Curve subdivision schemes for geometric modelling

Abstract

A new binary four-point approximating subdivision scheme has been presented that generates the limiting curve of C ¹ continuity. A global tension parameter has been introduced to improve the performance of the binary four-point approximating subdivision scheme that generates a family of C ¹ limiting curves. The ternary four-point approximating subdivision scheme has also been introduced that generates a limiting curve of C ² continuity. The proposed schemes are close to being interpolating. The Laurent polynomial method has been used to investigate the order of derivative continuity of the schemes and Hölder exponents of the schemes have also been calculated. Performances of the subdivision schemes have been exposed by considering several examples.

Keywords:

• binary
• ternary
• approximating subdivision scheme
• convergence and smoothness
• mask
• Laurent polynomial

2000 AMS Subject Classifications :

• 41A05
• 41A25
• 41A30
• 65D17
• 65D10

Acknowledgements

The authors are thankful to Nadeem Ahmad for his kind co-operation and valuable suggestions.