In Scientific Visualization

Scientific visualization

Scientific visualization is an interdisciplinary branch of science according to Friendly "primarily concerned with the visualization of three-dimensional phenomena , where the emphasis is on realistic renderings of volumes, surfaces, illumination sources, and so forth, perhaps...

 the Asymptotic Decider is an algorithm developed by Nielson and Hamann in 1991 that creates isosurfaces

Isosurface

An isosurface is a three-dimensional analog of an isoline. It is a surface that represents points of a constant value within a volume of space; in other words, it is a level set of a continuous function whose domain is 3D-space.Isosurfaces are normally displayed using computer graphics, and are...

 from a given scalar field. It was proposed as an improvement to the marching cubes

Marching cubes

Marching cubes is a computer graphics algorithm, published in the 1987 SIGGRAPH proceedings by Lorensen and Cline, for extracting a polygonal mesh of an isosurface from a three-dimensional scalar field...

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