Degree raising for splines
The authors study the problem of converting an mth order B-spline expansion into an equivalent \((m+1)th\) order B-spline expansion. Let a spline \(s=\sum^{n}_{i=1}c_ iN^ m_ i\) be given, where \(\{N^ m_ i\}^ n_ 1\) are normalized B-splines of order m associated with a knot sequence \(\tau_ 1,...,\tau_ k\) of multiplicities \(m_ 1,...,m_ k\). It is shown that s can be represented in the form \(s=\sum^{\tilde n}_{j=1}\tilde c_ j\tilde N_ j^{m+1}\), where \(\{\tilde N_ j^{m+1}\}_ 1^{\tilde n}\) are normalized B-splines of order \(m+1\) associated with the knot sequence \(\tau_ 1,...,\tau_ k\) of multiplicities \(m_ 1+1,...,m_ k+1\). Moreover, formulae for computing the coefficients \(\tilde c_ 1,...,\tilde c_{\tilde n}\) are derived. By using discrete B-splines a recursion relation is established which plays an important role in computing these coefficients. It is pointed out that these results can be used in computer-aided design to obtain flexibility in manipulating the shape of a given spline curve by degree raising.
scientific article; zbMATH DE number 4006894