Suitable computation of anisotropic size at required interfaces (and parallel entities)

[Algiane]

Mesh adaptation from an input metric far from the input mesh size at required points leads to:

• quality degeneration along required edges / triangles (points are OK)
• very long time for Mmg that doesn't doesn't converge

calculating and propagating (slightly) the required interface sizes should allow to accelerate Mmg while guaranteeing a quality mesh.

• For isotropic metric, the size at required points is computed as the mean of the lengths of required edges passing through this point
• For now, for anisotropic metric, the same isotropic computation is used

Opened questions:

• is it better to preserve input metric directions or can we modify it (using simultaneous reduction for example)? What we don't want for sure is to force the metric directions to be aligned with tangent plane and normal at point.
• can we compute anisotropic mean lengths using length distribution tensor computation (see T. Coupez paper: https://www.sciencedirect.com/science/article/pii/S002199911000656X and computation of optim option in aniso mode in Mmg)? In this case, the case where a required points belongs to at least 3 edges that are not in the same plane is OK but we have to treat differently the case where all edges belongs to the same plane.
• if yes, what is the better way to change the input metric so it imposes a size not too far from the computed metric (that can be 1D, 2D or 3D depending on the required edges repartition) in the direction of required edges? Note that size may have to be increased or reduced.

Proposition:

• Computation of length distribution tensor
• Modification of input metric in the tangent plane defined by required edges so it matches the edge lengths prescribed by length distribution tensor along this plane