# The parametric equation of an object in space: parameq

### 14.12.6 The parametric equation of an object in space: parameq

See Section 13.13.8 for parametric equations in two-dimensional geometry.

The parameq command finds parameterizations for geometric objects.

- parameq takes one argument:
  G, a geometric object.
- parameq(G) returns a parameterization for the object G.
  For a curve, the parameter is t, for a surface, the parameters are u and v. These variables must be unassigned. If they have assignments, they can be unassigned with purge(t) and purge(u,v).

#### Examples.

- Input:
  parameq(line(point(0,1,0),point(1,2,3)))
  Output:

  ⎡ ⎣ | t,t+1,3 t | ⎤ ⎦

- Input:
  parameq(sphere(point(0,1,0),2))
  Output:

  ⎡ ⎣ | 2 cosu· cosv,1+2 cosu· sinv,2 sinu | ⎤ ⎦

- Input:
  normal(parameq(ellipse(point(-1,1,1),point(1,1,1),point(0,1,2))))
  Output:

  ⎡
  ⎢
  ⎣

  √

  2

  cost,1,sint+1

  ⎤
  ⎥
  ⎦