Weighting Thiessen Polygons

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Clark University is collaborating with JSTOR to digitize, preserve and extend access to Economic Geography.Although tessellations of Thiessen polygons are attractive conceptually as simple spatial models, their value in this regard is limited by the restrictive nature of both the model assumptions and the patterns which they generate. This paper suggests two simple ways by which Thiessen polygon models can be modified to produce what are designated "weighted polygon" models. The approach involves the recognition that the edges in a tessellation of Thiessen polygons are a special case of Descartes' ovals. Two specific, weighted polygon models are produced using other realizations of Descartes' ovals. Both new models are given both assignment and growth interpretations, and their relationships with other existing geographic models are explored. Using equivalencies identified in this way, applications of the models are examined.Thiessen polygons are now familiar to many geographers as well as to a diversity of other scientists, including animal and plant biologists, anthropologists, archaeologists, astronomers, geologists, and statisticians; although to many of these groups they are more likely to be known by one of their other names of which the most current are Dirichlet Domains and Voronoi Polygons.The definition of Thiessen polygons is straightforward. Consider a labelled set of points, ai, a2, ..., an, located in a plane. With each point, ai, we associate a set of all locations, x, in the plane whose distance from ai is equal to their minimum distance from the points faj}. The set of all such locations x which thus satisfy (xai) < (xai)

Lecture notes in computer science: research on hybrid grid algorithm of voronoi diagram

“…This results in the slow coloring speed of the original algorithm in the early (when the radius is small) stage. The improved method is to set the angular increment as a dynamic value that decreases as the radius increases, see (2). It can satisfy the correctness of the algorithm with both small and large radius, and the efficiency of the algorithm is obviously higher.…”

“…The discontinuous region problem. The more important problem of this algorithm is that it does not consider the case of discontinuous Voronoi diagram (property Ⅳ of reference [2]). The algorithm is only correct in the situation when the discontinuous region is absent in the Voronoi diagram!…”

“…Voronoi diagram [1,2]is an important topic in computational geometry field, which is often used to solve problems of location optimization, space division and path planning in the fields of geography, meteorology and mobile communication. It has important theoretical and practical value.…”

Zastosowanie diagramu Woronoja w badaniu przestrzennych wzorców rozmieszczenia i dostępności sklepów dyskontowych = Application of the Voronoi Diagram in analysing of spatial patterns to the distribution of discount stores and access to them

“…Dalsze badania mogłyby zostać skoncentrowane na problemie konstrukcji diagramów ważonych (por. Boots, 1980;Dong, 2008), uwzględnieniu otoczenia konkurencyjnego i pogłębieniu analiz o ankietyzację klientów (identyfi kację realnego popytu, faktycznych miejsc zamieszkania klientów, środków transportu czy rodzaju kupowanych produktów). T he aim of the work detailed here has been to achieve a methodological goal relating to methods, which focuses on the application of the Voronoi diagram in studying spatial aspects of the accessibility of retail stores.…”

“Voting with Their Feet”: Delineating the Sphere of Influence Using Social Media Data

“…These partition space into regions surrounding points (or seeds), and the region boundaries have the same distances to the nearest points. To account for the differences between point characteristics, weighted Thiessen polygons have been suggested [33,34], and various versions of weighted Thiessen polygons have been used to study the regional structures of urban hierarchies by accounting for different socioeconomic variables pertaining to the cities [35].…”