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Bivariate non-uniform subdivision schemes based on L-systems

Author

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  • Gérot, Cédric
  • Ivrissimtzis, Ioannis

Abstract

L–systems have been used to describe non-uniform, univariate, subdivision schemes, which offer more flexible refinement processes than the uniform schemes, while at the same time are easier to analyse than the geometry driven non-uniform schemes. In this paper, we extend L–system based non-uniform subdivision to the bivariate setting. We study the properties that an L–system should have to be the suitable descriptor of a subdivision refinement process. We derive subdivision masks to construct the regular parts of the subdivision surface as cubic B-spline patches. Finally, we describe stencils for the extraordinary vertices, which after a few steps become stationary, so that the scheme can be studied through simple eigenanalysis. The proposed method is illustrated through two new subdivision schemes, a Binary-Ternary, and a Fibonacci scheme with average refinement rate below two.

Suggested Citation

  • Gérot, Cédric & Ivrissimtzis, Ioannis, 2023. "Bivariate non-uniform subdivision schemes based on L-systems," Applied Mathematics and Computation, Elsevier, vol. 457(C).
    • Handle: RePEc:eee:apmaco:v:457:y:2023:i:c:s0096300323003259
    DOI: 10.1016/j.amc.2023.128156
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