Complex Eigenvalues for Binary Subdivision Schemes

Details Complex Eigenvalues for Binary Subdivision Schemes Complex Eigenvalues for Binary Subdivision Schemes

2008-01-21

arxiv.org/abs/0801.3249v1

Computer Science

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7 pages, 2 figures

Scientific paper

Convergence properties of binary stationary subdivision schemes for curves have been analyzed using the techniques of z-transforms and eigenanalysis. Eigenanalysis provides a way to determine derivative continuity at specific points based on the eigenvalues of a finite matrix. None of the well-known subdivision schemes for curves have complex eigenvalues. We prove when a convergent scheme with palindromic mask can have complex eigenvalues and that a lower limit for the size of the mask exists in this case. We find a scheme with complex eigenvalues achieving this lower bound. Furthermore we investigate this scheme numerically and explain from a geometric viewpoint why such a scheme has not yet been used in computer-aided geometric design.

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