More intuitive explanation of PMP::Adaptive_sizing_field tolerance parameter?

[darikg]

The documentation says tol is "the error tolerance, used together with curvature to derive target edge length. Lower tolerance values will result in shorter mesh edges."

tol is used in the source code thusly:

const FT vertex_size_sq = 6 * tol / max_absolute_curv - 3 * CGAL::square(tol);

and then vertex_size_sq is compared against the minimum and maximum square edge lengths. Is the tolerance expected to be relative or absolute? It kinda seems like both.

[ipadjen]

Hi @darikg,

The error tolerance parameter comes directly from the mathematical formulation for the adaptive isotropic remeshing.

Check the paper the CGAL's implementation is based on: https://diglib.eg.org/server/api/core/bitstreams/c4d5096e-de41-466e-9e74-83a28da64d67/content

Take a look at section 3. From the assumptions mentioned in that section you can easily derive the formula.

Hope that helps.