From the title I somehow expected Planck taper window which comes up in partition of unity. The property of this is that you won’t find any discontinuity in an

From the title I somehow expected Planck taper window which comes up in partition of unity. The property of this is that you won’t find any discontinuity in any degree of derivatives. Ie it is smooth in the mathematical sense. If you want to make changes from a constant function (such as not moving at all) to something else (start moving), then this smoothness is a nice property.