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# Interpolation Method Comparison

You can select from three interpolation methods when you provide a data set to define force, torque, or motor profiles: Akima Spline, Cubic Spline, or Linear. The interpolation method you select is used to define the profile function between data points.

## Akima Spline

The Akima spline interpolation method performs a local fit. This method requires information about points in the vicinity of the interpolation interval in order to define the coefficients of the cubic polynomial. Consequently, each data point in an Akima spline affects only the nearby portion of the curve. Because it uses local methods, an Akima interpolation is calculated very quickly.

The Akima method produces good results for the value of the approximated function. This method also returns good estimates for the first derivative of the approximated function when the data points are evenly spaced. In instances where the data points are unevenly spaced, the estimate of the first derivative may be in error. The second derivative of the approximated function is unreliable with this method.

## Cubic Spline

The cubic spline interpolation method performs a global fit. Global methods use all the given points to calculate the coefficients for all interpolation intervals simultaneously. Therefore, each data point affects the entire cubic spline. If you move one point the whole curve changes accordingly, making a cubic spline rougher and harder to force into a desired shape. This is especially noticeable for functions with linear portions, or that have sharp changes in the curve. In these cases, a cubic spline is almost always rougher than an Akima spline.

## Linear

The linear interpolation method performs a local fit by defining a piecewise continuous linear function between adjacent data points.

## General Considerations

Both global and local methods work well on smoothly-curving functions.

The cubic spline interpolation method, though not as fast as Akima spline interpolation, produces good results for the value of the approximated function, as well as its first and second derivatives. The data points do not have to be evenly spaced. The solution process often requires estimates of derivatives of the functions being defined. The smoother a derivative is, the easier it is for the solution process to converge.

The linear interpolation method converges faster than the other two methods. The resulting function is a piecewise continuous linear function that has a discontinuous derivative at the data points you provide. The second derivative is zero, except at the provided data points, where it is infinite.

Smooth (continuous) second derivatives are important if you use the spline to define motion. The second derivative is the acceleration associated with the motion, which defines the reaction force required to drive the motion. A discontinuity in the second derivative implies a discontinuity in the acceleration and in the reaction force. This can cause poor performance or even failure to converge at the point of discontinuity.
To prevent motion solver failure, it is recommended that you define motor profiles only from Akima spline or cubic spline interpolated profiles.

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