Transitions between 4-intersection values of planar regions

• Autores: Kathleen Bell, Tom Richmond
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 18, Nº. 1, 2017, págs. 183-202
• Idioma: inglés
• DOI: 10.4995/agt.2017.6716
• Enlaces
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• Resumen

  • If A(t) and B(t) are subsets of the Euclidean plane which are continuously morphing, we investigate the question of whether they may morph directly from being disjoint to overlapping so that the boundary and interior of A(t) both intersect the boundary and interior of B(t) without first passing through a state in which only their boundaries intersect.  More generally, we consider which 4-intersection values---binary 4-tuples specifying whether the boundary and interior of A(t) intersect the boundary and interior of B(t)---are adjacent to which in the sense that one may morph into the other without passing through a third value.  The answers depend on what forms the regions A(t) and B(t) are allowed to assume and on the definition of continuous morphing of the sets.

• Referencias bibliográficas
  • C. Adams and R. Franzosa, Introduction to Topology: Pure and Applied, Pearson Prentice Hall, Upper Saddle River, NJ, 2008.
  • J. Chen, C. Li, Z. Li and C. Gold, A Voronoi-based 9-intersection model for spatial relations, International Journal for Geographical Information...
  • https://doi.org/10.1080/13658810151072831
  • E. Clementini, J. Sharma and M. Egenhofer, Modeling topological spatial relations: strategies for query processing, Computers and Graphics...
  • https://doi.org/10.1016/0097-8493(94)90007-8
  • M. Egenhofer and K. Al-Taha, Reasoning about gradual changes of topological relationships, in: A Frank, I. Campari, and U. Valueentini (Eds.),...
  • https://doi.org/10.1007/3-540-55966-3_12
  • M. Egenhofer, E. Clementini and P. di Felice, Topological relations between regions with holes, International Journal for Geographical Information...
  • https://doi.org/10.1080/02693799408901990
  • M. Egenhofer and R. Franzosa, Point-set topological spatial relations, International Journal for Geographical Information Systems 5, no. 2...
  • https://doi.org/10.1080/02693799108927841
  • M. Egenhofer and R. Franzosa, On equivalence of topological relations, International Journal for Geographical Information Systems 8, no. 6...
  • S. Francaviglia, A. Lechicki and S. Levi, Quasi-uniformization of hyperspaces and convergence of nets of semicontinuous multifunctions, J....
  • https://doi.org/10.1016/0022-247X(85)90246-X
  • N. M. Gotts, An axiomatic approach to topology for spatial information systems, Research Report 96.25, University of Leeds, School of Computer...
  • E. Klein and A. C. Thompson, Theory of Correspondences: Including Applications to Economics. Canadian Mathematical Society Series of Monographs...
  • Y. Kurata and M. Egenhofer, The e 9+-intersectionintersection for topological relations between a directed line segment and a region,...
  • D. Mark and M. Egenhofer, An evaluation of the 9-intersection for region-line relations, San Jose, CA: GIS/LIS '92, (1992) 513-521.
  • K. Nedas, M. Egenhofer and D. Wilmsen, Metric details of topological line-line relations, International Journal for Geographical Information...
  • https://doi.org/10.1080/13658810600852164
  • A. J. Roy and J. G. Stell, Indeterminate regions, Internat. J. Approximate Reasoning 27 (2001), 205-234.
  • https://doi.org/10.1016/S0888-613X(01)00033-0
  • T. Smith and K. Park, Algebraic approach to spatial reasoning, International Journal for Geographical Information Systems 6, no. 3 (1992),...
  • https://doi.org/10.1080/02693799208901904
  • J. Wu, C. Claramunt and M. Deng, Modelling movement patterns using topological relations between a directed line and a region, IWGS '14...