Shape_detection: using proper triangulated polygonal faces for linear_least_squares

[soesau]

Summary of Changes

Polygonal faces are now triangulated and face normals are calculated using PMP::compute_face_normal.

The calculated face normals and triangulations are buffered in Least_squares_plane_fit_region. However, Least_squares_plane_fit_sorting is independent and does not benefit from that buffered data.

Release Management

• Affected package(s): Shape_detection
• Issue(s) solved (if any): fix Least_squares_plane_fit_region is not using PCA #7992

[lrineau]

@afabri @sloriot @MaelRL: This bug-fix pull-request adds new dependencies to non-trivial parts of PMP. For the license checking, that means a user of CGAL-5.6.1 might have a new license issue after an update to CGAL-5.6.2. That does not seem right.

[soesau]

Sebastien motivated yesterday having a basic triangulation for exactly cases like this.
Here a simple triangulation of simple polygons is required. Using PMP::triangulate_hole_polyline creates all those mentioned dependencies.

[sloriot]

runtime error of test_region_growing_on_degenerated_meshfor shape detection in CGAL-6.0-Ic-279

[sloriot]

Successfully tested in CGAL-6.0-Ic-282

[afabri]

Can we not identify three points which are maximal un-collinear, by computing Eigen values/vectors ?

[sloriot]

I think the issue encountered by @lrineau would be fixed by only fixing this function. We should look for 3 non-collinear vertices to get a normal. I would then skip the proper 2D CDT and keep the centroid triangulation for the plane fitting (only matters for non exactly coplanar points anyway). @afabri what do you think?

[afabri]

I also thought that for computing a face normal it is enough to find 3 sufficiently non-collinear points, but Sven told me that for non-convex faces he has to compute some weight and for that he needs a triangulation. We have to check with him.

[soesau]

These were two separate problems:

1. get_face_normal is used for fitting a plane to a single face and for checking whether a face fits to an adjacent region. This was likely the issue encountered by @lrineau.
2. PCA was not using triangulated faces.

[github-actions]

This pull-request was previously marked with the label Tested, but has been modified with new commits. That label has been removed.

[sloriot]

Successfully tested in CGAL-6.0-Ic-307