Nearly arc-length parameterized quintic-spline interpolation for precision machining

The paper presents a method of interpolating a set of discrete data points to form a composite quintic spline for application in precision machining. Precision machining requires tight machining tolerance, i.e. the preselected data points on the original curve are approximately evenly distributed according to a small total curvature between two consecutive data points. With this restriction, the resultant composite quintic splines, in comparison with cubic splines, are closer to being arc-length parameterized. The quintic splines are also likely to have shapes that are close to those of the original curves with no unwanted high-order oscillations. Curves with these properties should be useful for reverse engineering and online motion-command generation for precision machining.