If I remenbered correctly, Origin firstly call internally a nag function to get the cubic spine approximation. The dSmoothness is to control the closeness between the data and the fit.After the spline is obtained, then it will get the derivatives. As how to choose the dSmoothness, you can take a look at http://www.nag.com/numeric/CL/manual/pdf/E02/e02bec.pdf Hope it will help.