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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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As Ulises Cervantes Pimentel uncovered in this Wolfram Community thread, Plot and ParametricPlot/ParametricPlot3D for curves can take as MeshFunctions the values "ArcLength" and "CurveLength". This functionality provides straightforward solution for the plots with AspectRatio -> Automatic: mpoints = Table[t, {t, 0, 1, 0.04}]; ...



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