Constrained Data Visualization Using Rational Bi-cubic Fractal Functions

  • S. K. KatiyarEmail author
  • K. M. Reddy
  • A. K. B. Chand
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 655)


This paper addresses a method to obtain rational cubic fractal functions, which generate surfaces that lie above a plane via blending functions. In particular, the constrained bivariate interpolation discussed herein includes a method to construct fractal interpolation surfaces that preserve positivity inherent in a prescribed data set. The scaling factors and shape parameters involved in fractal boundary curves are constrained suitably such that these fractal boundary curves are above the plane whenever the given interpolation data along the grid lines are above the plane. Our rational cubic spline FIS is above the plane whenever the corresponding fractal boundary curves are above the plane. We illustrate our interpolation scheme with some numerical examples.


Iterated function system Fractal interpolation functions Bicubic partially blended fractal surface Convergence Constrained interpolation Positivity 


28A80 26C15 41A20 65D10 41A29 65D05 


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Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  • S. K. Katiyar
    • 1
    Email author
  • K. M. Reddy
    • 1
  • A. K. B. Chand
    • 1
  1. 1.Department of MathematicsIndian Institute of Technology MadrasChennaiIndia

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