C-curves: an extension of cubic curves
Computer Aided Geometric Design
A subdivision scheme for surfaces of revolution
Computer Aided Geometric Design
A 4-point interpolatory subdivision scheme for curve design
Computer Aided Geometric Design
An interpolating 4-point C2 ternary non-stationary subdivision scheme with tension control
Computer Aided Geometric Design
Journal of Computational and Applied Mathematics
An interpolating 6-point C2 non-stationary subdivision scheme
Journal of Computational and Applied Mathematics
An approximating C2 non-stationary subdivision scheme
Computer Aided Geometric Design
Non-stationary subdivision schemes for surface interpolation based on exponential polynomials
Applied Numerical Mathematics
A circle-preserving C2 Hermite interpolatory subdivision scheme with tension control
Computer Aided Geometric Design
A generalized curve subdivision scheme of arbitrary order with a tension parameter
Computer Aided Geometric Design
Polynomial-based non-uniform interpolatory subdivision with features control
Journal of Computational and Applied Mathematics
Advances in Computational Mathematics
Algebraic conditions on non-stationary subdivision symbols for exponential polynomial reproduction
Journal of Computational and Applied Mathematics
Exponential splines and minimal-support bases for curve representation
Computer Aided Geometric Design
Full length article: Bivariate interpolation based on univariate subdivision schemes
Journal of Approximation Theory
Curvature of approximating curve subdivision schemes
Proceedings of the 7th international conference on Curves and Surfaces
Non-uniform non-tensor product local interpolatory subdivision surfaces
Computer Aided Geometric Design
Generalization of the incenter subdivision scheme
Graphical Models
Advances in Computational Mathematics
Original article: Uniform tension algebraic trigonometric spline wavelets of class C2 and order four
Mathematics and Computers in Simulation
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In this paper we propose a non-stationary C^1-continuous interpolating 4-point scheme which provides users with a single tension parameter that can be either arbitrarily increased, to tighten the limit curve towards the piecewise linear interpolant between the data points, or appropriately chosen in order to represent elements of the linear spaces spanned respectively by the functions {1,x,x^2,x^3}, {1,x,e^s^x,e^-^s^x} and {1,x,e^i^s^x,e^-^i^s^x}. As a consequence, for special values of the tension parameter, such a scheme will be capable of reproducing all conic sections exactly. Exploiting the reproduction property of the scheme, we derive an algorithm that automatically provides the initial tension parameter required to exactly reproduce a curve belonging to one of the previously mentioned spaces, whenever the initial data are uniformly sampled on it. The performance of the scheme is illustrated by a number of examples that show the wide variety of effects we can achieve in correspondence of different tension values.