Second-order prestress stability and third-order rigidity of polyhedral surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918072776916992 |
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| author | He, Zeyuan |
| author_facet | He, Zeyuan |
| contents | The energy-based definition provides a viable resolution to the longstanding confusion on the proper definition of $n$-th order rigidity and flexibility in geometric constraint systems. Applying an energy-based local rigidity analysis to polyhedral surfaces, we derive new criterion for testing second-order prestress stability. Additionally, we discuss the limitations of testing third-order rigidity, except in the special case where the null space of the rigidity matrix is one-dimensional. Although our primary focus is on polyhedral surfaces, the theory and methods developed in this article apply to general geometric constraint systems under certain conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22019 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Second-order prestress stability and third-order rigidity of polyhedral surfaces He, Zeyuan Metric Geometry The energy-based definition provides a viable resolution to the longstanding confusion on the proper definition of $n$-th order rigidity and flexibility in geometric constraint systems. Applying an energy-based local rigidity analysis to polyhedral surfaces, we derive new criterion for testing second-order prestress stability. Additionally, we discuss the limitations of testing third-order rigidity, except in the special case where the null space of the rigidity matrix is one-dimensional. Although our primary focus is on polyhedral surfaces, the theory and methods developed in this article apply to general geometric constraint systems under certain conditions. |
| title | Second-order prestress stability and third-order rigidity of polyhedral surfaces |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2506.22019 |