In the representation of a skinned surface using $B$-Spline, I have $K+1$ given curves of degree $p$ on a common partition $U$ and I want to construct the surface $S(u,v)$ with these curves as isoparametric curves. Assuming that $p$ is the degree in $u$, and $q$ is the degree in $v$, why should I ask that the degree $q$ must be less than or equal to $K$? I found this condition in my book.
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Constructing a skinning surface through given curves is pretty much the same calculation as constructing a curve through given points, so all the same rules apply.
A curve (or a skinned surface) of degree $q$ needs at least $q+1$ interpolation values to fully specify it. So, in the case of a skinning surface, the number of curves ($K+1$) must be at least $q+1$. In other words, $K+1 \ge q+1$, so $q \le K$.
bubba
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By the way ... if you want more b-spline questions answered, please upvote or accept the answers you have already been given (or tell us what's wrong with them). – bubba Feb 25 '13 at 14:17