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Surface Parameterization


A surface in 3-space can be parameterized by two variables (or coordinates) u and v such that

x=x(u,v)
(1)
y=y(u,v)
(2)
z=z(u,v).
(3)

If a surface is parameterized as above, then the tangent vectors

 T_u=(partialx)/(partialu)x^^+(partialy)/(partialu)y^^+(partialz)/(partialu)z^^
(4)
 T_v=(partialx)/(partialv)x^^+(partialy)/(partialv)y^^+(partialz)/(partialv)z^^
(5)

are useful in computing the surface area and surface integral.


See also

Parameter, Parameterization, Smooth Surface, Surface Area, Surface Integral

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Cite this as:

Weisstein, Eric W. "Surface Parameterization." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SurfaceParameterization.html

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