26.5.6  Finding a point of intersection of two objects in the plane

See Section 27.3.3 for single points of intersection of objects in space.

The single_inter or line_inter command finds an intersection point of two geometric objects.

• single_inter takes two mandatory arguments and one optional argument.
  • obj₁, obj₂, two geometric objects.
  • Optionally, pt, a point or list of points.
  line_inter(obj₁,obj₂ ⟨,pt ⟩) returns one of the points of intersection of obj₁ and obj₂.

  If pt is a single point, then the command returns the point of intersection closest to pt.

  If pt is a list of points, then the command tries to return a point not in pt.

Example

The command circle(0,1) creates the unit circle and line(-1,i) creates a line, these two objects intersect at the points (−1,0) and (0,1).

which is the point (−1,0).

which is the point (0,1). Similarly, since this second point of intersection is closest to (0,1/2), entering:

also draws the second point.