The 25-inch liquid hydrogen bubble chamber by F Barrera; University of California, Berkeley. Lawrence
By F Barrera; University of California, Berkeley. Lawrence Radiation Laboratory.; et al
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The Collocation Matrix - and its Null Space The collocation matrix maps between the Oe-Boor points and curve points that serve as Interpolation/Approximation points. e. :Nj,k(si)dj j=O Since there are n basis function and n parameter values one can organize the above equation in an n x n matrix M, where M iJ = Nj,k(si) and another two n x d matrices that contains the de-Boor points d = do, .. , dn - I and the interpolation points P = Po, ... ,Pn - I . The interpolation problem can be written as Mxd=P R.
In order to keep the notations simple, let F(XI, X2, b) be a function such that F(XI(t,b),X2(t,b),b) = G(c(t)) = 0, (6) see (2), (4) and (5). Similarly, F; = oFjox; and F;j = &Fjox;oxj for i,j E {1,2}. (7) The proof of the following lemma follows from the implicit function theorem. 44 P. Chalmoviansky and B. Jüttler Lemma 1. The derivatives of the abscissa y = y(t, b) with respect to the parameter t and with respect to the coefficients in b = (bi)lil=n,iEZ~ can be computed by differentiating (6).
Numerical Aigorithms 5, 229- 245 (1993). : Dyadic splines. D. Thesis, Department of Computer Science, University of California at Davis, 1996. , Gregory, J. : A butterfly subdivision scheme for surface interpolation with tension contro!. ACM Transactions on Graphics 9, 160-169 (1990). [6] Finkelstein, A. , Salesin, D. : Multiresolution curves. Proceedings of ACM Siggraph, pp. 261268, 1994. : Progressive geometry compression. Proceedings of ACM Siggraph, pp. 271-278, 2000. [8] Kobbelt, L. , Vorsatz, J.