Let C be the curve constructed using the 4-point scheme on an initial control point set S. We
prove that, in general, C is not invariant under any refinement of S except the refinement by …

… schemes applied on sequences of finite length. Thanks to the flexible properties of subdivision
schemes… An illustration in the case of the 4-point shifted Lagrange subdivision scheme, for …

… determine when a solution is refinable. This result is used to investigate refinable components
of multiple refinable functions. Finally, we investigate fully refinable functions for which all …

… 4 and Fig. 5 we demonstrate a planar curve and a 3D curve by using the 4-point ternary
interpolatory subdivision scheme from … The refinability of the four point scheme, Computer Aided …

… However, we can modify φ1 as in the above section such that the resulting refinable
function vector will yields an interpolatory scheme. Observe that φ1(0) = 1,φ1(1) = φ1(−1) = 1 …

… The convexity preserving properties of the interpolating four-point ternary subdivision
scheme are discussed in this paper. The conditions on the parameter of the scheme to preserve …

… schemes provide a large class of refinable functions which generate multiresolution analysis.
Thus, the refinable functions obtained by the new schemes … , shapes of refinable functions …

… 4-point scheme. In the remainder of this paper, we first present the unifying combined ternary
4-point scheme and … ternary schemes, but also the combined ternary 4-point C 2 scheme …

… point of view, the corresponding weights could be computed by solving a linear system. The
choice of the basis in the space where exactness is required determinates the linear system …

… class, is associated to subdivision schemes with an even-symmetric mask that … 4-refinable
functions that are generated by parameter-dependent, even-symmetric quaternary schemes …