Subgrid Marching Tetrahedra

2026-05-29

AI Summary

This work addresses the inability of traditional Marching Tetrahedra methods to accurately capture fine-scale features and thin-sheet structures by proposing a subgrid Marching Tetrahedra approach. The method reconstructs multiple surface patches independently within each tetrahedron, without requiring pre-defined inside–outside labels or consistent input normals. It overcomes the Nyquist–Shannon sampling limit by introducing a geometry-aware topological encoding: an integer count of surface intersections per mesh edge that characterizes surface connectivity via generalized normal coordinates. This enables faithful representation of features at arbitrary scales. While preserving local parallelism, the algorithm guarantees inter-element topological consistency, yielding high-fidelity, manifold, self-intersection-free triangle meshes. At comparable grid resolution and computational cost, the proposed method significantly outperforms classical Marching Cubes and Marching Tetrahedra techniques.

Abstract

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.

Problem

• manifold mesh
• intersection-free
• subgrid reconstruction
• surface extraction
• tetrahedral grid

Innovation

• Subgrid Marching
• Manifold Reconstruction
• Normal Coordinates
• Intersection-free Meshing
• Tetrahedral Contouring