Asymptotic Decider

In scientific visualization the Asymptotic Decider is an algorithm developed by Nielson and Hamann in 1991 that creates isosurfaces from a given scalar field. It was proposed as an improvement to the marching cubes algorithm, which can produce some "bad" topology, but should better not be seen as an addition to marching cubes, but as an algorithm of its own.
Principle
In general, the algorithm divides the scalar field first in regular cubes. Then it draws topologically correct contours on the sides (interface) of the cubes. These contours will then be connected to polygones and triangulated. The triangles of all cubes form the isosurfaces and are thus the output of the algorithm
 
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