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Interpolation is a term borrowed from the mathematics field of numerical analysis. Typically the machine tools that are numerically controlled by computer in CNC applications are capable of moving only in discrete, albeit small steps, rather than continuous motion. However, we want many machined objects to have curved surfaces. To make this possible, curved surfaces are approximated using numerous short steps. Interpolation is the mathematical process of calculating approximate points between fixed points on the desired machined surface. Once these are determined the CNC machine is set to work making its cuts between the fixed points and the interpolated points essentially. Various interpolating functions can be used, the simplest being line segments. More sophisticated machinery is capable of circular interpolation.

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