Mmg histograms

Understand Mmg histograms

In the following section we will describe the histograms printed by Mmg.

The verbosity level (-v command line argument) will determin input and output informations : 

  • at level 1 (-v 1) : main informations on input and output mesh qualities are printed -> minimal, maximal and mean element quality + index of the lowest quality element
  • level 2 (-v 2) : adds main informations on input edge lengths are printed -> smallest, average and largest edge length + indices of extremities of the smallest and largest edges
  • level 3 : adds statistic info on input edge length
  • level 4 : adds detailed histograms for input and output mesh quality and input edge lengths
  • level 5 : adds detailed histograms for output edge lengths

Element quality histogram

In the following, we note  Latex formula the element dimension (Latex formula for a triangle, Latex formula for a tetra), Latex formula the Latex formula edges of an element Latex formula, Latex formula their lengths, Latex formula the mean metric over this element  and Latex formula the volume of the element in this mean metric. The element quality is computed such as:
Latex formula  with  Latex formula a normalization coefficient such as an equilateral element has quality 1 in an isotropic metric.

— MESH QUALITY 11726   the mesh has 11726 elements (tetrahedra in 3D / triangles for surface meshes)
    BEST   1.000000     AVRG.    0.777858     WRST.     0.372378 (6029)  ←best elt quality is 1, average qual is 0.778, element of index 6029 is the worst and has a quality of 0.37
    HISTOGRAMM:      100.00 % > 0.12    ← 100% of the elements have a quality better than 0.12
                                            99.47 % > 0.5      ← 99% of the elements have a quality better than 0.5
            0.8 < Q < 1.0      5340      45.54 %   ← 5340 elements i.e. 45.54% of the elements have a quality between 0.8 and 1
            0.6 < Q < 0.8      5701      48.62 %   
            0.4 < Q < 0.6        681         5.81 %
            0.2 < Q < 0.4            4         0.03 %

Edge length histogram

— RESULTING EDGE LENGTHS     674      ← the mesh has 674 edges (internal and boundary ones)
   AVERAGE LENGTH                       3.0455  ← the average edge length is 3.045
   SMALLEST EDGE LENGTH         2.0000     88   108  ← the smallest edge is of length 2 and has vertices 88 and 108
   LARGEST EDGE LENGTH          10.1980      16   131   ← the largest edge is of length 10.198 and has vertices 16 and 131

   HISTOGRAMM:
    1.41 < L < 2.00         120     17.80 %    ← 120 edges (17.8%) have lengths between 1.41 and 2.00
    2.00 < L < 5.00        485      71.96 %
     5.     < L                       69       10.24 %

Note that we print the edge length computed in the input metric so we always target edges of size 1.

 

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