<< 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}};

convexhull = ConvexHull[data2D]

ConvexHull[{{0, 0}, {1, 0}, {0, 0}, {2, 0}, {1, 1}}]

(delval = DelaunayTriangulation[data2D]) // 
      Shallow[#, {5, 6}] &

{vorvert, vorval} = VoronoiDiagram[data2D];

{First[vorvert], Last[vorvert]}

vorval // Short

vorval[[1, 2]]

vorvert[[%]]

VoronoiDiagram[data2D, delval];

VoronoiDiagram[data2D, delval, convexhull];

PlanarGraphPlot[data2D, 
      TextStyle -> {"FontSize" -> 8}]

PlanarGraphPlot[data2D, convexhull]

trival = 
        Insert[Insert[Delete[delval, {{12, 2, 4}, {16, 2, 2}}], 
            15, {11, 2, 2}], 11, {15, 2, 3}];

PlanarGraphPlot[data2D, trival, 
      TextStyle -> {"FontSize" -> 8}]

DiagramPlot[data2D]

diagvert = 
        ReplacePart[vorvert, {-6. , 0. }, {27, 2}];

diagval = 
        Join[Drop[
            vorval, -8], {{9, {1, 6, 8, 3}}, {10, {2, 6, 1, 24, 27}}}, 
          Drop[vorval, 10]];

DiagramPlot[data2D, diagvert, diagval]

data3D = 
        Map[Append[#, 
              Sqrt[64 - (#[[1]] - 8)^2 - (#[[2]] - 8)^2]] &, 
          data2D];

TriangularSurfacePlot[data3D]

TriangularSurfacePlot[data3D, trival]

ConvexHull[{{0, 0}, {1, 0}, {0, 0}, {2, 0}, {1, 1}}, 
      AllPoints -> False]

DelaunayTriangulation[data2D, Hull -> True] // Shallow

random = Table[{Random[], Random[]}, {40}];

{randvert, randval} = VoronoiDiagram[random];

DiagramPlot[random, randvert, randval, 
      LabelPoints -> False]

DiagramPlot[random, randvert, randval, LabelPoints -> False, 
      TrimPoints -> 2]

DiagramPlot[random, randvert, randval, LabelPoints -> False, 
      TrimPoints -> 6]

DelaunayTriangulationQ[data2D, delval]

\[Placeholder]
<< DiscreteMath`ComputationalGeometry`

PlanarGraphPlot[{{-5.93,  0.9}, {-4.87,  2.46}, {-1.14,  
          4.89}, {-1.06,  -0.19}, {0.00,  0.00}, {0.48,  
          0.29}, {1.32,  -0.56}, {10.58,  
          3.73}, {13.33,  -5.11}, {-6.24,  -3.6}}]

VoronoiDiagram[{{-5.93,  0.9}, {-4.87,  2.46}, {-1.14,  
          4.89}, {-1.06,  -0.19}, {0.00,  0.00}, {0.48,  
          0.29}, {1.32,  -0.56}, {10.58,  
          3.73}, {13.33,  -5.11}, {-6.24,  -3.6}}]

DiagramPlot[{{-5.93,  0.9}, {-4.87,  2.46}, {-1.14,  
          4.89}, {-1.06,  -0.19}, {0.00,  0.00}, {0.48,  
          0.29}, {1.32,  -0.56}, {10.58,  
          3.73}, {13.33,  -5.11}, {-6.24,  -3.6}}]

PlanarGraphPlot[{{-4.55,  7.96}, {-5.29,  
          5.85}, {-1.56,  6.51}, {-2.8,  4.18}, {-3.76,  
          3.68}, {-2.96,  3.62}, {-2.99,  3.39}, {-3.17,  
          2.22}, {-3.86,  2.25}, {-2.35,  3.23},  {-2.49,  
          3.47},  {-2.54,  3.76},  {-1.85,  3.73},  {-1.3,  
          3.89},  {-0.69,  4.6},  {-0.82,  4.87},  {-0.71,  
          5.13},  {-0.95,  5.48},  {-0.61,  5.98},  {8.57,  
          5.11},  {9.02,  4.74},  {9.26,  4.92},  {9.5,  
          5.42},  {7.2,  4.87},  {5.79,  
          2.54},  {8.84,  -3.12},  {0.00,  0.00}}]

VoronoiDiagram[{{-4.55,  7.96}, {-5.29,  
          5.85}, {-1.56,  6.51}, {-2.8,  4.18}, {-3.76,  
          3.68}, {-2.96,  3.62}, {-2.99,  3.39}, {-3.17,  
          2.22}, {-3.86,  2.25}, {-2.35,  3.23},  {-2.49,  
          3.47},  {-2.54,  3.76},  {-1.85,  3.73},  {-1.3,  
          3.89},  {-0.69,  4.6},  {-0.82,  4.87},  {-0.71,  
          5.13},  {-0.95,  5.48},  {-0.61,  5.98},  {8.57,  
          5.11},  {9.02,  4.74},  {9.26,  4.92},  {9.5,  
          5.42},  {7.2,  4.87},  {5.79,  
          2.54},  {8.84,  -3.12},  {0.00,  
          0.00}}]

DiagramPlot[{{-4.55,  7.96}, {-5.29,  5.85}, {-1.56,  
          6.51}, {-2.8,  4.18}, {-3.76,  3.68}, {-2.96,  
          3.62}, {-2.99,  3.39}, {-3.17,  2.22}, {-3.86,  
          2.25}, {-2.35,  3.23},  {-2.49,  3.47},  {-2.54,  
          3.76},  {-1.85,  3.73},  {-1.3,  3.89},  {-0.69,  
          4.6},  {-0.82,  4.87},  {-0.71,  5.13},  {-0.95,  
          5.48},  {-0.61,  5.98},  {8.57,  5.11},  {9.02,  
          4.74},  {9.26,  4.92},  {9.5,  5.42},  {7.2,  
          4.87},  {5.79,  2.54},  {8.84,  -3.12},  {0.00,  
          0.00}}]