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2.1 Level-set-function parameterizations

The most general way to parameterize a 2-surface in a slice is to define a scalar “level-set function” F on some neighborhood of the surface, with the surface itself then being defined as the level set
F = 0 on the surface. (3 )
Assuming the surface to be orientable, it is conventional to choose F so that F > 0 (F < 0) outside (inside) the surface. The choice of level-set function for a given surface is non-unique, but in general this is not a problem.

This parameterization is valid for any surface topology including time-dependent topologies. The 2-surface itself can then be found by a standard isosurface-finding algorithm such as the marching-cubes algorithm [105]. (This algorithm is widely used in computer graphics and is implemented in a number of widely-available software libraries.)


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