Technical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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This report contains the lecture notes for the first of four lectures which comprise the course entitled The extension of B-spline curve algorithms to surfaces given at SIGRAPH86. It is an elaboration and extension of the MRC report 2896 by de Boor and Hollig, in which the basic B-spline theory is developed from the reccurence relation rather than the original definition in terms of divided differences of the truncated power. This avoids what, to the people in CAGD, amounts to a detour through the theory of divided differences. Somewhat surprisingly. The resulting development is no longer than the standard one, and in some respects seems even more direct. It does bring to the fore the dual functionals and stresses the point that B-splines are best treated in terms of their linear span.
- Theoretical Mathematics