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.

翻译：我们提出一种方法，从四面体网格边与连续曲面的交点中恢复流形、无相交三角网格。与经典的行进立方体或行进四面体算法不同，我们的子网格行进方案允许单个单元内存在任意多个曲面片，从而捕捉精细特征和薄板结构。此外，该方法既不需要明确定义内部/外部（允许带边界的曲面），也不需要一致定向的输入几何。然而我们保留了经典行进的局部并行特性：每个四面体独立进行重构，在四面体边界上生成一致网格。我们的核心创新是对几何拓扑中法向坐标的推广，通过每条网格边上的任意整数交点计数来编码曲面连通性。这种编码规避了传统的奈奎斯特-香农极限，对固定网格可分辨的特征尺寸不设下限。在实际应用中，在相似计算时间与相同网格分辨率（甚至相同数量的输出三角形）条件下，子网格行进生成的网格远优于经典行进方法。除标准等值面提取外，该方法还可用于将多边形汤转换为流形、无相交三角网格。