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doc review: rephrase AlphaComplex definition
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VincentRouvreau committed Jul 31, 2024
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5 changes: 2 additions & 3 deletions src/python/gudhi/delaunay_complex.pyx
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Expand Up @@ -161,9 +161,8 @@ cdef class DelaunayComplex:
cdef class AlphaComplex(DelaunayComplex):
"""AlphaComplex is a simplicial complex constructed from the finite cells of a Delaunay Triangulation.
The filtration value of each simplex is computed as the square of the circumradius of the simplex if the
circumsphere is empty (the simplex is then said to be Gabriel), and as the minimum of the filtration values of the
codimension 1 cofaces that make it not Gabriel otherwise.
The filtration value of each simplex is computed as the squared radius of the smallest empty sphere passing through
all of its vertices.
All simplices that have a filtration value strictly greater than a given alpha squared value are not inserted into
the complex.
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