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point_intersection_of_two_lines(P,s,m) states that point P is the intersection of lines s and m (actually, s and m must be elements of the line_family).

See also Intersection of extended elements.

Formal properties

point_intersection_of_two_lines(P,s,m) and point_intersection_of_two_lines(Q,s,m) => P=Q

Degenerate cases

If the intersection exists and is a point, return it.

If the two lines are parallel and there is no “finite intersection”, the behaviour of this function is DGS dependent:

  • Those DGS that can handle projective geometry are free to return a “point in the infinite” (see below)
  • Other DGS will return the undefined value
If the two lines are coincident, the behaviour is also DGS dependent, and two possible values are allowed:
  • return the undefined value
  • return the intersection line


  1. parabola defined as locus example: source JSXGraph
  2. extended intersections example: source JSXGraph