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.
Col·leccions
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Articles de revista [31]
Enviaments recents
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The [Theta]-operator and the low hierarchy
(1992-07)
Report de recerca
Accés obertLong 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
(Springer, 2020)
Text en actes de congrés
Accés obertLet 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
(2021)
Text en actes de congrés
Accés restringit per política de l'editorial -
On maximum-sum matchings of points
(2021)
Text en actes de congrés
Accés restringit per política de l'editorialHuemer 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
(2021)
Text en actes de congrés
Accés obertAn 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
(2021)
Text en actes de congrés
Accés restringit per política de l'editorial -
Shortest paths in portalgons
(2021)
Text en actes de congrés
Accés restringit per política de l'editorial -
Maximum box problem on stochastic points
(Springer Nature, 2021-10-28)
Article
Accés obertGiven 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
(2021)
Text en actes de congrés
Accés obertThis 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
(2021)
Text en actes de congrés
Accés obertWe 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
(Springer Nature, 2021-05-01)
Article
Accés obertWe 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
(Elsevier, 2022-01-15)
Article
Accés restringit per política de l'editorialWe 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 ...
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