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Patch


A patch (also called a local surface) is a differentiable mapping x:U->R^n, where U is an open subset of R^2. More generally, if A is any subset of R^2, then a map x:A->R^n is a patch provided that x can be extended to a differentiable map from U into R^n, where U is an open set containing A. Here, x(U) (or more generally, x(A)) is called the map trace of x.


See also

Gauss Map, Injective Patch, Map Trace, Monge Patch, Regular Patch

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References

Gray, A. "Patches in R^n" and "Patches in R^3." §12.1 and 12.2 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 269-278, 1997.

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Patch

Cite this as:

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

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