Abstract
A family of smooth rational spline fractal interpolation function (SRFIF) is presented with the help of classical rational cubic spline. Each SRFIF of the family is identified uniquely by the values of vertical scaling factor and shape parameters
and
, and the shape of the fractal interpolating curves can be constrained and modified by selecting suitable parameters and vertical scaling factor. In order to meet the needs of practical design, a new method is developed to visualize constrained data in the view of constrained curves. In the special case, the methods of linear constraint and quadratic constraint are discussed. Also, convergence analysis shows that SRFIF gives a good approximation to the original function.
Acknowledgements
The authors are thankful to the anonymous referees for their helpful and valuable comments and suggestions in the development of the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.