Skip to main content

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


Comments

Post a Comment

Popular posts from this blog

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more