Subgrid Marching Tetrahedra
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913175018930176 |
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| author | Baktash, Hossein Gillespie, Mark Crane, Keenan |
| author_facet | Baktash, Hossein Gillespie, Mark Crane, Keenan |
| contents | We describe a method for recovering a manifold, intersection-free triangle mesh from the points where edges of a tetrahedral grid pierce a continuous surface. Unlike classic marching cubes or tets, our subgrid marching scheme allows arbitrarily many surface patches within a single cell, capturing fine features and thin sheets. Moreover, it requires neither a well-defined inside/outside (allowing surfaces with boundary), nor consistently-oriented input geometry. Yet we retain the local, parallel nature of classic marching: reconstruction is performed independently per tet, yielding a conforming mesh across tet boundaries. Our key innovation is a generalization of normal coordinates from geometric topology, which encode surface connectivity via arbitrary integer intersection counts along each grid edge. This encoding sidesteps the usual Nyquist--Shannon limit, putting no lower bound on the size of features that can be resolved on a fixed grid. In practice, for similar compute time and equal grid resolution -- or even an equal number of output triangles -- meshes produced by subgrid marching are far more accurate than those from classic marching. Beyond standard contouring, our method can be used to convert polygon soup into a manifold, intersection-free mesh. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00454 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Subgrid Marching Tetrahedra Baktash, Hossein Gillespie, Mark Crane, Keenan Graphics Computational Geometry We describe a method for recovering a manifold, intersection-free triangle mesh from the points where edges of a tetrahedral grid pierce a continuous surface. Unlike classic marching cubes or tets, our subgrid marching scheme allows arbitrarily many surface patches within a single cell, capturing fine features and thin sheets. Moreover, it requires neither a well-defined inside/outside (allowing surfaces with boundary), nor consistently-oriented input geometry. Yet we retain the local, parallel nature of classic marching: reconstruction is performed independently per tet, yielding a conforming mesh across tet boundaries. Our key innovation is a generalization of normal coordinates from geometric topology, which encode surface connectivity via arbitrary integer intersection counts along each grid edge. This encoding sidesteps the usual Nyquist--Shannon limit, putting no lower bound on the size of features that can be resolved on a fixed grid. In practice, for similar compute time and equal grid resolution -- or even an equal number of output triangles -- meshes produced by subgrid marching are far more accurate than those from classic marching. Beyond standard contouring, our method can be used to convert polygon soup into a manifold, intersection-free mesh. |
| title | Subgrid Marching Tetrahedra |
| topic | Graphics Computational Geometry |
| url | https://arxiv.org/abs/2606.00454 |