Abstract
We attempt to show that a tessellated spatial model has definite advantages for cartographic applications, and facilitates a kinetic structure for map updating and simulation. We develop the moving-point Delaunay/Voronoi model that manages collision detection snapping and intersection at the data input stage by maintaining a topology based on a complete tessellation. We show that the Constrained Delaunay triangulation allows the simulation of edges, and not just points, with only minor changes to the moving-point model. We then develop an improved kinetic Line-segment Voronoi diagram, which is a better-specified model of the spatial relationships for compound map objects than is the Constrained Triangulation. However, until now it has been more difficult to implement. We believe that this method is now viable for 2D cartography, and in many cases it should replace the Constrained approach. Whichever method is used, the concept of using the moving point as a pen, with the ability to delete and add line segments as desired in the construction and updating process, appears to be a valuable development.
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Anton F, Gold CM (1997) An iterative algorithm for the determination of Voronoi vertices in polygonal and non-polygonal domains. In: Proc Ninth Canadian Conf on Computational Geometry, Kingston, ON, Canada, pp 257–262
Anton F, Snoeyink J, Gold CM (1998) An iterative algorithm for the determination of Voronoi vertices in polygonal and non-polygonal domains on the plane and the sphere. In: Proc 14th European Workshop on Computational Geometry (CG’98), Barcelona, Spain, pp 33–35
Aurenhammer F (1991) Voronoi Diagrams — A Survey of a Fundamental Geometric Data Structure. ACM Computing Surveys 23(3):345–405
Chew P (1988) Constrained Delaunay Triangulations. Algorithmica 4:97–108
Devillers O (1999) On deletion in Delaunay triangulations. 15th Annual ACM Symp on Computational Geometry, pp 181–188
Gold CM (1990) Spatial Data Structures — The Extension from One to Two Dimensions. In: Pau LF (ed) Mapping and Spatial Modelling for Navigation (= NATO ASI Series F No 65). Springer-Verlag, Berlin, pp 11–39
Gold CM, Remmele PR, Roos T (1995) Voronoi diagrams of line segments made easy. In: Gold CM, Robert JM (eds) Proc 7th Canadian Conf on Computational Geometry, Quebec, QC, Canada, pp 223–228
Gold CM, Snoeyink J (2001) A one-step crust and skeleton extraction algorithm. Algorithmica 30:144–163
Guibas L, Mitchell JSB, Roos T (1991) Voronoi diagrams of moving points in the plane. In: Proc 17th Int Workshop on Graph Theoretic Concepts in Computer Science, Fischbachau, Germany (= Lecture Notes in Computer Science 70). Berlin, Springer-Verlag, pp 113–125
Guibas L, Stolfi J (1985) Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams. Transactions on Graphics 4: 74–123
Held M (2001) VRONI: an engineering approach to the reliable and efficient computation of Voronoi diagrams of points and line segments. Computational Geometry, Theory and Application 18(2):95–123
Imai T (1996) A topology oriented algorithm for the Voronoi diagram of polygons. In: Proc 8th Canadian Conf on Computational Geometry, Carleton University Press, Ottawa, Canada, pp 107–112
Jones CB, Bundy GL, Ware JM (1995) Map generalization with a triangulated data structure. Cartography and Geographic Information Systems 22(4): 317–331
Jones CB, Ware JM (1998) Proximity Search with a Triangulated Spatial Model. Computer J 41(2):71–83
Karavelas MI (2004) A robust and efficient implementation for the segment Voronoi diagram. In: Int Symp on Voronoi Diagrams in Science and Engineering (VD2004), pp 51–62
Mostafavi M, Gold CM, Dakowicz M (2003) Dynamic Voronoi / Delaunay Methods and Applications. Computers and Geosciences 29(4):523–530
Okabe A, Boots B, Sugihara K (1992) Spatial Tessellations — Concepts and Applications of Voronoi Diagrams. John Wiley and Sons, Chichester, 521 p
Roos T (1990) Voronoi Diagrams over Dynamic Scenes. In: Proc Second Canadian Conf on Computational Geometry, Ottawa, pp 209–213
Shewchuk JR (1996) Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator. First Workshop on Applied Computational Geometry (Philadelphia, Pennsylvania), Ass for Computing Machinery, pp 124–133
Shewchuk JR (1997) Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates. Discrete and Computational Geometry 18(3): 305–363
Ware JM, Jones CB (1998) Conflict Reduction in Map Generalization Using Iterative Improvement. GeoInformatica 2(4):383–407
Yang W, Gold CM (1995) Dynamic spatial object condensation based on the Voronoi diagram. In: Chen J, Shi X, Gao W (eds) Proc Fourth Int Symp of LIESMARS’95 — Towards three-dimensional, temporal and dynamic spatial data modelling and analysis, Wuhan, China, pp 134–145
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© 2006 Springer-Verlag Berlin Heidelberg
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Dakowicz, M., Gold, C. (2006). Structuring Kinetic Maps. In: Riedl, A., Kainz, W., Elmes, G.A. (eds) Progress in Spatial Data Handling. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-35589-8_31
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DOI: https://doi.org/10.1007/3-540-35589-8_31
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