TOPICS
Search

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

Explore with Wolfram|Alpha

Cite this as:

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

Subject classifications