The Closest Point Heat Method for Solving Eikonal Equations on Implicit Surfaces
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909779831554048 |
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| author | Wong, Tony Leung, Shingyu Lee, Byungjoon |
| author_facet | Wong, Tony Leung, Shingyu Lee, Byungjoon |
| contents | We introduce the Closest Point Heat Method (CPHM), a novel approach for solving the surface Eikonal equation on general smooth surfaces. Building on the strengths of the classical heat method, such as simplicity of implementation and computational efficiency, CPHM integrates closest point techniques to reduce dependence on surface meshes. This embedding framework naturally extends the heat method to implicit surfaces while preserving both its efficiency and intrinsic geometric properties. Numerical experiments on benchmark geometries confirm the accuracy and convergence of the proposed method and demonstrate its effectiveness on complex shapes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08158 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Closest Point Heat Method for Solving Eikonal Equations on Implicit Surfaces Wong, Tony Leung, Shingyu Lee, Byungjoon Numerical Analysis 58J05, 65M06, 65M20, 65N06, 65N40, 65D18 We introduce the Closest Point Heat Method (CPHM), a novel approach for solving the surface Eikonal equation on general smooth surfaces. Building on the strengths of the classical heat method, such as simplicity of implementation and computational efficiency, CPHM integrates closest point techniques to reduce dependence on surface meshes. This embedding framework naturally extends the heat method to implicit surfaces while preserving both its efficiency and intrinsic geometric properties. Numerical experiments on benchmark geometries confirm the accuracy and convergence of the proposed method and demonstrate its effectiveness on complex shapes. |
| title | The Closest Point Heat Method for Solving Eikonal Equations on Implicit Surfaces |
| topic | Numerical Analysis 58J05, 65M06, 65M20, 65N06, 65N40, 65D18 |
| url | https://arxiv.org/abs/2509.08158 |