C-B样条基是B基

C-B-spline basis is B-basis

证明了空间Γn+1=span{1,t,…,tn-2,sint,cost}n≥2中的定义域两端是n重节点的非均匀C-B样条基是B基,是适合CAGD多种需要的具有良好性质的基.B基具有deCasteljau类型算法,同时也提供求值和细分.这表明非均匀C-B样条基可作为CAGD新的造型工具.

The non-uniform C-B-spline basis of order n+1 whose multiplicity of endpoint is n in the space Γ_(n+1)=span {1, t, ..., t^(n-2), sin t, cos t} n≥2 which is totally positive is presented. Furthermore, that it is a B-basis is proved. B-basis is the only basis furnishing a de Casteljau-type algorithm, called B-algorithm, that provides evaluation and subdivision simultaneously. Therefore non-uniform C-B-spline has many good properties. As special cases of C-B-spline basis, uniform C-B-spline basis is also a B-basis and presents good properties.