Inversion in the plane: inversion

### 12.15.7 Inversion in the plane: inversion

See section 13.14.7 for inversions in space.

Given a circle C with center O and radius r, the inversion of a point A with respect to C is the point A′ on the ray OA satisfying OA·OA′ = r2.

The inversion command takes two or three arguments.

If inversion has two arguments, they are a point (the center of inversion) and a real number (the radius). inversion returns a new command which performs the inversion.
Input:

inver := inversion(i, 2)

then:

inver(circle(1+i,1))

Output:

then:

inver(circle(1+i,1/2))

Output:

If inversion has three arguments, the first two arguments are a point and number as above, and the third argument is a geometric object. inversion returns and draws the inverted object.
Input:

inversion(i, 2, circle(1+i,1))

Output:

Input:

inversion(i, 2, circle(1+i,1/2))

Output: