Improved binary four point subdivision scheme and new corner cutting scheme

A binary 4-point approximating subdivision scheme, presented by Siddiqi and Ahmad (2006) [9], has been improved by introducing a global tension parameter. An improved form of the scheme generates a family of Cn, n D 1; 2; 3; 4 limiting curves for certain range of global tension parameter and a C5 limiting curve for a fixed value. Also a new corner cutting subdivision scheme has been proposed which generates a limiting curve of C1 continuity. The Laurent polynomial method has been used to investigate the order of the derivative continuity of both subdivision schemes. The performance of the subdivision schemes has been exposed by considering examples and compared with the existing schemes.