Geometric Algorithm for Curve Interpolation with Non Uniform B-splines

The interpolation of a sequence of points is an important task in Engineering. In this work, three different interpolation methods are studied and expanded. The first method is the conventional interpolation Spline. The second method is a subdivision based geometric algorithm. The third method interpolates a given set of points with additional point normal constraints. The last two methods were implemented with uniform B-Splines curves. In this work, both methods are expanded to use non uniform B-Spline curves. Three critical curves are used to test the developed methods: circle involute, bowditch and epitrochoid. The results show that the non uniform B-Spline implementations have better quality with smaller errors, once the value of the distance error of the curve is in the order of 10−15 % of the bound box diagonal of the initial input data points and the normal error is around 10−4 rad in the worst case. Keywords— Non Uniform B-Spline, Interpolation, Curves, Geometric Algorithm, Point Normal Constraint.