Alpha complex reference manual¶

class
gudhi.
AlphaComplex
¶ Bases:
object
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.
All simplices that have a filtration value strictly greater than a given alpha squared value are not inserted into the complex.
Note
When Alpha_complex is constructed with an infinite value of alpha, the complex is a Delaunay complex.

__init__
()¶ AlphaComplex constructor.
 Parameters
points¶ (list of list of double) – A list of points in dDimension.
Or

create_simplex_tree
()¶  Parameters
max_alpha_square¶ (float) – The maximum alpha square threshold the simplices shall not exceed. Default is set to infinity, and there is very little point using anything else since it does not save time.
default_filtration_value¶ (bool) – Set this value to True if filtration values are not needed to be computed (will be set to NaN). Default value is False (which means compute the filtration values).
 Returns
A simplex tree created from the Delaunay Triangulation.
 Return type

get_point
()¶ This function returns the point corresponding to a given vertex from the
SimplexTree
. Parameters
vertex¶ (int) – The vertex.
 Return type
list of float
 Returns
the point.
