Types of Curves (3)

Parametric Curve

Parametrically defined curve in three/two dimensions is given by three/two univariate functions:

x = f(u)
y = g(u)
(   z = h(u)   )

where u varies between two explicit values (could be [0;1] or [- ; +])

Parametric surface

Parametrically defined surface in three dimensions is given by three bivariate functions:

x = f(u,v)
y = g(u,v)
z = h(u,v)

where u an v vary between two explicit values (could be [0;1] or [- ;+])

x = x0 + r cos q
y = y0 + r sin q

q [ 0 ; 2P ] 

x = u
y = v
z = - (Au + Bv + D) / C

x = x0 + (x1 - x0)t
y = y0 + (y1 - y0)t
z = z0 + (z1 - z0)t

t [- ;+]

x = x0 + r . cos u . cos v
y = y0 + r . sin u . cos v
z = z0 + r . sin v

u[ 0 ; 2P ] / v[ - P/2; P/2]