Subgrid Marching Tetrahedra

Fuente: arXiv
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Autori principali: Baktash, Hossein, Gillespie, Mark, Crane, Keenan
Natura: Preprint
Pubblicazione: 2026
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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