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International Conference on Mathematics and Computing

ICMC 2017: Mathematics and Computing pp 265–277Cite as

Constrained Data Visualization Using Rational Bi-cubic Fractal Functions

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 655))

Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600036, India

    S. K. Katiyar, K. M. Reddy & A. K. B. Chand

Authors
  1. S. K. Katiyar
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  2. K. M. Reddy
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  3. A. K. B. Chand
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Corresponding author

Correspondence to S. K. Katiyar .

Editor information

Editors and Affiliations

  1. Haldia Institute of Technology, Haldia, India

    Debasis Giri

  2. University of Central Florida, Orlando, Florida, USA

    Ram N. Mohapatra

  3. Freie Universität Berlin, Berlin, Germany

    Heinrich Begehr

  4. Fordham University, Bronx, New York, USA

    Mohammad S. Obaidat

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Katiyar, S.K., Reddy, K.M., Chand, A.K.B. (2017). Constrained Data Visualization Using Rational Bi-cubic Fractal Functions. In: Giri, D., Mohapatra, R., Begehr, H., Obaidat, M. (eds) Mathematics and Computing. ICMC 2017. Communications in Computer and Information Science, vol 655. Springer, Singapore. https://doi.org/10.1007/978-981-10-4642-1_23

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  • DOI: https://doi.org/10.1007/978-981-10-4642-1_23

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-4641-4

  • Online ISBN: 978-981-10-4642-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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