Regularised marching tetrahedra: improved iso-surface extraction

Marching cubes is a simple and popular method for extracting iso-surfaces from implicit functions or discrete three-dimensional (3-D) data. However, it does not guarantee the surface to be topologically consistent with the data, and it creates triangulations which contain many triangles of poor aspect ratio. Marching tetrahedra is a variation of marching cubes, which overcomes this topological problem. Improvement in triangle aspect ratio has generally been achieved by mesh simplification, a group of algorithms designed to reduce the large number of triangles. Vertex clustering is one of the simplest of these algorithms, but does not in general maintain the topology of the original mesh. We present a new algorithm, regularised marching tetrahedra, which combines marching tetrahedra and vertex clustering to generate iso-surfaces which are topologically consistent with the data and contain a number of triangles appropriate to the sampling resolution (typically 70% fewer than marching tetrahedra) with significantly improved aspect ratios. This improvement in aspect ratio greatly enhances the display of the surface, particularly when it is rendered using simple interpolated shading. Surface triangulations are shown for implicit surfaces, thresholded medical data, and surfaces created from object cross-sections. The application to data sampled on non-parallel planes is also considered.