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

# Patch

## See also

Gauss Map, Injective Patch, Map Trace, Monge Patch, Regular Patch## Explore with Wolfram|Alpha

## References

Gray, A. "Patches in " and "Patches in ." §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.

## Referenced on Wolfram|Alpha

Patch## Cite this as:

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