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

  ⎤ ⎥ ⎦