MMG2D metric, non orthogonal parametrization

[gbettega]

This is a very interesting post.

How to scale the metric for anisotropic meshing in MMG2D? Example provided

Hello, there is only one recently added example of how to set a tensorial metric in MMG2D, for anisotropic meshing but it relies on a mesh/sol file. I thought it would be great to have an example that demonstrates: how to first compute a mesh from boundary using MMG2D_mmg2dmesh and then how to remesh it using MMG2D_mmg2dlib using an anisotropic metric. so that the example is self-contained and does not rely on a mesh/sol file, so that one learns from the example how to compute the metric. Si…

In summary: generate a mesh of a rectangle which represents the u.,v mapping of a sphere, and re-map the resulting mesh onto a sphere.
An anisotropic metric is used in meshing the u, rectangle, with the aim of accounting for the mesh distrorsion induced by the mapping from a planar mesh to a 3d mesh,
and obtain a set of “not distorted” triangles in 3d.

So the author uses

MMG2D_Set_tensorSol(mmgSol, m11, m12, m22, pos);

m11 = 1/sqrt(l1), m12 = 0, m22 = 1/sqrt(l2)

where l1, l2 are eigenvalues.
This because for a unit radius sphere, m11 = cos(phi), m12 = m21 = 0, m22 = 1;

Now let suppose that the surface has not an orthogonal parametrization, that is the coefficient F of the first fundamental form is not zero.
Which is the value for m12 in MMG2D_Set_tensorSol for this case?
Grazie
Giovanni

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[gbettega]

I partially reply to myself
the metric tensor is symmetric, so eigenvalues are real, and eigenvector orthogonal.
So my question was wrong.
BUt keeping the symmetry (m12 = m21) what about the scaling of m12?
Ciao
Giovanni