Cubical Marching Squares: Adaptive Feature Preserving Surface Extraction from Volume Data

In this paper, we present a new method for surface extraction from volume data which preserves sharp features, maintains consistent topology and generates surface adaptively without crack patching. Our approach is based on the marching cubes algorithm, a popular method to convert volumetric data to polygonal meshes. The original marching cubes algorithm suffers from problems of topological inconsistency, cracks in adaptive resolution and inability to preserve sharp features. Most of marching cubes variants only focus on one or some of these problems. Although these techniques could be combined to solve these problems altogether, such a combination might not be straightforward. Moreover, some feature-preserving variants introduce an additional problem, inter-cell dependency. Our method provides a relatively simple and easy-to-implement solution to all these problems by converting 3D marching cubes into 2D cubical marching squares, resolving topology ambiguity with sharp features and eliminating inter-cell dependency by sampling face sharp features. We compare our algorithm with other marching cubes variants and demonstrate its effectiveness on various applications.