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I am trying to read Fortune's description of his additively weighted Voronoi algorithm but I am experiencing some difficulty in understanding it.

I imagine the algorithm as being like that for regular voronoi diagrams with beach line parabolas of different sizes as to take into account the point weights but if that's the case I am not sure how the edges of the resulting weighted voronoi diagram aren't straight lines.

Can someone explain the additively weighted version of Fortune's algorithm?

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