Create Presentation
Download Presentation

Download Presentation

Exponential Quasi-interpolatory Subdivision Scheme

Download Presentation
## Exponential Quasi-interpolatory Subdivision Scheme

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Exponential Quasi-interpolatory Subdivision Scheme**Yeon Ju Lee and Jungho Yoon Department of Mathematics, Ewha W. University Seoul, Korea**Contents**• Subdivision scheme – several type of s.s. • Quasi-interpolatory subdivision scheme • Construction • Smoothness & accuracy • Example • Exponential quasi-interpolatory subdivision scheme • Construction • Smoothness • Example**Subdivision scheme**• Useful method to construct smooth curves and surfaces in CAGD • The rule :**Subdivision scheme**• Rule : • Interpolatory s.s. & Non-interpolatory s.s • Stationary s.s. & Non-stationary s.s**B-spline subdivision scheme**• It has maximal smoothness Cm-1 with minimal support. • It has approximation order only 2 for all m. • Cubic-spline :**Interpolatory subdivision scheme**• 4-point interpolatory s.s. : • The Smoothness is C1 in some range ofw. • The Approximation order is 4 with w=1/16.**Goal**We want to construct a new scheme which has good smoothness and approximation order.**Quasi-interpolatory subdivision scheme**• Construction**Quasi-interpolatory subdivision scheme**• Advantage • L : odd (L+1,L+2)-scheme. So in even pts case, it has tension. • L : even (L+2,L+2)-scheme. It has tension in both case. • This scheme has good smoothness. • It has approximation order L+1.**Quasi-interpolatory subdivision scheme**• The mask set of cubic case In cubic case, the mask can reproduce polynomials up to degree 3. odd case : use 4-pts even case : use 5-pts with tension v**Quasi-interpolatory subdivision scheme**• Various basic limit function which start with d**Quasi-interpolatory subdivision scheme**• Comparison of schemes which use cubic**Comparison with some example**• Example < cubic-spline > < Sa > E=0.8169 E=0.1428**Quasi-interpolatory subdivision scheme**• General case**Exponential quasi-interpolatory s.s.**• Construction**Exponential quasi-interpolatory s.s.**• Example E=7.7716e-016 E=0.1434