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.

Recent Submissions

  • The [Theta]-operator and the low hierarchy 

    Castro Rabal, Jorge; Seara Ojea, Carlos (1992-07)
    Research report
    Open Access
    Long and Sheu in their paper [LS-91] introduced a refinement of the low hierarchy based on the [Theta]-levels of the polynomial time hierarchy which gives a deeper sight of the internal structure of NP. In this paper we ...
  • Matching random colored points with rectangles 

    Corujo, Josué; Flores Peñaloza, David; Huemer, Clemens; Seara Ojea, Carlos; Pérez Lantero, Pablo (Springer, 2020)
    Conference report
    Open Access
    Let S[0,1]2 be a set of n points, randomly and uniformly selected. Let RB be a random partition, or coloring, of S in which each point of S is included in R uniformly at random with probability 1/2. We study the random ...
  • Algorithmic geometry with infinite time computation 

    Huemer, Clemens; Muller, Moritz Martin; Seara Ojea, Carlos; Tobar Nicolau, Adrián (2021)
    Conference report
    Restricted access - publisher's policy
  • On maximum-sum matchings of points 

    Bereg, Sergey; Chacón Rivera, Oscar; Flores Peñaloza, David; Huemer, Clemens; Pérez Lantero, Pablo; Seara Ojea, Carlos (2021)
    Conference report
    Restricted access - publisher's policy
    Huemer et al. (Discrete Math., 2019) proved that for any two point sets R and B with |R| = |B|, the perfect matching that matches points of R with points of B, and maximizes the total squared Euclidean distance of the ...
  • Terrain prickliness: theoretical grounds for high complexity viewsheds 

    Acharyya, Ankush; Jallu, Ramesh; Löffler, M.; Meijer, Geert; Saumell Mendiola, Maria; Silveira, Rodrigo Ignacio; Staals, Frank (2021)
    Conference report
    Open Access
    An important task when working with terrain models is computing viewsheds: the parts of the terrain visible from a given viewpoint. When the terrain is modeled as a polyhedral terrain, the viewshed is composed of the union ...
  • Terrain prickliness: theoretical grounds for low complexity viewsheds 

    Acharyya, Ankush; Jallu, Ramesh; Löffler, M.; Meijer, Geert; Saumell Mendiola, Maria; Silveira, Rodrigo Ignacio; Staals, Frank; Tiwary, Hans Raj (2021)
    Conference report
    Restricted access - publisher's policy
  • Shortest paths in portalgons 

    Löffler, M.; Silveira, Rodrigo Ignacio; Staals, Frank (2021)
    Conference report
    Restricted access - publisher's policy
  • Maximum box problem on stochastic points 

    Caraballo, Luis E.; Pérez Lantero, Pablo; Seara Ojea, Carlos; Ventura, Inmaculada (Springer Nature, 2021-10-28)
    Article
    Open Access
    Given a finite set of weighted points in Rd (where there can be negative weights), the maximum box problem asks for an axis-aligned rectangle (i.e., box) such that the sum of the weights of the points that it contains is ...
  • On (a, k)-sets and (a, k)-hulls in the plane 

    Claverol Aguas, Mercè; Herrera Becerra, Luís Hernán; Seara Ojea, Carlos; Pérez Lantero, Pablo (2021)
    Conference report
    Open Access
    This abstract reports first the study of upper and lower bounds for the maximum number of all the combinatorially different (a, k)-sets of an n-point set P in the plane, 0 < a = p and 0 < 2k < n, depending on the ...
  • The edge labeling of higher order Voronoi diagrams 

    Claverol Aguas, Mercè; de las Heras Parrilla, Andrea; Huemer, Clemens; Martínez Moraian, Alejandra (2021)
    Conference report
    Open Access
    We present an edge labeling of order-k Voronoi diagrams, Vk(S), of point sets S in the plane, and study properties of the regions defined by them. Among them, we show that Vk(S) has a small orientable cycle and path double ...
  • A new meta-module design for efficient reconfiguration of modular robots 

    Parada, Irene; Sacristán Adinolfi, Vera; Silveira, Rodrigo Ignacio (Springer Nature, 2021-05-01)
    Article
    Open Access
    We propose a new meta-module design for two important classes of modular robots. The new metamodule is three-dimensional, robust and compact, improving on the previously proposed one. It applies to socalled “edge-hinged” ...
  • New production matrices for geometric graphs 

    Esteban Pascual, Guillermo; Huemer, Clemens; Silveira, Rodrigo Ignacio (Elsevier, 2022-01-15)
    Article
    Restricted access - publisher's policy
    We use production matrices to count several classes of geometric graphs. We present novel production matrices for non-crossing partitions, connected geometric graphs, and k-angulations, which provide another, simple and ...

View more