Abstract
The n-ary subdivision schemes contrast favorably with their binary analogues because they are capable to produce limit functions with the same (or higher) smoothness but smaller support. We present an algorithm to generate the 4-point n-ary non-stationary scheme for trigonometric, hyperbolic and polynomial case with the parameter for describing curves. The performance, analysis and comparison of the 4-point ternary scheme are also presented.
Highlights
Subdivision is a method for making smooth curves/surfaces, which first emerged an addition of splines to arbitrary topological control nets
If the mask ak is independent of k, namely if ak a, k, the subdivision scheme is called stationary otherwise it is called non-stationary
In computer graphics and geometric modeling, it is required to have schemes to construct circular parts or parts of conics. It seems that stationary schemes cannot generate conics and non-stationary schemes have such a capability to generate trigonometric polynomials, trigonometric splines and, in particular, circles, ellipses and so on. Such schemes are useful in computer graphics and geometric modeling
Summary
Subdivision is a method for making smooth curves/surfaces, which first emerged an addition of splines to arbitrary topological control nets. Jena et al [1] worked on 4-point binary non-stationary subdivision scheme for curve interpolation. Yoon [2] presented the analysis of binary non-stationary interpolating scheme based on exponential polynomials. Beccari et al [3] worked on 4-point binary non-stationary uniform tension controlled interpolating scheme reproducing conics. Daniel and Shunmugaraj [4] presented 4-point ternary non-stationary interpolating subdivision scheme. We present an algorithm to construct 4-point n-ary scheme. In the last section conclusion and visual performance of proposed schemes are presented
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