Subgrid Marching Tetrahedra
For computer graphics and geometry processing, this method enables high-quality mesh extraction from implicit surfaces or polygon soups without requiring inside/outside or consistent orientation, overcoming Nyquist limitations.
Subgrid Marching Tetrahedra recovers manifold, intersection-free triangle meshes from points where grid edges pierce a surface, handling multiple surface patches per cell and surfaces with boundary. It achieves far higher accuracy than classic marching methods at equal grid resolution or output triangle count.
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.