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bugs - MeshCoordinates from a RegionBoundary no longer in proper order in version 10.4


Bug introduced in V10.4 and persists through 10.4.1



Given that I have the following data set


mat = 
 {{{0.,-5.,0.},{-5.22027,0.,1.79454}},
 {{-0.858274,-4.93844,0.0924},{-5.41893,0.782172,1.77784}}, 
 {{-1.82027,-4.75528,-0.109357},{-5.60223,1.54509,1.95084}},
 {{-2.94275,-4.45503,-0.550252},{-5.77547,2.26995,2.3602}},
 {{-4.31974,-4.04509,-1.18618},{-5.94562,2.93893,3.03783}},

 {{-6.12372,-3.53553,-2.00001},{-6.12372,3.53553,3.99999}}};

domain = 
  {{{5.0165, 2 Pi}, {0, 0.756304}}, {{3.4076, 2 Pi}, {0, 2.31521}}, 
   {{3.7396, 2 Pi}, {0, 1.93244}}, {{3.85122, 2 Pi}, {0, 1.86739}},  
   {{3.91005, 2 Pi}, {0, 1.87528}}, {{3.94139, 2 Pi}, {0, 1.91028}}};

ellipsePoints[mat_, {x_, y_}] := 
  mat.{Sin[#], Cos[#], 1} & /@ Range[x, y, 0.02 Pi]
ellipsePoints[mat_, {{a_, b_}, {c_, d_}}] := 

  mat.{Sin[#], Cos[#], 1} & /@ 
   Join[Range[a, b, 0.02 Pi], Range[c, d, 0.02 Pi]]

pts = Flatten[MapThread[ellipsePoints, {mat, domain}], 1];

With help of RunnyKine's alphaShapes2DC[] function, I can find the approximate boundary


Show[Graphics[Point[pts]], RegionBoundary@alphaShapes2DC[pts, 5.5]]

enter image description here




However, when I get the coordinates of the boundary via MeshCoordinates[], which gives me a wrong order of point-set.


ListLinePlot@MeshCoordinates@RegionBoundary@alphaShapes2DC[pts, 5.5]

enter image description here


So my question is:(I using the Mathematica V$10.4$ on Windows $32$ bit system)



  • How to do to achieve the right order of point-set?



Answer



Let's look at a simpler example to show the problem. We'll create a Delaunay mesh from some random points, and generate a RegionBoundary from that.



In version 10.4:


SeedRandom[4];
mr1 = DelaunayMesh[RandomReal[1, {15, 2}]];
mr2 = RegionBoundary[mr1];
Show[mr1, HighlightMesh[mr2, 1], 
 ListLinePlot[MeshCoordinates@mr2, 
  PlotStyle -> Directive[Thick, Red]]]

10.4 output


compared with version 10.3.1 (or any previous version 10.x)



output from earlier versions


Let's look at the InputForm for this in 10.4,


mr2 // InputForm


MeshRegion[{.....}, {Line[{{2, 6}, {1, 2}, {4, 1}, {3, 5}, {6, 3}, {5, 4}}]}]

versus for 10.3,


MeshRegion[{.....}, {Line[{{1, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 6}, {6,1}}]}]


How to get around this? Create a BoundaryMeshRegion and extract the polygon points from that (the points of a polygon must be in the right order or it's nonsense). The following gives identical results in 10.3 and 10.4


SeedRandom[4];
mr1 = DelaunayMesh[RandomReal[1, {15, 2}]];
mr2 = BoundaryDiscretizeRegion[mr1];
Show[mr1, HighlightMesh[mr2, 1], 
 ListLinePlot[First@First@MeshPrimitives[mr2, 2], 
  PlotStyle -> Directive[Thick, Red]]]

fixed version


And, applied to the OP,



ListLinePlot@First@First@MeshPrimitives[#, 2] &@
 BoundaryDiscretizeRegion@alphaShapes2DC[pts, 5.5]

the alpha shape


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