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Research Interests: Computational Geometry

See the Madrid CG group page to see information about activities related to CG in Madrid.

See the Computational Geometry Internet Resources page to find information about CG sites, mailing lists, news groups, courses, books, journals, events, and many other informations about Computational Geometry.

• The number of generalized balanced lines. David Orden, Pedro Ramos, Gelasio Salazar. Submitted. Available as http://arxiv.org/abs/0904.4429v3.  
  
• Decomposition of multiple coverings into more parts. Greg Aloupis, Jean Cardinal, Sébastien Colette, Stefan Langerman, David Orden, Pedro Ramos. Submitted. Availabe as http://arXiv.org/abs/0807.0552.    
• Depth of segments and circles through points enclosing many points: a note. Pedro Ramos, Raquel Viaña. Computational Geometry: Theory and Applications 42(4), pp. 338-341, May 2009. http://dx.doi.org/10.1016/j.comgeo.2008.07.001. Preliminary version available as http://arxiv.org/abs/0803.1088.
  
• New results on lower bounds for the number of  <=-facets. Oswin Aichholzer, Jesús García, David Orden, Pedro  Ramos, European Journal of Combinatorics, in press doi:10.1016/j.ejc.2009.03.010.
  Available as  http://arxiv.org/abs/0801.1036.  Extended abstract in Electronic Notes in Discrete Mathematics 29 (2007), 189-193.
  
• On Structural and Graph Theoretic Properties of Higher Order Delaunay Graphs.  Manuel Abellans, Prosenjit Bose, Jesús García, Ferran Hurtado, Carlos M. Nicolás, Pedro Ramos, to appear in International Journal of Computational Geometry and Applications.
  
• New lower bounds for the number  of  <=-edges and the rectilinear crossing number of Kn. Oswin Aichholzer, Jesús García, David Orden,  Pedro  Ramos,  Discrete & Computational Geometry 38, pp. 1-14 (2007).
  
• On Local Transformations in Plane Geometric Graphs Embedded on Small Grids. Manuel Abellanas, Prosenjit Bose, Alfredo Garcia, Ferran Hurtado, Pedro Ramos, Eduardo Rivera-Campo, Javier Tejel,  Computational Geometry: Theory and Applications 39, pp. 65-77 (2007).
  
• The maximin line problem with regional demand. José Miguel Díaz-Bañez, Pedro A. Ramos and Pilar Sabariego, European Journal of Operation Research 181, pp. 20-29 (2007).
  
• Multi-VMap: a Multi-Scale Model for Vector Maps. Raquel Viaña, Paola Magillo, Enrico Puppo and Pedro A. Ramos, Geoinformatica 10, pp. 359-395 (2006).
• Separability by two lines and by flat polygonals.  Ferran Hurtado, Mercè Mora, Pedro A. Ramos and Carlos Seara, Discrete Applied Mathematics 144 (1-2), p. 110-122 (2004).
• Minimal set of constraints for 2D constrained Delaunay triangulation. Olivier Devillers, Regina Estkowski, Pierre-Marie Gandoin, Ferran Hurtado, Pedro A. Ramos and Vera Sacristán,  International Journal of Computational Geometry and Applications 13 (5), pp. 391-398 (2003) .
• Computing roundness is easy if the set is almost round. Olivier Devillers and Pedro A. Ramos, International Journal of Computational Geometry and Applications 12 (3),pp. 229-248 (2002).
• Separating objects in the plane with wedges and strips. Ferran Hurtado, Marc Noy, Pedro A. Ramos and Carlos Seara, Discrete Applied Mathematics 109 (1-2), pp. 109-138 (2001).
• A unified approach to conic visibility.  Jesús García-López and Pedro A. Ramos, Algorithmica 28 (3), pp. 307-322 (2000).
• Structural tolerance and Delaunay triangulation. Manuel Abellanas, Ferran Hurtado and Pedro A. Ramos, Information Processing Letters 71, pp. 221-227 (1999).
• Drawing nice projections of objects in space. Prosenjit Bose, Francisco Gómez, Pedro A. Ramos and Godfried Toussaint, Journal of Visual Communication and Image Representation 10 (2), pp. 155-172 (1999).
• Bipartite embeddings of trees in the plane. Manuel Abellanas, Jesús García-López, Gregorio Hernández, Marc Noy and Pedro A. Ramos, Discrete Applied Mathematics 93, 2-3 pp. 141-148 (1999).
• Fitting a set of points by a circle. Jesús García-López, Pedro A. Ramos and Jack Snoeyink. Discrete & Computational Geometry  20, pp. 389-402 (1998).
• Converting triangulations to quadrangulations. Suneeta Ramaswami, Pedro A. Ramos and Godfried Toussaint. Computational Geometry: Theory and Applications 9, pp. 257-276 (1998). 

