Marching tetrahedra

More than 20 years have passed from the patent filing date (June 5, 1985), and the marching cubes algorithm can now be used freely.

Just like in marching cubes, the intersections of these edges with the isosurface are approximated by linearly interpolating the values at the grid points.

This is an important property to prevent cracks in the rendered surface, because interpolation of the two distinct diagonals of a face usually gives slightly different intersection points.

It is straightforward to enumerate all sixteen configurations and map them to vertex index lists defining the appropriate triangle strips.

The number of configurations, determining the size of the commonly used lookup tables, is much smaller, since only four rather than eight separate vertices are involved per tetrahedron.

When sliced this way, additional planes of symmetry are provided; having a tetrahedron around the centroid of the cube also generates very open spaces around points that are outside of the surface.

Calculation of color based on a spacial texture system[4] can be done using the current fragment position to select from a repeating texture based on the pairs of texel coordinates (x,y), (y,z) and (x,z) and scaling those values by the absolute value of each respective component of the normal z, x, and y respectively.