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<p>In this paper, an innovative hybrid family of even-point non-uniform ternary schemes featuring mixed symmetry is introduced. The subdivision rules for the interior points of the control polygon exhibit both shift-invariance and flip-invariance. This ensures the symmetric behaviour of the schemes for the interior part of the polygon. In contrast, the initial and endpoint subdivision rules are non-symmetric. These features of the schemes distinguish our approach and produce shapes with higher smoothness compared to traditional stationary interpolating schemes. The minimal support size for the refinement rule makes the family members more attractive for end users. As examples, we present some even-point non-uniform ternary interpolatory subdivision schemes. Their numerical applications demonstrate improved flexibility in approximating shapes.</p>

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A hybrid family of non-uniform ternary schemes with mixed symmetry for approximating shapes

  • 期刊论文

  • 发表日期：

    2025年1月4日

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  • Sidra Razaq,
  • Rakib Mustafa,
  • Ghulam Mustafa

摘要

In this paper, an innovative hybrid family of even-point non-uniform ternary schemes featuring mixed symmetry is introduced. The subdivision rules for the interior points of the control polygon exhibit both shift-invariance and flip-invariance. This ensures the symmetric behaviour of the schemes for the interior part of the polygon. In contrast, the initial and endpoint subdivision rules are non-symmetric. These features of the schemes distinguish our approach and produce shapes with higher smoothness compared to traditional stationary interpolating schemes. The minimal support size for the refinement rule makes the family members more attractive for end users. As examples, we present some even-point non-uniform ternary interpolatory subdivision schemes. Their numerical applications demonstrate improved flexibility in approximating shapes.