A family of ternary subdivision schemes for curves

A family of ternary 3-point subdivision schemes is introduced and has a degree of smoothness C1 continuity. A family of ternary 4-point subdivision schemes is derived and has degrees of smoothness C1 and C2 continuities. Also a ternary 4-point approximating subdivision scheme is proposed that generates the limiting curve of C3 continuity. The eigenvalue analysis and generating function formalism are used to analyze the continuity properties of these subdivision schemes. Also these subdivision schemes are compared with the established subdivision schemes.