A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
A subdivision algorithm for trigonometric spline curves
Computer Aided Geometric Design
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Computer Aided Geometric Design
A non-stationary uniform tension controlled interpolating 4-point scheme reproducing conics
Computer Aided Geometric Design
An interpolating 4-point C2 ternary non-stationary subdivision scheme with tension control
Computer Aided Geometric Design
Journal of Computational and Applied Mathematics
A new class of non-stationary interpolatory subdivision schemes based on exponential polynomials
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
A subdivision scheme for surfaces of revolution
Computer Aided Geometric Design
A 4-point interpolatory subdivision scheme for curve design
Computer Aided Geometric Design
Advances in Computational Mathematics
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This paper is concerned with non-stationary interpolatory subdivision schemes that can reproduce a large class of (complex) exponential polynomials. It enables our scheme to exactly reproduce the parametric surfaces such as torus and spheres. The subdivision rules are obtained by using the reproducing property of exponential polynomials which constitute a shift-invariant space S. In this study, we are particularly interested in the schemes based on the known butterfly-shaped stencils, proving that these schemes have the same smoothness and approximation order as the classical Butterfly interpolatory scheme.