We present generalized and unified families of (2n)-point and (2n − 1)-point p-ary interpolating subdivision schemes originated from Lagrange polynomialfor any integers n ≥ 2 and p ≥ 3. Almost all existing even-poin...We present generalized and unified families of (2n)-point and (2n − 1)-point p-ary interpolating subdivision schemes originated from Lagrange polynomialfor any integers n ≥ 2 and p ≥ 3. Almost all existing even-point and odd-pointinterpolating schemes of lower and higher arity belong to this family of schemes. Wealso present tensor product version of generalized and unified families of schemes.Moreover error bounds between limit curves and control polygons of schemes arealso calculated. It has been observed that error bounds decrease when complexityof the scheme decrease and vice versa. Furthermore, error bounds decrease withthe increase of arity of the schemes. We also observe that in general the continuityof interpolating scheme do not increase by increasing complexity and arity of thescheme.展开更多
基金The first author was supported by Pakistan Program for Collaborative Research-foreign visit of local faculty member,Higher Education Commission(HEC)PakistanThe second author was supported by Indigenous Ph.D.Scholarship Scheme of HEC PakistanThe third author was supported by NSF of China(No.61073108)
文摘We present generalized and unified families of (2n)-point and (2n − 1)-point p-ary interpolating subdivision schemes originated from Lagrange polynomialfor any integers n ≥ 2 and p ≥ 3. Almost all existing even-point and odd-pointinterpolating schemes of lower and higher arity belong to this family of schemes. Wealso present tensor product version of generalized and unified families of schemes.Moreover error bounds between limit curves and control polygons of schemes arealso calculated. It has been observed that error bounds decrease when complexityof the scheme decrease and vice versa. Furthermore, error bounds decrease withthe increase of arity of the schemes. We also observe that in general the continuityof interpolating scheme do not increase by increasing complexity and arity of thescheme.
