A complete lookup table for marching cubes

The well-known marching cubes method is used to generate isosurfaces from volume data or data on a 3D rectilinear grid.To do so,it refers to a lookup table to decide on the possible configurations of the isosurface within a given cube,assuming we know whether each vertex lies inside or outside the surface.However,the vertex values alone do not uniquely determine how the isosurface may pass through the cube,and in particular how it cuts each face of the cube.Earlier lookup tables are deficient in various respects.The possible combinations of the different configurations of such ambiguous faces are used in this paper to find a complete and correct lookup table.Isosurfaces generated using the new lookup table here are guaranteed to be watertight.