The driving factor of this dissertation is the constant effort by environmental planners and GIScience researchers to look for better ways to characterize, store, and compare their research subject: the landscape in general. This dissertation is rooted in a spatial metric, the multiplicatively weighted Voronoi (MW-Voronoi) diagram to characterize the landscape. The objectives are to (1) contribute to a better understanding of the metric from the perspective of environmental planners and GIScience researchers, (2) develop methods and implementations as an application metric instead of viewing it the decomposition of the metric to characterize the landscape from physical space to virtual space.; The MW-Voronoi diagram overcomes the largest shortcoming of the planar ordinary Voronoi—only location is considered—and considers both location and weights of the interested sites. This dissertation implements the composition of the MW-Voronoi diagram with topological overlay, growth simulation, and vertex calculation methods. Designed with GIScience concepts such as polygon overlay, agent-based simulation, and topological relationships, the methods not only improve the understanding of the MW-Voronoi diagram from the viewpoint of environmental planners and GIScience researchers, but also provide a practical way to generate MW-Voronoi diagrams.; This dissertation also develops a reversed process to decompose a polygon. A polygon is approximated with segments of circular arcs and lines, then decomposed into pairs of points with weight following the reversed MW-Voronoi process. The decomposition provides a new approach to record, characterize and compare polygons with form and process. A Visual Basic program CDWVD and several AML scripts were written to facilitate the implementations of the composition and decomposition and also serves as an educational tool.; Two case studies are presented to discuss the applications and improvements of the MW-Voronoi diagram. The first one applies the composition of MW-Voronoi diagram to estimate the average areal precipitation value from limited scattered point data, and finds that the MW-Voronoi method always results in a higher estimation than the planar ordinary Voronoi. It provides a more stable estimation than the Voronoi when sample sizes are different and it has less edge effect. The second case study applies the decomposition of MW-Voronoi diagrams to fire history data, and concludes this metric can help automate the process of recording and characterizing fire polygons. This decomposition metric reduces data storage. The same method can also help compare polygons, even though there are still many questions to be addressed. Limitations and future research in this field are summarized.
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