Weight control and knot placement for rational B-spline curve interpolation

We consider an interpolation problem with nonuniform rational B-spline curv es given ordered data points. The existing approaches assume that weight fo r each point is available. But, it is not the case in practical application s. Schneider suggested a method which interpolates data points by automatic ally determining the weight of each control point. However, a drawback of S chneider's approach is that there is no guarantee of avoiding undesired pol es: avoiding negative weights. Based on a quadratic programming technique, we use the weights of the control points for interpolating additional data. The weights are restricted to appropriate intervals; this guarantees the r egularity of the interpolating curve. In addition, a knot placement is prop osed for pleasing interpolation. In comparison with integral B-spline inter polation, the proposed scheme leads to B-spline curves with fewer control p oints.