Parametric Representations of Four Surfaces

surface

sphere

ellipsoid

double lobe

hyperboloid

box

a

3

b

1

c

3

U

2π

V

π

2

xacos(u)cos(v), yacos(u)sin(v), zasin(u)

Parametric representation of surfaces is

x=x(u,v),y=y(u,v),z=z(u,v)

, where

u

and

v

take values from intervals

I

and

J

, respectively. In this example,

I=[0,U],J=[-π/2,V]

. This Demonstration is allowing us to see how surfaces look as the intervals

I

and

J

vary.