This ASCII format is a very simple one. It consists in a list of all the critical points with some useful information for each of them.

crits_ascii format
#critical points Header
#X0 X1 X2 value type pair_id boundary Header identifying each column
#NDIMS NPOINTS Number of dimensions and number of points
X0 X1 X2 value type pair_id boundary The value of the fields for the first point
.... One such line for each NPOINTS points


  • -X_0,..., X_ndims : the coordinates of the pooint
  • -value : Value of the field.
  • -type : the critical index of the point. A value of NDIMS+1 indicates a bifurcation point or a trimmed extremity.
  • -pair_id : index of the other critical point in the persistence pair. C style convention is used, indices starting at 0, and points without perisstence pairs have their own index for pair_id.
  • -boundary : value can be 0, 1 or 2 when the point is inside the domain, on the boundary, or outside (e.g. at infinity)