Scholarlink

<p>We study flexible polyhedral nets in isotropic geometry. This geometry has a degenerate metric, but there is a natural notion of flexibility. We study infinitesimal and finite flexibility, and classify all finitely flexible polyhedral nets of arbitrary size. We show that there are just two classes, in contrast to Izmestiev’s rather involved classification in Euclidean geometry, for size <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(3\times 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>3</mn> <mo>×</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation> only. Using these nets to initialize the optimization algorithms, we turn them into approximate Euclidean mechanisms. We also explore the smooth versions of these classes.</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

Flexible polyhedral nets in isotropic geometry

  • 期刊论文

  • 发表日期：

    2025年12月27日

查看全文
  • Olimjoni Pirahmad,
  • Helmut Pottmann,
  • Mikhail Skopenkov

摘要

We study flexible polyhedral nets in isotropic geometry. This geometry has a degenerate metric, but there is a natural notion of flexibility. We study infinitesimal and finite flexibility, and classify all finitely flexible polyhedral nets of arbitrary size. We show that there are just two classes, in contrast to Izmestiev’s rather involved classification in Euclidean geometry, for size \(3\times 3\) 3 × 3 only. Using these nets to initialize the optimization algorithms, we turn them into approximate Euclidean mechanisms. We also explore the smooth versions of these classes.