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Conference Papers

• New results on lower bounds for the number of (<k)-facets. Oswin Aichholzer, Jesús García, David Orden, Pedro Ramos. Kyoto International Conference on Computational Geometry and Graph Theory, (KyotoCGGT2007), Kyoto, Japan, June 11-15, 2007.                                                   Versión EuroComb: Electronic Notes in Discrete Mathematics, Volume 29, 15 August 2007, Pages 189-193
  
• New lower bounds for the number of (<k)-edges and the rectilinear crossing number of K_n. Oswin Aichholzer, Jesús García, David Orden, Pedro Ramos. V Jornadas de Matemática Discreta y Algorítmica, Soria, July, 12-14, 2006. Actas de las IV Jornadas de Matemática Discreta y Algorítmica, pp. 57-64.
  
• On the structure of sets attaining the rectilinear crossing number. Oswin Aichholzer, Jesús García, David Orden, Pedro Ramos. 22nd European Workshop on Computational Geometry. Delphi, March 27-29, 2006.
  
• Creación de mallas cuadrangulares a partir de mallas triangulares. Pedro A. Ramos, Javier Sanguino. XI Encuentros de Geometría Computacional. Santander, 27-29 junio, 2005.
  
• The maximin line problem with polygonal demand. José Miguel Díaz-Bañez, Pedro A. Ramos, Pilar Sabariego. XI Encuentros de Geometría Computacional. Santander, 27-29 junio, 2005.
  
• On properties of higher-order Delaunay graphs with applications. Manuel Abellanas, Prosenjit Bose, Jesús García, Ferran Hurtado, Mariano Nicolás and Pedro A. Ramos. 21st European Workshop on Computational Geometry. Eindhoven, March 9-11, 2005.
  
• Depth of segments and circles through points enclosing many points. Pedro A. Ramos. Japan Conference on Discrete and Computational Geometry.  Tokyo, 8-11 octubre, 2004.
• Un nuevo enfoque de una conjetura de Urrutia. Pedro A. Ramos. IV Jornadas de Matemática Discreta y Algorítmica, Cercedilla, 6-8 de septiembre de 2004. Actas de las IV Jornadas de Matemática Discreta y Algorítmica, pp. 215-221.
  
• Cálculo eficiente de una recta nociva en presencia de obstáculos poligonales. José Miguel Díaz Báñez, Pedro A. Ramos y Pilar Sabariego. IV Jornadas de Matemática Discreta y Algorítmica, Cercedilla, 6-8 de septiembre de 2004. Actas de las IV Jornadas de Matemática Discreta y Algorítmica, pp. 231-238.
  
