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.