Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
441648 | Computer Aided Geometric Design | 2009 | 12 Pages |
Abstract
Our main result is that two point interpolatory subdivision schemes using Ck nonlinear averaging rules on pairs of real numbers generate real-valued functions that are also Ck. The significance of this result is the following consequence: Suppose that S is a subdivision algorithm operating on sequences of real numbers using linear binary averaging that generates Cm real-valued functions and is the same subdivision procedure where linear binary averaging is replaced everywhere in the algorithm by a Cn nonlinear binary averaging rule on pairs of real numbers; then the functions generated by the nonlinear subdivision scheme are Ck, where k=min(m,n).
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Graphics and Computer-Aided Design