Tessellations in GIS: Part Ⅱ-making changes

摘要

We attempt to describe the role of tessellated models of space within the discipline of Geographic Information Systems (GIS) - a speciality coming largely out of Geography and Land Surveying, where there was a strong need to represent information about the land's surface within a computer system rather than on the original paper maps. We look at some of the basic operations in GIS, including dynamic and kinetic applications. We examine issues of topology and data structures, and produced a tessellation model that may be widely applied both to traditional"object"and"field"data types.The Part Ⅰ of this study examined object and field spatial models, the Voronoi extension of objects, and the graphs that express the resulting adjacencies. The required data structures were also briefly described, along with 2D and 3D structures and hierarchical indexing. The importance of graph duality was emphasized. Here, this second paper builds on the structures described in the first, and examines how these may be modified:change may often be associated with either viewpoint or time. Incremental algorithms permit additional point insertion, and applications involving the addition of skeleton points, for map scanning, contour enrichment or watershed delineation and simulation. Dynamic algorithms permit skeleton smoothing, and higher order Voronoi diagram applications, including Sibson interpolation. Kinetic algorithms allow collision detection applications, free-Lagrange flow modeling, and pen movement simulation for map drawing. If desired these methods may be extended to 3D. Based on this framework, it can be argued that tessellation models are fundamental to our understanding and processing of geographical space, and provide a coherent framework for understanding the"space"in which we exist.