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A Convolution-Based Computational Technique for Subdivision Depth of Doo-Sabin Subdivision Surface

Author

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  • Faheem Khan
  • Bushra Shakoor
  • Ghulam Mustafa
  • Sidra Razaq
  • R. U. Gobithaasan

Abstract

Subdivision surface schemes are used to produce smooth shapes, which are applied for modelling in computer-aided geometric design. In this paper, a new and efficient numerical technique is presented to estimate the error bound and subdivision depth of the uniform Doo-Sabin subdivision scheme. In this technique, first, a result for computing bounds between Pk (a polygon at kth level) and P∞ (limit surface) of the Doo-Sabin scheme is obtained. After this, subdivision depth (the number of iterations) is computed by using the user-defined error tolerance. In addition, the results of the proposed technique are verified by taking distinct valence numbers of the Doo-Sabin surface scheme.

Suggested Citation

  • Faheem Khan & Bushra Shakoor & Ghulam Mustafa & Sidra Razaq & R. U. Gobithaasan, 2022. "A Convolution-Based Computational Technique for Subdivision Depth of Doo-Sabin Subdivision Surface," Journal of Mathematics, Hindawi, vol. 2022, pages 1-12, September.
    • Handle: RePEc:hin:jjmath:2510204
    DOI: 10.1155/2022/2510204
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