• Delaunay graphs of order k. Manuel Abellanas, Jit Bose, Jesús García, Ferran Hurtado y Pedro A. Ramos. First Joint Meeting RSME-AMS, Sevilla, June 18-21, 2003.
• Best fitting rectangles. Manuel Abellanas, Ferran Hurtado, Cristian Icking, Lihong Ma, Belén Palop, Pedro A. Ramos. Abstracts 19th European Workshop on Computational Geometry (2003), pp. 147-150.
• Codificación de triangulaciones mediante restricciones. Olivier Devillers, Regina Estkowski, Pierre-Marie Gandoin, Ferran Hurtado, Pedro A. Ramos, Vera Sacristán.  Actas de los IX Encuentros de Geometría Computacional, pp. 167-174 (2001).
• Optimización geométrica y medida de tolerancias. Pedro A. Ramos. Actas de los VIII Encuentros de Geometría Computacional, pp. 11-18 (1999).
• Separación de objetos en el plano por doble cuña y por Theta-poligonal. Ferran Hurtado, Mercè Mora, Pedro A. Ramos, Carlos Seara. Actas de los VIII Encuentros de Geometría Computacional, pp. 73-82 (1999).
• Computing roundness is easy if the set is almost round. Pedro A  Ramos. Proceedings 15th ACM Symp. on Computational Geometry, pp. 307-315 (1999).
• Two problems on separability with lines and polygonals. Ferran Hurtado, Mercè Mora, Pedro A. Ramos, Carlos Seara. Abstracts 15th European Workshop on Computational Geometry, pp. 33-36 (1999).
• Shortest paths and visibility inside triangulated curved polygons with applications to conic visibility. Jesús García-López, Pedro A. Ramos, Proceedings 10th Canadian Conference on Computational Geometry, pp. 60-61 (1998).
• Separating objects in the plane with wedges and strips. Ferran Hurtado, Marc Noy, Pedro A. Ramos, Carlos Seara.  Proceedings 10th Canadian Conference on Computational Geometry, pp. 50-51 (1998).
• Computing roundness in practice. Pedro A. Ramos. Abstracts of the 14th European Workshop on Computational Geometry, pp. 125-126 (1998).
• Fitting a set of points by a circle. Jesús García-López, Pedro A. Ramos. Proceedings 13th ACM Ann. Symp. on Computational Geometry 1997, pp. 139-146 (1997).
• Bipartite embeddings of trees in the plane. Manuel Abellanas, Jesús García-López, Gregorio Hernández, Marc Noy, Pedro A. Ramos. Proceedings of Graph Drawing 96. LNCS 1190, Springer-Verlag 1997, pp. 1-10.
• Optimization problems in Computational Metrology. Pedro A. Ramos. Proceedings French-Spanish Workshop on Algorithmic Geometry, Barcelona (Spain), pp. 108-113 (1997).
• Visibilidad y caminos mínimos en polígonos curvilíneos triangulados. Jesús García-López, Pedro A. Ramos. Actas de los VII Encuentros de Geometría Computacional, pp. 29-44 (1997).
• Drawing nice projections of objects in space. Jit Bose, Francisco Gómez, Pedro A. Ramos, Godfried Toussaint. Proceedings of Graph Drawing 95. LNCS 1027, Springer-Verlag 1996, pp. 52-63.
• Incidence angle constrained visibility. Gregoria Blanco, Jesús García-López, Ferran Hurtado, Pedro A. Ramos, Vera Sacristán. Abstract 12th European Workshop on Computational Geometry, Münster (Germany), 1996. Full version (in spanish): Fotografías de calidad, in Actas de los VI Encuentros de Geometría Computacional, Barcelona, 1995.
• Redrawing a graph within a geometric tolerance. Manuel Abellanas, Ferran Hurtado, Pedro A. Ramos. Proceedings of Graph Drawing 94. LNCS 894, Springer-Verlag 1995, pp. 246-253.
• Tolerancia de arreglos de segmentos. Manuel Abellanas, Ferran Hurtado, Pedro A. Ramos. Actas de los VI Encuentros de Geometría Computacional, Barcelona, (1995).
• Tolerance of geometric structures. Manuel Abellanas, Ferran Hurtado, Pedro A. Ramos. Proceedings 6th Canadian Conference on Computational Geometry, Saskatoon (1994).
• Circular visibility and separability. Jesús García-López, Pedro A. Ramos. Proceedings 5th Canadian Conference on Computational Geometry, Waterloo (1993).

• Tolerancia de estructuras geométricas y combinatorias (in spanish). My Ph.D. Thesis.

Abstract:  In this thesis we introduce the concept of tolerance of a structure or property, combinatorial or geometric, associated to a set $S$. The tolerance of a structure or property is a measure of stability of the structure or property under perturbations of $S$. The computation of tolerance can be useful when input data are subjected to errors, because a big tolerance guarantees that the solution is stable under small errors in data.  The tolerance is also useful in dynamic maintenance of structures associated to moving objects, because it allows us to discretize the problem in  intervals of time such that the structure has no changes.

Mixed Informations:

• Departamento de Matemáticas (in spanish)
• Universidad de Alcalá (in spanish)