Trace (Map)

Let a Patch be given by the map ${\bf x}:U\to\Bbb{R}^n$, where $U$ is an open subset of $\Bbb{R}^2$, or more generally by ${\bf x}: A\to \Bbb{R}^n$, where $A$ is any Subset of $\Bbb{R}^2$. Then ${\bf x}(U)$ (or more generally, ${\bf x}(A)$) is called the trace of x.

See also Patch

References

Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 183-184, 1993.