TetGen example: Boeing 747


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The input surface mesh, 2866 nodes, 5732 triangles. There are 7 boundary markers defined in this model, shown in different colors. The bounding box has been removed in this picture for better viewing.

The refined mesh (see Statistics for mesh size information).

An overview of the remaining poor-quality tets

A detailed view of the remaining poor-quality tets on one of the wings.


TetGen runtime output

Opening 747heat.smesh.
Opening 747heat.node.
Opening 747heat.b.node.
Opening 747heat.b.ele.
Opening 747heat.b.mtr.
Constructing Delaunay tetrahedralization.
  Creating initial tetrahedralization.
  Incrementally inserting points.
  48838 Flips (T23 28698, T32 18399, T22 1, T44 1740)
Delaunay seconds:  0.46
Creating surface mesh.
  Constructing mapping from indices to points.
  Constructing mapping from points to tetrahedra.
  Unifying segments.
  Constructing mapping from points to subfaces.
  Merging coplanar facets.
Perturbing vertices.
  Removing degenerate subfaces.
  139 break points.
Delaunizing segments.
  Marking segments have acute corners.
  Constructing mapping from points to segments.
  3351 protect points.
Constraining facets.
  Constructing mapping from points to tetrahedra.
  The biggest cavity: 14 faces, 9 vertices
  Enlarged 0 times
Segment and facet seconds:  0.97
Removing unwanted tetrahedra.
  Marking holes for elimination.
  Marking concavities for elimination.
  Marking neighbors of marked tetrahedra.
  Deleting marked tetrahedra.
Hole seconds:  0.02
Repairing degenerate tets.
  0 degeneracies are removed.
Steiner seconds:  0
Reconstructing mesh.
  Constructing mapping from indices to points.
  Constructing mapping from points to tetrahedra.
  Constructing mapping from points to subfaces.
  Checking Delaunay property of the mesh...
  Interpolating size map.
Background mesh reconstruct seconds:  0.35
Adding Steiner points to enforce quality.
  Marking sharp subsegments.
  36 sharp segments.
  Marking skinny subfaces.
  6714 skinny subfaces.
  Splitting encroached subsegments.
  20677 split points.
  Splitting encroached subfaces.
  209 split points.
  Splitting bad tetrahedra.
  273251 refinement points.
  Removing slivers.
  5103 slivers are removed.
  404 sliver(s) survived.
  211 points.
  Totally added 294348 points.
Quality seconds:  36.8

Writing 747heat.1.node.
Writing 747heat.1.mtr.
Writing 747heat.1.ele.
Writing 747heat.1.face.

Output seconds:  4.6
Total running seconds:  43.21

Statistics:

  Input points: 2874
  Input facets: 5738
  Input holes: 1
  Input regions: 0

  Mesh points: 300712
  Mesh tetrahedra: 1783953
  Mesh faces: 3611435
  Mesh subfaces: 87143
  Mesh subsegments: 44414

Mesh quality statistics:

  Smallest volume:       2.3835e-08   |  Largest volume:            69815
  Shortest edge:          0.0026018   |  Longest edge:                112
  Smallest dihedral:     0.00023076   |  Largest dihedral:       179.9995

  Radius-edge ratio histogram:
         < 0.707     :    147514      |    1.6 - 1.8        :     12793
   0.707 - 1         :   1476625      |    1.8 - 2          :      6797
       1 - 1.1       :     45664      |      2 - 2.5        :      5080
     1.1 - 1.2       :     23162      |    2.5 - 3          :      2924
     1.2 - 1.4       :     32879      |      3 - 10         :      8337
     1.4 - 1.6       :     21457      |     10 -            :       721
  (A tetrahedron's radius-edge ratio is its radius of circumsphere divided
    by its shortest edge length)

  Aspect ratio histogram:
         < 1.5       :     83218      |      6 - 10         :     30025
     1.5 - 2         :    741164      |     10 - 15         :      9126
       2 - 2.5       :    529980      |     15 - 25         :      2408
     2.5 - 3         :    181989      |     25 - 50         :       453
       3 - 4         :    134125      |     50 - 100        :        72
       4 - 6         :     71349      |    100 -            :        44
  (A tetrahedron's aspect ratio is its longest edge length divided by its
    smallest side height)

  Dihedral angle histogram:
       0 -  5 degrees:       664      |     90 - 100 degrees:    477246
       5 - 10 degrees:     15697      |    100 - 110 degrees:    347076
      10 - 30 degrees:    209254      |    110 - 120 degrees:    223637
      30 - 40 degrees:    302183      |    120 - 130 degrees:    138368
      40 - 50 degrees:    593537      |    130 - 140 degrees:     86107
      50 - 60 degrees:    555118      |    140 - 150 degrees:     55103
      60 - 70 degrees:    107489      |    150 - 170 degrees:     52319
      70 - 80 degrees:     43547      |    170 - 175 degrees:      1971
      80 - 90 degrees:    358554      |    175 - 180 degrees:        36


si@david-04: ~/tetgen-dbg/747 > ../qualchk -rV 747heat.1
Opening 747heat.1.node.
Opening 747heat.1.ele.
Opening 747heat.1.face.
Opening 747heat.1.edge.
Opening 747heat.1.mtr.
Reconstructing mesh.
  Constructing mapping from indices to points.
  Constructing mapping from points to tetrahedra.
  Constructing mapping from points to subfaces.
Writing 747heat.2.lua.
  Radiu-edge ratio bound: 2.
  Upper dihedral angle bound: 175 (degree).
  17062 bad-qual tets.
    36 slivers.
Checking interior mesh conformity.
  Constructing mapping from points to tetrahedra.
Writing 747heat.2.txt.

Mesh conformity statistics:

  Longest edge length to node size ratio histogram:
           < 0.25      :         0    |        1 - 1.41421    :     14528
      0.25 - 0.353553  :         0    |  1.41421 - 2          :     27840
  0.353553 - 0.5       :        97    |        2 - 2.82843    :    252009
       0.5 - 0.707107  :       638    |  2.82843 - 4          :        27
  0.707107 - 1         :      5573    |        0 -            :         0

  Smallest edge length to node size ratio histogram:
           < 0.25      :     10861    |        1 - 1.41421    :    118632
      0.25 - 0.353553  :      5961    |  1.41421 - 2          :    134265
  0.353553 - 0.5       :      8696    |        2 - 2.82843    :         0
       0.5 - 0.707107  :      6452    |  2.82843 - 4          :         0
  0.707107 - 1         :     15845    |        0 -            :         0

  Average edge length to node size ratio histogram:
           < 0.25      :         8    |        1 - 1.41421    :     16635
      0.25 - 0.353553  :       155    |  1.41421 - 2          :    239819
  0.353553 - 0.5       :      2028    |        2 - 2.82843    :     18746
       0.5 - 0.707107  :     10023    |  2.82843 - 4          :         0
  0.707107 - 1         :     13298    |        0 -            :         0


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Hang Si