### 27.10.6 Parametric equation of an object in space

See Section 26.12.8 for parametric equations in 2D geometry.

The parameq command finds parameterizations for geometric objects.

- parameq takes 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

parameq(line(point(0,1,0),point(1,2,3)))

| ⎡ ⎣ | t,t+1,3 t | ⎤ ⎦

parameq(sphere(point(0,1,0),2))

| ⎡ ⎣ | 2 cos u cos v,1+2 cos u sin v,2 sin u | ⎤ ⎦

normal(parameq(ellipse(point(-1,1,1),point(1,1,1),point(0,1,2))))

⎡
⎢
⎣

√

2

cos t,1,sin t+1

⎤
⎥
⎦