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Parametric Representations of Four Surfaces

​
surface
sphere
ellipsoid
double lobe
hyperboloid
box
a
3
b
1
c
3
U
2π
V
π
2
xacos(u)cos(v), yacos(u)sin(v), zasin(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.
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