, ...
  • Order types of random point sets can be realized with small integer coordinates 

    Fabila-Monroy, Ruy; Huemer, Clemens (2017)
    Text en actes de congrés
    Accés obert
    Let S := {p1, . . . , pn} be a set of n points chosen independently and uniformly at random from the unit square and let M be a positive integer. For every point pi = (xi , yi) in S, let p 0 i = (bMxic, bMyic). Let S 0 := ...
  • Matching points with diametral disks 

    Huemer, Clemens; Pérez-Lantero, Pablo; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio (2017)
    Text en actes de congrés
    Accés obert
    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 ...
  • The connectivity of the flip graph of Hamiltonian paths of the grid graph 

    Duque, Frank; Fabila Monroy, Ruy; Flores Peñazola, David; Hidalgo Toscano, Carlos; Huemer, Clemens (2017)
    Text en actes de congrés
    Accés obert
    Let Gn,m be the grid graph with n columns and m rows. Let Hn,m be the graph whose vertices are the Hamiltonian paths in Gn,m, where two vertices P1 and P2 are adjacent if we can obtain P2 from P1 by deleting an edge in P1 ...
  • Distance 2-domination in prisms of graphs 

    Hurtado Díaz, Fernando Alfredo; Mora Giné, Mercè; Rivera Campo, Eduardo; Zuazua Vega, Rita Esther (2017-01-01)
    Article
    Accés restringit per política de l'editorial
    A set of vertices D of a graph G is a distance 2-dominating set of G if the distance between each vertex u ¿ ( V ( G ) - D ) and D is at most two. Let ¿ 2 ( G ) denote the size of a smallest distance 2 -dominating set of ...
  • On Hamiltonian alternating cycles and paths 

    Claverol Aguas, Mercè; García, Alfredo; Garijo Royo, Delia; Seara Ojea, Carlos; Tejel, Javier (2018-03)
    Article
    Accés obert
    We undertake a study on computing Hamiltonian alternating cycles and paths on bicolored point sets. This has been an intensively studied problem, not always with a solution, when the paths and cycles are also required to ...
  • Carathodory's theorem in depth 

    Fabila Monroy, Ruy; Huemer, Clemens (2017-07-01)
    Article
    Accés restringit per política de l'editorial
    Let X be a finite set of points in RdRd . The Tukey depth of a point q with respect to X is the minimum number tX(q)tX(q) of points of X in a halfspace containing q. In this paper we prove a depth version of Carathéodory’s ...
  • Characteristic polynomials of production matrices for geometric graphs 

    Huemer, Clemens; Pilz, Alexander; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio (2017-08-01)
    Article
    Accés restringit per política de l'editorial
    An n×n production matrix for a class of geometric graphs has the property that the numbers of these geometric graphs on up to n vertices can be read off from the powers of the matrix. Recently, we obtained such production ...
  • Locating domination in bipartite graphs and their complements 

    Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel (2017-11-03)
    Report de recerca
    Accés obert
    A set S of vertices of a graph G is distinguishing if the sets of neighbors in S for every pair of vertices not in S are distinct. A locating-dominating set of G is a dominating distinguishing set. The location-domination ...
  • Metric-locating-dominating partitions in graphs 

    Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel (2017-11-03)
    Report de recerca
    Accés obert
    A partition ¿ = { S 1 ,...,S k } of the vertex set of a connected graph G is a metric-locating partition of G if for every pair of vertices u,v belonging to the same part S i , d ( u,S j ) 6 = d ( v,S j ), for some other ...
  • Dominating 2- broadcast in graphs: complexity, bounds and extremal graphs 

    Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Cáceres, José; Puertas, M. Luz (2017-10-16)
    Report de recerca
    Accés obert
    Limited dominating broadcasts were proposed as a variant of dominating broadcasts, where the broadcast function is upper bounded. As a natural extension of domination, we consider dominating 2-broadcasts along with the ...
  • Coloración de grafos por vecindades diferentes. 

    Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Alcom, Liliana; Gutierrez, Marisa (2017-07-07)
    Capítol de llibre
    Accés restringit per política de l'editorial
    En este trabajo de nimos las coloraciones de un grafo que lo resuelven por vecindad. Notamos NL ( G ) al cardinal m nimo de una de estas coloraciones consideradas del grafo G . Estudiamos propiedades generales de estas ...

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