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mesh - Meshing the surface of a non-convex object



I would like to mesh the surface of a cloud of points that may not be completely convex, for example the points in this question. Mathematica does not provide triangulation of 3D points, but there is a link to TetGen


 Needs["TetGenLink`"]

 {mypts, mysurface} = TetGenConvexHull[dat];
 Graphics3D[GraphicsComplex[mypts, Polygon[mysurface]], Boxed -> False]

which results in this


enter image description here


Notice it doesn't get the surface meshing associated with subtle twist in the curved shape, and meshes points further away in the goal of creating a convex object. I suppose one could try to mesh the surface piece by piece and slowly merge it as in this answer, but that sounds like a nightmare.


Here is the cloud of points for reference:



enter image description here



Answer



Using Simon's answer (all credit to him):


Needs["TetGenLink`"]
file = "https://dl.dropboxusercontent.com/u/68983831/curved_pipe02.txt";
dat = Import[file, "Table"];
{pts, tetrahedra} = TetGenDelaunay[dat];
csr[{aa_, bb_, cc_, dd_}] := 
 With[{a = aa - dd, b = bb - dd, c = cc - dd}, 
  Norm[a.a Cross[b, c] + b.b Cross[c, a] + 

     c.c Cross[a, b]]/(2 Norm[a.Cross[b, c]])]
radii = csr[pts[[#]]] & /@ tetrahedra;
alphashape[rmax_] := Pick[tetrahedra, radii, r_ /; r < rmax]
faces[tetras_] := 
 Flatten[tetras /. {a_, b_, c_, 
     d_} :> {{a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}}, 1]
externalfaces[faces_] := 
 Cases[Tally[Sort /@ faces], {face_, 1} :> face]
polys = externalfaces@faces@alphashape[.001];
Graphics3D[GraphicsComplex[pts, Polygon@polys], Boxed -> False]


polys = externalfaces@faces@alphashape[.001];
Graphics3D[GraphicsComplex[pts, Polygon@polys], Boxed -> False]

Mathematica graphics


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