data3C = RandomReal[1, {10, 6}];
 func3C = Nearest[{#, #2, #3} -> {##4, .03} & @@@ data3C];
 tbl3C = Table[  First[func3C[{x, y, z}]] // Quiet, {x, 0, 1, .01},
  {y, 0, 1, .01}, {z, 0, 1, .01}];

Row[Labeled[Graphics3D[Raster3D[tbl3C, ColorFunction -> #,
  Method -> {"InterpolateValues" -> True}],
 Background -> Black, ImageSize -> 400,
 SphericalRegion -> True], #, Top] & /@
{Hue, RGBColor, (GrayLevel[#[[1]], .03] &)}, Spacer[5]]

colorRules = Thread[# -> (ColorData[1, "ColorList"][[;; Length@#]])] &[
Flatten[tbl3C, 2] // DeleteDuplicates] /.  RGBColor -> List;
Row[Labeled[ Graphics3D[Raster3D[tbl3C /. colorRules, ColorFunction -> #,
  Method -> {"InterpolateValues" -> True}],
 Background -> Black, ImageSize -> 400,
 SphericalRegion -> True], #, Top] & /@
{(RGBColor[#[[1]], #[[2]], #[[3]], .01] &),
(RGBColor[#[[1]], #[[2]], #[[3]], .03] &),
(RGBColor[#[[1]], #[[2]], #[[3]], .05] &)}, Spacer[5]]

data = RandomReal[1, {20, 4}];
func = Nearest[{#, #2, #3} -> #4 & @@@ data];
dta = Table[func[{x, y, z}] // Quiet, {x, 0, 1, .005}, {y, 0, 1, .005}, {z, 0, 1, .005}];

Grid[Partition[
 Image3D[dta,
 ImageSize -> 350, ColorFunction -> #, Background -> Black] & /@
 {"SunsetColorsOpacity", "RainbowOpacity", "WhiteBlackOpacity",
  (Append[Blend[{LightBlue, Blue, Yellow}, #], #] &)}, 2]]

data = RandomReal[1, {20, 4}];

func = Nearest[{#, #2, #3} -> #4 & @@@ data];

ContourPlot3D[
 func[{x, y, z}] // Quiet,
 {x, 0, 1}, {y, 0, 1}, {z, 0, 1},
 ColorFunction -> (Hue@#3 &)
]

BlockRandom[SeedRandom["voronoi"]; pts = RandomReal[{-1, 1}, {32, 3}]];
nf = Nearest[pts];

(* gradient-normalized function *)
vfun[x_?NumericQ, y_?NumericQ, z_?NumericQ] := With[{np = nf[{x, y, z}, 2]},
     (EuclideanDistance[{x, y, z}, np[[2]]] - EuclideanDistance[{x, y, z}, np[[1]]])/
     EuclideanDistance[Normalize[{x, y, z} - np[[2]]], Normalize[{x, y, z} - np[[1]]]]]

With[{ε = 1/100}, (* tiny number, increase if you want to see gaps between cells *)
     ContourPlot3D[vfun[x, y, z] == ε, {x, -1, 1}, {y, -1, 1}, {z, -1, 1},
                   MaxRecursion -> 1, Mesh -> False, PlotPoints -> 35]]

$QHULL::usage="$QHULL should contain the name (as a string) of the folder that contains the QHULL binaries on your system.
$QHULL = ToFileName[{$UserBaseDirectory, "Applications", "qhull", "src"}];

$QHULL = ToFileName[{NotebookDirectory[], "qhull", "bin"}];

SetDirectory[NotebookDirectory[]]
<< "mPower.m"

Warning: regtet binary not found. Expected location: /mPower-1.0-11-May-2008-1631/qhull/bin/

Warning: pwrvtx binary not found. Expected location: /mPower-1.0-11-May-2008-1631/qhull/bin/

(* random 3D points *)
points = RandomReal[1, {40, 3}];
(* construct 3D convexhull *)
ch = convexHull[points, convexHullFormat -> {facetNormals -> True, facets -> True}];
(* generate facets for 3D convexhull *)
facetIndices = facets /. ch;
loop[alist_] := Append[alist, alist[[1]]];
loopedFacetIndices = loop /@ facetIndices;
index2xyz[ijklist_] := points[[#]] & /@ ijklist;
loopedFacetCoordinates = index2xyz /@ loopedFacetIndices;
(* visulization 3D convexhull *)
convexObject =
 Graphics3D[{PointSize[Large], Point[points], FaceForm[],
   EdgeForm[Blue], Polygon /@ loopedFacetCoordinates},
  ImageSize -> 500]

pad[δ_][{min_, max_}] := {min, max} + δ(max-min){-1, 1}

VoronoiCells[pts_] :=
  Block[{bds, dm, init, conn, adj, lc, pc, cpts, hpts, hns, hp, vcells},
    bds = pad[.1] /@ MinMax /@ Transpose[pts];
    dm = DelaunayMesh[pts];
    init = BoundaryMeshRegion[Tuples[bds], Polygon[{{1,2,4,3},{2,4,8,6},{8,6,5,7},{1,5,7,3},{1,5,6,2},{3,7,8,4}}]];

    conn = dm["ConnectivityMatrix"[0, 1]];
    adj = conn . Transpose[conn];

    lc = conn["MatrixColumns"];
    pc = adj["MatrixColumns"];
    cpts = MeshCoordinates[dm];

    vcells = Table[
      hpts = PropertyValue[{dm, {1, lc[[i]]}}, MeshCellCentroid];
      hns = Transpose[Transpose[cpts[[DeleteCases[pc[[i]], i]]]] - cpts[[i]]];
      hp = MapThread[HalfSpace, {hns, hpts}];
      RegionIntersection @@ Prepend[BoundaryDiscretizeGraphics[Graphics3D[#, PlotRange -> bds]]& /@ hp, init],
      {i, MeshCellCount[dm, 0]}
    ];

    AssociationThread[cpts, vcells]
  ]

SeedRandom[10000];
pts = RandomReal[1, {10, 3}];

vc = VoronoiCells[pts]

Show[MapIndexed[
  BoundaryMeshRegion[#, MeshCellStyle -> {1 -> {Black, Thick}, 2 -> {ColorData[112][First[#2]]}}] &,
  Values[vc]
]]

Show[
  MapIndexed[
    BoundaryMeshRegion[#, MeshCellStyle -> {1 -> {Black, Thick}, 2 -> {ColorData[112][First[#2]]}}] &,
    Values[vc]
  ],
  Graphics3D[{PointSize[Large], Point[pts]}],
  Method -> {"RelieveDPZFighting" -> True}
]