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.


When Alpha_complex is constructed with an infinite value of alpha, the complex is a Delaunay complex.


AlphaComplex constructor.


points (list of list of double) – A list of points in d-Dimension.


  • off_file (string) – An OFF file style name.

  • precision (string) – Alpha complex precision can be ‘fast’, ‘safe’ or ‘exact’. Default is ‘safe’.

  • 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).


A simplex tree created from the Delaunay Triangulation.

Return type



This function returns the point corresponding to a given vertex from the SimplexTree.


vertex (int) – The vertex.

Return type

list of float


the point.