13.6.7  Finding the points of intersection of two geometric objects in the plane: inter

See Section 14.4.4 for points of intersection of objects in space.

The inter command finds the intersection of two geometric objects in the plane.

• inter takes two mandatory arguments and one optional argument.
  • obj₁, obj₂, two geometric objects.
  • Optionally, P, a point.
  inter(obj₁,obj₂ ⟨ P⟩) returns a list of points of intersection of obj₁ and obj₂.
  With the argument P, the command returns the point of intersection closest to P.

Examples.

• Input:
  inter(circle(0,1),line(1,i))
  Output:
  
  which are the points at (1,0) and (0,1). To get just one of the points, use the usual list indices.
  Input:
  inter(circle(0,1),line(1,i))[0]
  Output:
  
  just one of the points. To get the point closest to (0,1/2):
  Input:
  inter(circle(0,1),line(1,i),i/2)
  Output: