Getting ordered coordinates out of ConvexHullRegion

For graphing, my preferred approach is posted already by user21.

To get the ordered coordinates you can reorder MeshCoordinates[ConvexHullMesh[d] using FindCurvePath:

With[{d = RandomReal[{0, 1}, {20, 2}]}, mc=MeshCoordinates[ConvexHullMesh[d]];
ListPlot[ d, AspectRatio -> 1, Prolog -> {Yellow,Polygon[mc[[FindCurvePath[mc][[1]]]]]}]]

Mathematica graphics

An alternative way to get the ordering of the coordinates is to use the "BoundaryVertices" property of ConvexHullMesh[d]:

ConvexHullMesh[d]["BoundaryVertices"]

{1,8,4,5,6,3,10,9,2,7,11,1}

which is a rotated version of

FindCurvePath[MeshCoordinates[ConvexHullMesh[d]]][[1]]

{4,5,6,3,10,9,2,7,11,1,8,4}

And, the property "Coordinates" can be used instead of MeshCoordinates; so

#["Coordinates"][[#["BoundaryVertices"][[1]]]]&@ConvexHullMesh[d]

gives the ordered coordinates.

d = RandomReal[{0, 1}, {20, 2}];
chcoords=#["Coordinates"][[#["BoundaryVertices"][[1]]]]&@ConvexHullMesh[d];
ListPlot[ d, AspectRatio -> 1, Prolog -> {Yellow,Polygon[chcoords]}]

Mathematica graphics

Yet another way to get the ordered coordinates is to get the "GraphicsComplex" property and extract

Cases[Normal@ConvexHullMesh[d]["GraphicsComplex"],Polygon[x_]:>x,Infinity][[1]]

Assuming the goal is to create the graphics:

With[{d = RandomReal[{0, 1}, {20, 2}]},
 Show[ListPlot[d, AspectRatio -> 1], ConvexHullMesh[d]]]

enter image description here

And here is a more efficient version than FindPath:

With[{d = RandomReal[{0, 1}, {20, 2}]}, 
 ListPlot[d, AspectRatio -> 1, 
  Epilog -> 
     GraphicsComplex[
      MeshCoordinates[#], {Opacity[0.2], MeshCells[#, {2, All}]}] &[
   ConvexHullMesh[d]]]]

enter image description here


d = RandomReal[{0, 1}, {20, 2}];
hull = ConvexHullMesh[d];

The ordering can be obtained directly using MeshCells:

MeshCells[hull, 2]
(* {Polygon[{2, 6, 5, 4, 3, 1}]} *)

So:

points = MeshCoordinates[hull];
order = MeshCells[hull, 2][[1, 1]];
Graphics[{Yellow, Polygon[points[[order]]], Black, Point[d]}]

enter image description here