14.14.5  Homothety in space: homothety

See Section 13.15.5 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.

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