The GUDHI library is a generic open source C++ library, with a Python interface, for Topological Data Analysis (TDA) and Higher Dimensional Geometry Understanding.
Fix #1030.
After that, I think (could be wrong though) the problems caused by Epick_d are no worse for Cech than for the alpha-complex. That is, we could investigate more numerically stable ways to compute a circumradius (especially since for the Cech we can assume that the center is inside the triangle), or mitigation strategies (like the one suggested in the new comment), to get a better balance between speed and safety, but nothing urgent.
[ ] Check the impact on performance. I would expect a negligible slowdown if maxdim ≤ ambient dimension, and possibly a small speed up if maxdim is larger.
Fix #1030. After that, I think (could be wrong though) the problems caused by Epick_d are no worse for Cech than for the alpha-complex. That is, we could investigate more numerically stable ways to compute a circumradius (especially since for the Cech we can assume that the center is inside the triangle), or mitigation strategies (like the one suggested in the new comment), to get a better balance between speed and safety, but nothing urgent.