Special Issue "Computational Geometry"

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A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: closed (30 July 2009)

Special Issue Editors

Editorial Board Member
Prof. Dr. Takeshi Tokuyama (Website)

Graduate School of Information Sciences (GSIS), Tohoku University, Aramaki Aza-Aoba, Aoba, Sendai, 980-8579, Japan
Interests: theoretical computer science and discrete mathematics; computational geometry and related combinatorics; new horizons in computing: recent trends in theoretical computer science
Editorial Board Member
Dr. Adrian Dumitrescu (Website)

University of Wisconsin-Milwaukee; 3200 N. Cramer Street Milwaukee, WI 53211, USA
Fax: +1 414 229 6958
Interests: theory of algorithms; computational and combinatorial geometry; combinatorics; computational morphology; robotics

Special Issue Information

"Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry." (from http://en.wikipedia.org/wiki/Computational_geometry)

Keywords

  • combinatorial computational geometry
  • algorithmic geometry
  • numerical computational geometry (machine geometry)
  • computer-aided geometric design (CAGD)
  • geometric modeling

Published Papers (3 papers)

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Research

Open AccessArticle Delaunay Meshing of Piecewise Smooth Complexes without Expensive Predicates
Algorithms 2009, 2(4), 1327-1349; doi:10.3390/a2041327
Received: 25 September 2009 / Revised: 17 October 2009 / Accepted: 19 October 2009 / Published: 11 November 2009
Cited by 16 | PDF Full-text (3512 KB) | HTML Full-text | XML Full-text
Abstract
Recently a Delaunay refinement algorithm has been proposed that can mesh piecewise smooth complexes which include polyhedra, smooth and piecewise smooth surfaces, and non-manifolds. However, this algorithm employs domain dependent numerical predicates, some of which could be computationally expensive and hard to [...] Read more.
Recently a Delaunay refinement algorithm has been proposed that can mesh piecewise smooth complexes which include polyhedra, smooth and piecewise smooth surfaces, and non-manifolds. However, this algorithm employs domain dependent numerical predicates, some of which could be computationally expensive and hard to implement. In this paper we develop a refinement strategy that eliminates these complicated domain dependent predicates. As a result we obtain a meshing algorithm that is practical and implementation-friendly. Full article
(This article belongs to the Special Issue Computational Geometry)
Open AccessArticle Optimal 2-Coverage of a Polygonal Region in a Sensor Network
Algorithms 2009, 2(3), 1137-1154; doi:10.3390/a2031137
Received: 19 July 2009 / Accepted: 25 August 2009 / Published: 14 September 2009
Cited by 3 | PDF Full-text (1896 KB)
Abstract
Wireless sensor networks are a relatively new area where technology is developing fast and are used to solve a great diversity of problems that range from museums’ security to wildlife protection. The geometric optimisation problem solved in this paper is aimed at [...] Read more.
Wireless sensor networks are a relatively new area where technology is developing fast and are used to solve a great diversity of problems that range from museums’ security to wildlife protection. The geometric optimisation problem solved in this paper is aimed at minimising the sensors’ range so that every point on a polygonal region R is within the range of at least two sensors. Moreover, it is also shown how to minimise the sensors’ range to assure the existence of a path within R that stays as close to two sensors as possible. Full article
(This article belongs to the Special Issue Computational Geometry)
Open AccessArticle How Many Lions Are Needed to Clear a Grid?
Algorithms 2009, 2(3), 1069-1086; doi:10.3390/a2031069
Received: 30 July 2009 / Revised: 3 September 2009 / Accepted: 4 September 2009 / Published: 7 September 2009
Cited by 4 | PDF Full-text (251 KB) | HTML Full-text | XML Full-text
Abstract
We consider a pursuit-evasion problem where some lions have the task to clear a grid graph whose nodes are initially contaminated. The contamination spreads one step per time unit in each direction not blocked by a lion. A vertex is cleared from [...] Read more.
We consider a pursuit-evasion problem where some lions have the task to clear a grid graph whose nodes are initially contaminated. The contamination spreads one step per time unit in each direction not blocked by a lion. A vertex is cleared from its contamination whenever a lion moves to it. Brass et al. [5] showed that n/2 lions are not enough to clear the n x n-grid. In this paper, we consider the same problem in dimension d > 2 and prove that Θ(nd-1/√d) lions are necessary and sufficient to clear the nd-grid. Furthermore, we analyze a problem variant where the lions are also allowed to jump from grid vertices to non-adjacent grid vertices. Full article
(This article belongs to the Special Issue Computational Geometry)

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