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, but further degrades the triangle aspect ratios. Improvement in triangle aspect ratio has generally been achieved by mesh simplification, a group of algorithms designed mainly to reduce the triangle count. Vertex clustering is one of the simplest, but does not necessarily maintain the topology of the original mesh. We present a new algorithm, regularised marching tetrahedra (RMT), 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 smooth shaded displays of the surface. Surface triangulations are shown for implicit surfaces, thresholded medical data, and surfaces created from object cross-sections — implementations of RMT appropriate to each of these situations are available. 1 http://svr-www.eng.cam.ac.uk/∼gmt11/software.html. 1 The application to data sampled on non-parallel planes is also considered.