An interpolating 6-point \(C^2\) non-stationary subdivision scheme
An interpolating 6-point \(C^2\) non-stationary scheme for generating smooth curves and surfaces from discrete sets of control points is investigated. The considered interpolating scheme is a particular member of a family of approximating subdivision schemes that generate piecewise exponential polynomials and can be converted into interpolating schemes. The presented scheme is able to reproduce important trigonometric and transcendental curves, in particular circle, ellipse and cardioid. The outstanding properties of the considered scheme are demonstrated and a wide comparison with some known interpolating schemes is presented. Many examples of smooth curves generated by different interpolating schemes are shown, too. The conclusion from this paper can be used in computer graphics and geometric modelling of both, curves and surfaces, therefore the schemes for generating curves can be considered as the basic tools for the design of schemes for generating surfaces.
scientific article; zbMATH DE number 5570565