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We propose a uniform and general framework for defining and dealing with Voronoi diagrams. In this framework a Voronoi diagram is a partition of a domain D induced by a finite number of real valued functions on D. Valuable insight can be gained when one considers how these real valued functions partition D ×R. With this view it turns out that the standard Euclidean Voronoi diagram of point sets in R d along with its order-k generalizations are intimately related to certain arrangements ofdoi:10.1007/bf02187681 fatcat:qaoojhms2va7ve7u7ejuzmkqwe