Abstract
We present a new class of non-stationary, interpolatory subdivision schemes that can exactly reconstruct parametric surfaces including exponential polynomials. The subdivision rules in our scheme are interpolatory and are obtained using the property of reproducing exponential polynomials which constitute a shift-invariant space. It enables our scheme to exactly reproduce rotational features in surfaces which have trigonometric polynomials in their parametric equations. And the mask of our scheme converges to that of the polynomial-based scheme, so that the analytical smoothness of our scheme can be inferred from the smoothness of the polynomial based scheme.
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Choi, YJ., Lee, YJ., Yoon, J., Lee, BG., Kim, Y.J. (2006). A New Class of Non-stationary Interpolatory Subdivision Schemes Based on Exponential Polynomials. In: Kim, MS., Shimada, K. (eds) Geometric Modeling and Processing - GMP 2006. GMP 2006. Lecture Notes in Computer Science, vol 4077. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11802914_41
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DOI: https://doi.org/10.1007/11802914_41
Publisher Name: Springer, Berlin, Heidelberg
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