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A spatial data structure integrating GIS and simulation in a marine environment

Christopher M. Gold, Alfonso R. Condal

1995
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Marine Geodesy
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Traditional geographic information system (GIS) data structures have always been something of a problem in a marine context. as so much of the available information is collected in point form, while the spatial structuring available within a land-based GIS is usually based on vector line segments or arcs, or else on a raster-based "image" approach (or some hybrid system converting back and forth between the two). it would thus be very desirable to be able to work within spatial data structures
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... hat could both handle objects that were unconnected and provide the necessary basis of spatial adjacency or proximity. People have no difficulty navigating around isolated features, so why should a computer? Additionally. in a marine environment even more than in a land-based one. objects are likely to change location, and it would be nice if this could be handled in a dynamic system. Finally, w h i l e in both terrestrial and marine systems we may be representing both discrete objects and "fields" that vary continuously over the map. in a marine context these fields are less often classified into a discrete polygon tiling. Our recent work has been concerned with the development of spatial data structures with some of the desired properties mentioned above, as a potential replacement for the usual terrestrial techniques. This matters because SO often the operations we wish to perform are severely restricted by the available tool set and, even worse, we attempt to pose the problem in available. but inappropriate terms. The spatial data structures used are based on the concepts of space used for the software development and may not be appropriate elsewhere. Finally, we have questions of theoretical computational efficiency that are relevant when we are concerned with time-varying situations-because the objects have changed, or because the operator wishes to interact with the system in a timely (and maybe urgent!) fashion. The techniques developed at Laval University are based on the idea of Voronoi tesselations, used as a dynamic spatial data structure. These are described in various articles (e.g.. Gold. 1990a. 199Oc. 1991. 1992a. 1992b, and the purpose of this article is to evaluate them for USC in a marine GIS. We consider that a reasonable "wish list" for a marine GIS would include the ability to handle nonconnected and connected objects, as well as field-type data. that would be able to vary their relative positions and values over time. At any appropriate moment the spatial structure should respond to queries concerning values or spatial relationships, e.g., for navigation purposes. Implementation is not feasible with static polygon structures. but it is possible using dynamic Voronoi tesselations. Principles of Voronoi Methods Static point-Voronoi tesselations are well known in the literature, and algorithms have been used for many years (see Aurenhammer, 199 1. for a summary). Less well known are dynamic algorithms that allow point creation, deletion. and movement. and also Voronoi tesselations of more complex objects-typically line segments as well as points. These have been the subject of considerable research at Laval University, and they are being used in terrestrial GIS applications, especially those concerned with managing the history of map changes. We have also been involved in the evaluation of Voronoi fieldmodeling techniques in the marine context. This article will explore the state of current dynamic Voronoi techniques, and their potential application in marine applications. The basic point Voronoi tesselation in the Euclidean plane is a tiling of the mapping plane such that each convex tile contains that portion of the plane closest to any one of an arbitrarily distributed set of data points (Figure 1a ). This figure shows the Voronoi tesselation for each data point. as well as the dual Delaunay triangulation. [It should be noted that one is not necessarily restricted to the plane: Augenbaum and Peskin ( 1985) have developed methods for the sphere. and Tanemura et al. (1983). among others. have developed methods for three dimensions. A large variety of algorithms exist to generate this tesselation, from the simple point-by-point insertion methods (e.g.. Green & Sibson. 1978). to more elaborate sweep-line (e.g.. Fortune. 1987) and divide-and-conquer techniques (e.g.. Guibas & Stolfi. 1985). There are no particular resolution constraints. except those of preserving large. high-precision coordinate values. and the limitations of the precision of geometric calculations using finite-precision arithmetic. that are standard for all vector GIS operations. Indeed, as they are intended to express local spatial relationships, as far as possible minimizing the USC of global coordinates, they are excellent for

doi:10.1080/15210609509379757
fatcat:5656znyzxjdrrbh6m5esazuaia