class foronoi.nodes.Breakpoint(breakpoint: tuple, edge=None)

A breakpoint between two arcs.

The breakpoint is stored by an ordered tuple of sites (p_i, p_j) where p_i defines the parabola left of the breakpoint and p_j defines the parabola to the right. Furthermore, the internal node v has a pointer to the half edge in the doubly connected edge list of the Voronoi diagram. More precisely, v has a pointer to one of the half-edges of the edge being traced out by the breakpoint represented by v.


breakpoint ((Point, Point)) – A point where two arcs intersect, represented as a tuple of the two site points that the arcs refer to


A guard that handles the edge-case where two arcs were initialized at the same time due to their sites having the same y-coordinate. This guard makes sure that the left arc intersects once with the right arc and not the other way around.


intersects – Returns false when p_i and p_j have the same y-coordinate and p_j is situated left of p_i.

Return type


get_intersection(l, max_y=None)

Calculate the coordinates of the intersection Modified from

  • l (float) – The y-coordinate of the sweep line

  • max_y (float) – The top of the bounding box/polygon for clipping infinite breakpoints


coordinate – The current coordinates of the breakpoint

Return type