Avoiding Smoothing in ListSurfacePlot3D

Question

I'm loading a dataset {x,y,z,v} from a text file. It is about a triangulated surface and then I am using ListSurfacePlot3D to plot it. However, ListSurfacePlot3D is smoothing the surface, that is something I do not want.

There is an option to avoid this? Should I use a different method to plot?

Thanks.

Data:
https://www.dropbox.com/sh/ll9hb3oxxreufsg/AABvU7nufHhyHY3W4ausanJ6a?dl=0

Code:

data = Import["geometry.txt", "Table"];
ListSurfacePlot3D[data[[;; , 1 ;; 3]]]

This is not the intended shape, which can be discerned by doing a ListPointPlot3D

ListPointPlot3D[data[[All, ;; 3]], PlotStyle -> PointSize[.008]]

You can see that ListSurfacePlot3D omits a large number of points by overlaying the types of plot,

Show[ListSurfacePlot3D[#], ListPointPlot3D[#]] &@data[[All, ;; 3]]

ListSurfacePlot3D clearly does some interpolation, but there is no documentation on how to apply the Method option, which controls "the method to use for interpolation and data reduction".

Answer 1

Going off of Lou's comments, it looks like setting the option MaxPlotPoints to a value of 20 or higher gives a better plot than the default. (I had tried PlotPoints but that isn't an option for ListSurfacePlot3D)

ListSurfacePlot3D[data[[All, ;; 3]], MaxPlotPoints -> #, 
    ImageSize -> 400] & /@ {6, 8}~Join~Range[10, 70, 10];
Grid@(%~Partition~4)

The option , PerformanceGoal -> "Quality" did not have an effect.

Answer 2

The way I solved is quite complicated and use gmsh http://gmsh.info/ to generate the stl file.

I have this package that enables loading .geo file and generation of stl file with gmsh

BeginPackage["Gmsh`"];

GmshCommandLine="~/Tools/gmsh-2.11.0-Linux/bin/gmsh";

RunGmsh[ifile_,ofile_]:=Run[GmshCommandLine<>" -2 "<>ifile<> " -o "<>ofile];

GmshArc3D[{a_, m_, b_}, n_:10, prim_: Line] := 
 Module[{\[Alpha], lab, axis, aarc, tm, alpha}, 
  lab = m + Norm[a - m]*Normalize[b - m];
  axis = (a - m)\[Cross](b - m);
  aarc = (VectorAngle[a - m, b - m]);
  tm = RotationMatrix[alpha, axis];
  prim@Table[m + tm.(a - m), {alpha, 0, aarc, aarc/n}]];

GmshParameters/:(var_/;Head@var===GmshGeo)[GmshParameters]:=var[[1]];
GmshPoints/:(var_/;Head@var===GmshGeo)[GmshPoints]:=var[[2]];
GmshLines/:(var_/;Head@var===GmshGeo)[GmshLines]:=var[[3]];
GmshCircles/:(var_/;Head@var===GmshGeo)[GmshCircles]:=var[[4]];

GmshPointFormat:="Point("~~n__~~")={"~~x__~~","~~y__~~","~~z__~~","~~l__~~"}";
GmshLineFormat:="Line("~~n__~~")={"~~p1__~~","~~p2__~~ "}";
GmshCircleFormat:="Circle("~~n__~~")={"~~s__~~","~~c__~~","~~e__~~"}";

GmshImportGeo[ifile_,evaluate_:False]:=Module[

  {temp,parameters,points,lines,circles},

  temp=ReadList[ifile,"String"];

  temp=StringDelete[temp,{" ",";"}];

  temp=Select[
    temp,
    StringMatchQ[
      #,
      {"LineLoop"~~___,"PlaneSurface"~~___,"RuledSurface"~~___}
    ]==False&
  ];

  parameters=Select[
    temp,
    StringMatchQ[
        #,
        {"Point"~~___,"Line"~~___,"Circle"~~___}
    ]==False&];

  parameters=ToExpression[
    StringReplace[
      parameters,
      {"="->"\[Rule]"}
    ]
  ];

  points=Select[
    temp,
    StringMatchQ[
      #,
      "Point"~~__
    ]==True&];

  points=ToExpression[
    StringReplace[
      points,
      {GmshPointFormat:>ToString[{n,{x, y, z},True}]}
    ]
  ];

  lines=Select[
    temp,
    StringMatchQ[
      #,
      "Line"~~__
    ]==True&
  ];

  lines=ToExpression[
    StringReplace[
      lines,
      {GmshLineFormat:>ToString[{n,{p1, p2},True}]}
    ]

just change the GmshCommandLine to point your gmsh binary.

Let's say you want draw a sphere, you have to create sphere.geo that contains commands for gmsh (see the help)

lc=0.1;
Point(1)={0,0,0,lc};
Point(2)={1,0,0,lc};
Point(3)={-1,0,0,lc};
Point(4)={0,1,0,lc};
Point(5)={0,-1,0,lc};
Point(6)={0,0,1,lc};
Point(7)={0,0,-1,lc};

Circle(1) = {2, 1, 4};
Circle(2) = {4, 1, 3};
Circle(3) = {3, 1, 5};
Circle(4) = {5, 1, 2};
Circle(5) = {7, 1, 3};
Circle(6) = {3, 1, 6};
Circle(7) = {6, 1, 2};
Circle(8) = {2, 1, 7};
Circle(9) = {7, 1, 4};
Circle(10) = {4, 1, 6};
Circle(11) = {6, 1, 5};
Circle(12) = {5, 1, 7};
Line Loop(13) = {7, 1, 10};
Ruled Surface(14) = {13};
Line Loop(15) = {1, -9, -8};
Ruled Surface(16) = {15};
Line Loop(17) = {9, 2, -5};
Ruled Surface(18) = {17};
Line Loop(19) = {2, 6, -10};
Ruled Surface(20) = {19};
Line Loop(21) = {4, -7, 11};
Ruled Surface(22) = {21};
Line Loop(23) = {4, 8, -12};
Ruled Surface(24) = {23};
Line Loop(25) = {12, 5, 3};
Ruled Surface(26) = {25};
Line Loop(27) = {3, -11, -6};
Ruled Surface(28) = {27};

and then run this mathematica script

<< Gmsh`
geo = GmshImportGeo["sphere.geo"];
RunGmsh["sphere.geo", "sphere.stl"];
mesh = Import["sphere.stl", "STL"];
geo = geo /. geo[GmshParameters];
Graphics3D[{GmshCompileGeo[geo, False], mesh[[1]]}]

here you have the results

looking at the package you can hide geometric features, i.e.

GmshHideLine[geo, {1,2}];

hides line 1,2 (see the .geo file)

That's all folk! F