Marching cubes 33 : construction of topologically correct isosurfaces

Abstract

An algorithm implemented in the HIGZ graphics package for the construction of isosurfaces from volumetric datasets is discussed. This algorithm is an improved version of the Marching Cubes method. For each cell considered independently, the algorithm permits the construction of a triangle model, the topology of which coincides exactly with the topology of the isosurface of the trilinear function. It is shown that there are 33 topologically different configurations, instead of 15 as with the MC-method. 1 Introduction The Marching Cubes (MC) method [1] is a wellknown method for volume visualization. It produces triangle models of isosurfaces F (x; y; z) = ff of a scalar function given by samples over a cuberille grid. Usually the MC-method is considered as the basic method for surface rendering in medical applications. However, it can also be applied in many other areas as, for example, for the visualization of implicitly specified functions or for the visualization of calculation resu...