Future tasks for Alpha_shapes_[23]

[MaelRL]

A bunch of feature requests for the Alpha Shapes packages from @mglisse.

• filtration_with_alpha_values for 2D alpha shapes.
• 2D/3D: functions to get the filtration value of a simplex (i.e. the one obtained with filtration_with_alpha_values when using the GENERAL tag).
• Rework filtration_with_alpha_values to not use the overly complex dispatch_output to simply dump an object followed by a value (return directly a pair<variant, value> ?).
• Replace Object with variant.

[MaelRL]

• The General classification of Alpha_Shape_2 is currently bugged: no vertex can ever be classified as Exterior. Alpha_shape_2's classification should be mirrored with Alpha_shape_3 to use Is_Gabriel() functions from 2D triangulations.

[mglisse]

* functions to get the filtration value of a simplex

In 2D, from an edge iterator ei, I can get an Interval_3 ei->first->get_ranges(ei->second) (find_interval is private). And apparently, the value I need is then first, except if that's UNDEFINED (i.e. -2) in which case I want second (I didn't check very carefully). But that's using quite a bit of undocumented information. Also, the use of -2 as magic value seems dangerous to me if we can have weighted points with negative weights.

[mglisse]

(not for me, but based on https://stackoverflow.com/q/76720956/1918193 )

• Check if performance can be improved
  • Most of the time in 2D is spent in multimap
  • In principle, it should be possible to parallelize the computation of alpha values (computing the triangulation is negligible)

(and from https://stackoverflow.com/q/76669841/1918193 )

• Implement dynamic operations (insert, remove)