## A $$C^2$$ four-point subdivision scheme with fourth order accuracy and its extensions.(English)Zbl 1080.65526

Dæhlen, Morten (ed.) et al., Mathematical methods for curves and surfaces: Tromsø 2004. Sixth international conference on mathematical methods for curves and surfaces, celebrating the 60th birthday of Tom Lyche, Tromsø, Norway, July 1–6, 2004. Brentwood, TN: Nashboro Press (ISBN 0-9728482-4-X/hbk). Modern Methods in Mathematics, 145-156 (2005).
Summary: We present a new four-point subdivision scheme that generates $$C^2$$ curves. It reproduces cubic polynomials, has a basic limit function with support $$[-4, 3]$$, and is close to being interpolatory. The refinement rule is based on local cubic interpolation, followed by evaluation at $$1/4$$ and $$3/4$$ of the refined interval. We investigate the approximation properties of this four-point scheme and extend it to a new family of $$2n$$-point schemes. The performance of the new schemes is demonstrated by several examples.
For the entire collection see [Zbl 1065.65003].

### MSC:

 65D18 Numerical aspects of computer graphics, image analysis, and computational geometry