Homothety in space

### 27.12.5 Homothety in space

See Section 26.14.5 for homotheties in the plane.

A homothety is a dilation about a given point. The homothety command creates a homothety.

- homothety takes two mandatory arguments and one optional argument:
  - P, a point (the center of the homothety).
  - r, a number (the scaling ratio).
  - Optionally, G, a geometric object.
- homothety(P,r) returns a new command which dilates about P by a factor of r. If r is complex, this will rotate as well as scale.
- homothety(P,r,G) returns and draws the dilation of G about P by a factor or r.

#### Examples

h:=homothety(point(0,0,0),2); S:=sphere([0,0,0],0.5); color(S,blue),h(S)

homothety(point(0,0,0), 2, S)