In scientific visualization the asymptotic decider is an algorithm developed by Nielson and Hamann in 1991 that creates isosurfaces from a given scalar field.
[2] The algorithm first divides the scalar field into uniform cubes.
It draws topologically correct contours on the sides (interface) of the cubes.
The triangles of all cubes form the isosurfaces and are thus the output of the algorithm.
This algorithm describes a method for resolving these ambiguous configurations in a consistent manner.
[3] Ambiguous cases often occur if diagonally opposing points are found on the same side of the isoline, but on a different side to the other points in the square (for 2D systems) or cube (for 3D systems).
The correct situation depends on the value at the asymptote of the isolines.
is the normalised distance in the square from the left-hand side, and
is greater than the value of the isoline the positive corners are in the main section of the square and the negative corners are separated by two isolines, and if
is less than the value of isoline the negative corners are in the main section of the square and the positive corners are separated by two isolines.
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