Description of Marching Cubes on Wikipedia

Marching CubesIs a computer graphics algorithm, published in the 1987 Siggraph proceedings by Lorenz and Cline,^{[1] for extracting a polygonal mesh of an isosurface from a three-dimen1_scalar field (sometimes called voxels). An equivalent two-dimen1_method is called the marching squares algorithm.}

The algorithm proceeds through the scalar field, taking eight
Neighbor locations at a time (thus forming an imaginary cube), then
Determining the polygon (s) needed to represent the part of
Isosurface that passes through this cube. The individual polygons are
Then fused into the desired surface.

This is done by creating an index to a precalculated array of 256 possible polygon deployments (28 = 256)
Within the cube, by treating each of the 8 scalar values as a bit in
8-bit integer. If the scalar's value is higher than the iso-Value
(I. e., it is inside the surface) then the appropriate bit is set
One, while if it is lower (outside), it is set to zero. The final value
After all 8 scalars are checked, is the actual index to the Polygon
Configuration array.

Finally each vertex of the generated polygons is placed on
Appropriate position along the Cube's edge by linearly interpolating
The two scalar values that are connected by that edge.

15 unique cube tolerations

The precalculated array of 256 cube tolerations can be obtained by reflections and adjust rical rotations of 15 unique cases.

The gradient
Of the scalar field at each grid point is also the normal vector of
Hypothetical isosurface passing from that point. Therefore, we may interpolate
These normals along the edges of each cube to find the normals of
Generated vertices which are essential for shading the resulting Mesh
With some illumination model.

The applications of this algorithm are mainly concerned with medical visualizations such as CT and MRI scan data images, and special effects or 3-D Modelling with what is usually called metabils or other metasurfaces.

Patent issues

This algorithm was the prime example in the graphics field of the woes of patenting software,
Patented despite being a relatively obvious solution to
Surface-generation problem. Another similar algorithm was developed,
Called marching tetrahedrons,
In order to circumvent the patent as well as a minor ambiguity problem
Of Marching Cubes with some cube deployments. This patent has
Recently expired, and it is legal for the graphics community to use it
Now without royalties since more than 20 years have passed from its
Filing date (June 5, 1985) (Marching Cubes, US Patent Office entry ).

William E. Lorenz, Harvey E. Cline:Marching Cubes: a high resolution 3D Surface Construction Algorithm.In:Computer Graphics, Vol. 21, Nr. 4, July 1987