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.

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


Parameters:off_file (string) – An OFF file style name.
Parameters:max_alpha_square (float) – The maximum alpha square threshold the simplices shall not exceed. Default is set to infinity.
Returns:A simplex tree created from the Delaunay Triangulation.
Return type:SimplexTree

This function returns the point corresponding to a given vertex.

Parameters:vertex (int) – The vertex.
Return type:list of float
Returns:the point.