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).

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))))

⎡
⎢
⎣

√

cos t,1,sin t+1

⎤
⎥
⎦