# Inversion in space: inversion

### 14.14.7 Inversion in space: inversion

See Section 13.15.7 for inversions in the plane.

Given a point P and a real number k, the corresponding inversion of a point A is the point A′ on the ray PA satisfying PA·PA′ = k2. The inversion command creates inversions.

- inversion takes two mandatory and one optional argument:
  - P, a point.
  - k, the inversion ratio.
  - Optionally, G, a geometric object.
- inversion(P,k) returns a new command which does an inversion about P with a ratio k.
- inversion(P,k,G) returns and draws the inversion of G.

#### Examples.

- Input:

  S := sphere([0,1,0],0.5)
  inver:= inversion(point(0,0,0), 2)
  color(S,blue),inver(S)

  Output:
- Input:
  inversion(point(0,0,0),2,S)
  Output: