Piecewise property

A function property holds piecewise for a function, if the function can be piecewise-defined in a way that the property holds for every subdomain. Examples of functions with such piecewise properties are:

• Piecewise constant function, also known as a step function
• Piecewise linear function
• Piecewise continuous function
• Piecewise function or piecewise smooth function
• Piecewise differentiable function

The concept of piecewise-defined functions is often generalized:

• Piecewise linear curve
• Piecewise polynomial curve, also known as a spline (mathematics)
• Piecewise linear manifold

 

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