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VoronoiDiagram site with various norms

I had a big math problem (using version 8). Building a Voronoi diagram is simple stuff, but what about changing the norm?

<< DiscreteMath`ComputationalGeometry` data2D = {{4.4, 14}, {6.7, 15.25}, {6.9, 12.8}, {2.1, 11.1}, {9.5, 14.9}, {13.2, 11.9}, {10.3, 12.3}, {6.8, 9.5}, {3.3, 7.7}, {0.6, 5.1}, {5.3, 2.4}, {8.45, 4.7}, {11.5, 9.6}, {13.8, 7.3}, {12.9, 3.1}, {11, 1.1}}; DiagramPlot[data2D, LabelPoints -> False]

Gives me a Voronoi diagram corresponding to the L_2-norm (Euclidean norm). I need a diagram corresponding to the L_1 norm and L_infinity-norm, and also ...

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From MMA Help (approximation only):

enter image description here

enter image description here

 ColorCombine[{Image[ WatershedComponents[ DistanceTransform[i, DistanceFunction -> ManhattanDistance]], "Bit"], i, i}]

enter image description here

NB: Note that the convexity property for the Voronoi polygon is lost ...

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Source: https://habr.com/ru/post/900346/

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