Subject 5.10: What is the marching cubes algorithm?

The marching cubes algorithm is used in volume rendering to construct an isosurface from a 3D field of values. The 2D analog would be to take an image, and for each pixel, set it to black if the value is below some threshold, and set it to white if it's above the threshold. Then smooth the jagged black outlines by skinning them with lines.

The marching cubes algorithm tests the corner of each cube (or voxel) in the scalar field as being either above or below a given threshold. This yields a collection of boxes with classified corners. Since there are eight corners with one of two states, there are 256 different possible combinations for each cube.

Then, for each cube, you replace the cube with a surface that meets the classification of the cube. For example, the following are some 2D examples showing the cubes and their associated surface. The result of the marching cubes algorithm is a smooth surface that approximates the isosurface that is constant along a given threshold.

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