Differentiability of a 4-point Ternary Subdivision Scheme and its Applications
نویسندگان
چکیده
Hassan et al. proposed a 4-point ternary interpolatory scheme with smaller sizes of the templates for the local averaging rules and with higher order smoothness property compared to most of the existing binary ones. It can be C-continuous when the subdivision parameter is chosen in a certain range. In this paper, we further investigate its differentiable properties to extend its application in the generating of smooth curves and surfaces with different continuity. Some important results about this scheme such as the conditions of C, C-continuous, Hölder exponent and the derivatives of the limit function are obtained and applied. A modified 4-point ternary interpolatory scheme for end points is also proposed to ameliorate the modelling ability of this scheme.
منابع مشابه
A ternary 4-point approximating subdivision scheme
In the implementation of subdivision scheme, three of the most important issues are smoothness, size of support, and approximation order. Our objective is to introduce an improved ternary 4-point approximating subdivision scheme derived from cubic polynomial interpolation, which has smaller support and higher smoothness, comparing to binary 4-point and 6-point schemes, ternary 3-point and 4-poi...
متن کاملUnification and Application of 3-point Approximating Subdivision Schemes of Varying Arity
In this paper, we propose and analyze a subdivision scheme which unifies 3-point approximating subdivision schemes of any arity in its compact form and has less support, computational cost and error bounds. The usefulness of the scheme is illustrated by considering different examples along with its comparison with the established subdivision schemes. Moreover, B-splines of degree 4and well know...
متن کاملAn interpolating 4-point C2 ternary non-stationary subdivision scheme with tension control
In this paper we present a non-stationary 4-point ternary interpolatory subdivision scheme which provides the user with a tension parameter that, when increased within its range of definition, can generate C2-continuous limit curves showing considerable variations of shape. As a generalization we additionally propose a locally-controlled C2-continuous subdivision scheme, which allows a differen...
متن کاملSymmetric Ternary Interpolating C Subdivision Scheme
A ternary 4-point interpolating subdivision scheme is proposed that generates the limiting curve of C1 continuity. Performance of the proposed subdivision scheme is improved using a tension parameter. The improved subdivision scheme generates a family of C1 limiting curves for certain range of tension parameter. Laurent polynomial method is used to investigate the derivative continuity of the s...
متن کاملA Controllable Ternary Interpolatory Subdivision Scheme
A non-uniform 3-point ternary interpolatory subdivision scheme with variable subdivision weights is introduced. Its support is computed. The C and C convergence analysis are presented. To elevate its controllability, a modified edition is proposed. For every initial control point on the initial control polygon a shape weight is introduced. These weights can be used to control the shape of the c...
متن کامل