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Parametric surface
A
parametric surface
is a
surface
in the
Euclidean space
R
3
which is defined by a
parametric equation
with two parameters Parametric representation is a very general way to specify a surface, although
implicit equations
are even more general. Surfaces that occur in two of the main theorems of
vector calculus
,
Stokes' theorem
and the
divergence theorem
, are frequently given in a parametric form. The curvature and
arc length
of
curves
on the surface,
surface area
, differential geometric invariants such as the
first
and
second
fundamental forms,
Gaussian
,
mean
, and
principal
curvatures can all be computed from a given parametrization.
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