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

1. Clipping is piecewise linear.

2. 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.

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

1. Clamping is piecewise linear.

2. 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.

It will depend on the context.

• I recall the term "clamping" being used.

• 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.

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

1. Clipping is piecewise linear.

2. 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.