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

See section 11.13.8 for parametric equations in two-dimensional geometry.

The parameq command takes as argument a geometric object.

equation returns a parameterization for the object. 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,u,v).

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*cos(u)*cos(v),2*cos(u)*sin(v)+1,2*sin(u)]

Input:

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

Output:

[sqrt(2)*cos(t),1,sin(t)+1]