The Geometric Stability of Voronoi Diagrams with Respect to Small Changes of the Sites
Proceedings of the twenty-seventh annual symposium on Computational geometry
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Geographic space is typically conceptualized either as discrete objects or as continuous fields. Considerable efforts have been carried out for the representation and management of the spatial data, based on the object view of the space. However field-based data models are less developed in GIS especially when it comes to the modeling and representation of dynamic fields. Dynamic phenomena such as urban dynamics, air pollution, fire propagation, etc. are examples of dynamic fields with important spatial and temporal components. These phenomena should be represented in GIS in order to help users and decision makers in different disciplines to better understand and predict their dynamic behaviour. The limitations of GIS for modeling and simulation of those phenomena are mostly related to the 2D and static nature of their spatial data structures. In this paper, we explore the potentials of the Voronoi diagram as an alternative spatial data model that allows realistic representation of the spatial dynamic fields in 2D and 3D spaces. The paper presents how different types of Voronoi diagrams for points in two and three dimensional spaces as well as Voronoi diagrams for line segments and polygons could be effectively used in different contexts to represent and simulate different dynamic spatial fields and processes.