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GUDHI / gudhi-devel

The GUDHI library is a generic open source C++ library, with a Python interface, for Topological Data Analysis (TDA) and Higher Dimensional Geometry Understanding.
https://gudhi.inria.fr/
MIT License
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AlphaComplex documentation #500

Open abst0603 opened 3 years ago

abst0603 commented 3 years ago

I guess the documentation of alpha complex greatly benefits from expressing this point that "the Vertices added to the alpha complex are not in the same order of point list given to the AlphaComplex". It is strange that by using alpha complex on a 2D point set, the order doesn't change, however, for a 3D point set, the order changes. I just realize this after facing a problem that takes me a long time to solve. Then, I found in AlphaComplex reference manual that there is a function to map vertices to points. Also, if the same thing is true for Rips or other complexes, it should be noted in the reference manual.

VincentRouvreau commented 3 years ago

For alpha complex, if points dimension is 3 and points are not on the same plane, the algorithm is using behind the scene is not the same as it will use the CGAL 3D Alpha Shapes (as it was faster with CGAL versions < 5.0), and otherwise it is using CGAL dD Triangulations. We did some specific code for vertices to be ordered with the dD version and we didn't do the effort for the 3D version, sorry about that.

It may change in a future version (cf. #462 ) with weighted alpha complex, where we may split the dD and 3D version of the alpha complex. The 3D version may benefit of weighted, periodic and/or weighted periodic version.

You can be reassured that this is not the case for Rips and other complexes.

mglisse commented 3 years ago

See also #410.