Abstract
The conventional B-splines possess the de Boor–Cox formula, which relates to a pyramid algorithm. However, for multi-degree splines, a de Boor–Cox-type evaluation algorithm only exists in some special cases. This paper considers any multi-degree spline with arbitrary degree and continuity, and provides two generalized de Boor–Cox-type relations. One uses several lower degree polynomials to build a combination to evaluate basis functions, whose form is similar to using the de Boor–Cox formula several times. The other is a linear combination of two functions out of the recursive definition, which keeps the combination coefficient polynomials of degree 1, so it is more similar to the de Boor–Cox formula and can be illustrated by several pyramids with different heights. In the process of calculating the recursions, a recursive representation using the Bernstein basis is used and numerically analyzed.
Funder
the National Natural Science Foundation of China
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Cited by
3 articles.
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