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Before posting the solution I found, let me reformulate the problem and give more details about what I am trying to acheive. A Robotic arm grabs a turbine blade. All the robot positional data is available and the blade geometry as well. I need to find the exact position of the blade relative to the grabber, using positional information provided as a point ...


The default method is Hermite: data = {{-2, 0}, {-1, -1}, {1, 1}, {2, 0}}; Interpolation[data]["InterpolationMethod"]; (* "Hermite" *) With spline interpolation the second derivative is piecewise linear, and is not necessarily zero at the endpoints: Plot[Interpolation[data, Method -> "Spline"]''[x], {x, -3, 3}]

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