CGAL users discussion list

[Jane Tournois <>]

Hi Chris,

I understand what you mean.
Actually, your input mesh is pretty coarse close to constraints, so the Lloyd optimization cannot do much about it.

You can have a look at this paper for more details on our algorithm :
www.global-sci.org/nmtma/volumes/v3n2/pdf/32-212.pdf

The triangles that are called "blind" (meaning that their circumcenter is on the other side of a constrained edge) can hardly have a good shape without refining the associated constrained edge.
See for example Figure 5, where such triangles are colored.

If you want better shaped triangles close to constrained edges, they should be refined using the Delaunay_mesh_size_criteria_2 [1].

Also note that the Lloyd smoothing algorithm is enriched with a sizing field that locally preserves the mesh density through iterations. So, the vertices that are close to constraints should remain close to constraints. It avoids creating needle-shaped triangles next to constraints.

Best regards,

Jane.

[1] https://doc.cgal.org/latest/Mesh_2/classCGAL_1_1Delaunay__mesh__size__criteria__2.html

Le 26/02/2018 à 18:06, chrism a écrit :

Ah, sorry. Please find the comparison as presented above with the constraint
shown in red.

<http://cgal-discuss.949826.n4.nabble.com/file/t375307/lloyd.png> 

As I cannot attach a large image, it may be difficult to see exactly? If so,
I have paraview compatible VTU files as well as the triangulation and
constraint in ESRI shape files (shp) to load into a GIS, such as qGIS.



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-- 
Jane Tournois, PhD
R&D Engineer at GeometryFactory
http://www.geometryfactory.com/