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I am looking for a term used to describe an analog to Voronoi diagrams where instead of a single point defining a cell, a continuous set of points is used. For example, starting with five triangles on the plane, you could construct a diagram that contained regions where each point in that region would be closer to a certain triangle than any other triangle.

Is anyone aware of any papers dealing with this type of construction? I'm having a hard time searching for any since I don't know if there is a name for it.

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up vote 5 down vote accepted

Here is one reference, to the CGAL manual section explaining its computation of the Voronoi diagram of segments, e.g.:

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It's still called a Voronoi diagram.

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The original paper for Fortune's algorithm for constructing Voronoi diagrams deals with the case of line segment sites (Section 3).

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