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rational b-splines

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rational b-splines

Many years ago I was involved with representing 3-d surfaces using rational b-splines. One particular question was setting up algorithms for finding the intersection of a line in space with a surface patch. The representations used were either biquadratic or bicubic. The problems could then be reduced to finding real roots of polynomials. For biquadratic, the polynomial was eighth degree, while for bicubic it was eighteenth degree. There appears to be a pattern - the polynomial is 2n^2 degree for a patch represented as bi-n. Has this ever been proved for general n?


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