High-Order Continuous Geometrical Validity
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913932861505536 |
|---|---|
| author | Sichetti, Federico Huang, Zizhou Attene, Marco Zorin, Denis Puppo, Enrico Panozzo, Daniele |
| author_facet | Sichetti, Federico Huang, Zizhou Attene, Marco Zorin, Denis Puppo, Enrico Panozzo, Daniele |
| contents | We propose a conservative algorithm to test the geometrical validity of simplicial (triangles, tetrahedra), tensor product (quadrilaterals, hexahedra), and mixed (prisms) elements of arbitrary polynomial order as they deform over a piecewise-linear trajectory.
Our algorithm uses a combination of adaptive Bézier refinement and bisection search to determine if, when, and where the Jacobian determinant of an element's polynomial geometric map becomes negative in the transition from one configuration to another.
Unlike previous approaches, our method preserves its properties also when implemented using floating point arithmetic: This feature comes at a small additional runtime cost compared to existing inexact methods, making it a drop-in replacement for current validity tests, while providing superior robustness and generality.
To prove the practical effectiveness of our algorithm, we demonstrate its use in a high-order Incremental Potential Contact (IPC) elastodynamic simulator, and we experimentally show that it prevents invalid, simulation-breaking configurations that would otherwise occur using inexact methods, without the need for manual parameter tuning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03756 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High-Order Continuous Geometrical Validity Sichetti, Federico Huang, Zizhou Attene, Marco Zorin, Denis Puppo, Enrico Panozzo, Daniele Computational Geometry Graphics We propose a conservative algorithm to test the geometrical validity of simplicial (triangles, tetrahedra), tensor product (quadrilaterals, hexahedra), and mixed (prisms) elements of arbitrary polynomial order as they deform over a piecewise-linear trajectory. Our algorithm uses a combination of adaptive Bézier refinement and bisection search to determine if, when, and where the Jacobian determinant of an element's polynomial geometric map becomes negative in the transition from one configuration to another. Unlike previous approaches, our method preserves its properties also when implemented using floating point arithmetic: This feature comes at a small additional runtime cost compared to existing inexact methods, making it a drop-in replacement for current validity tests, while providing superior robustness and generality. To prove the practical effectiveness of our algorithm, we demonstrate its use in a high-order Incremental Potential Contact (IPC) elastodynamic simulator, and we experimentally show that it prevents invalid, simulation-breaking configurations that would otherwise occur using inexact methods, without the need for manual parameter tuning. |
| title | High-Order Continuous Geometrical Validity |
| topic | Computational Geometry Graphics |
| url | https://arxiv.org/abs/2406.03756 |