Choosing nodes and knots in closed B-spline curve interpolation to point data

Abstract

Node and knot placement for closed B-spline curve interpolation to point data heavily depends on whether the degree of B-splines is odd or not. For odd degree B-splines, the natural method of setting knots to coincide with nodes (i.e. parameters) works very well and provides the good quality. However, when the degree is even, the usual methods including the natural method can have problems and result in the bad quality. This paper presents a method, called the shifting method, which works well for even degree B-spline interpolation. It has nearly the same properties as the natural method does for odd degree B-splines. It is simple and provides the good quality of a resultant curve.