Real functions can have domain-value sets {level set} {fiber, set} that make function constant. Real-equation roots are level sets. For two-dimensional domains f(x,y), level sets are curves {implicit curve} {isocontour}. For three-dimensional domains f(x,y,z), level sets are surfaces {implicit surface} {isosurface}.
function
Functions are positive inside surface, zero on surface, and negative outside surface. At points, function gradient is perpendicular to level-set surface.
shape
Closed planar curves can be isocontours. Closed surfaces can be isosurfaces. Shape boundaries are level sets. Shapes have real-function positive values. As object changes, level-set function translates by non-parametric methods {level set method} {Eulerian approach} (Stanley Osher and James Sethian) [1988].
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Date Modified: 2022.0224