Name of transformation that maps numbers outside of interval onto endpoints? I am looking for the term for a transformation that maps numbers outside of an interval onto the endpoints:
My interval is $[a,b]$. Any number $x < a$ will be transformed to $a$ and any number $y > b$ will be transformed to $b$. 
Is there a term for these kind of functions?
 A: It will depend on the context. 


*

*I recall the term "clamping" being used.    It appears in various disciplines including numerical optimization and computer graphics.

*In the computer graphics area this is needed to distinguish it from an important, ubiquitous, but different operation called "clipping" 

*Despite that, "clipping" is used in signal processing to denote your operation.

*There is a closely allied operation in statistics called "Winsorizing".  Winsorizing can be construed as beginning with a data-dependent clipping operation.

This graph of the "clipping" or "clamping" operation was created by plotting the function $x \to a \vee (b\wedge x)$ (where $\vee$ is the maximum and $\wedge$ is the minimum).  It visually demonstrates that


*

*Clamping is piecewise linear.

*It can be construed as a special form of linear "spline" connecting the points $(a,a)$ and $(b,b).$  (Applying affine transformations to either or both coordinate will transform it into a linear spline between any pair of distinct points.)  See https://stats.stackexchange.com/a/291598/919 for the theory and code.
