Scholarlink

<p>This study explores key properties of non-uniform, non-symmetric subdivision schemes of higher arity. It focuses on smoothness, support size, and approximation order. A novel family of n-ary interpolatory subdivision schemes with 4-point is introduced. These schemes are non-uniform, both level-dependent and location-dependent. They achieve higher continuity while maintaining localized support. In this study, traditional Laurent polynomial smoothness-checking techniques are not used. Instead, the proposed framework takes a different approach. It employs a sufficiently smooth function to define the mask of the scheme, ensuring the generation of smooth limiting shapes. Minimal mask complexity in subdivision schemes is achieved in the proposed framework to ensure high smoothness. New vertices are refined based on local data, reducing computational overhead while improving continuity. The resulting limiting curves exhibit diverse shapes. These properties make the proposed schemes well-suited for computer graphics and engineering shape design.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A family of non-uniform, non-symmetric higher-arity interpolatory schemes with function-based mask design for enhanced smoothness and localized support

  • 期刊论文

  • 发表日期：

    2026年1月8日

查看全文
  • Sidra Razaq,
  • Rakib Mustafa,
  • Ghulam Mustafa,
  • Qamar Abbas,
  • Abdul Ghaffar

摘要

This study explores key properties of non-uniform, non-symmetric subdivision schemes of higher arity. It focuses on smoothness, support size, and approximation order. A novel family of n-ary interpolatory subdivision schemes with 4-point is introduced. These schemes are non-uniform, both level-dependent and location-dependent. They achieve higher continuity while maintaining localized support. In this study, traditional Laurent polynomial smoothness-checking techniques are not used. Instead, the proposed framework takes a different approach. It employs a sufficiently smooth function to define the mask of the scheme, ensuring the generation of smooth limiting shapes. Minimal mask complexity in subdivision schemes is achieved in the proposed framework to ensure high smoothness. New vertices are refined based on local data, reducing computational overhead while improving continuity. The resulting limiting curves exhibit diverse shapes. These properties make the proposed schemes well-suited for computer graphics and engineering shape design.