An implicit surface is a set of points p such that f(p) = 0, where f is a trivariate function (i.e., p ∈ ℜ3). The surface is also known as the zero set of f and may be written Z(f). According to the implicit surface theorem, if zero is a regular value of f, then the zero set is a two-dimensional manifold. An iso-surface is a similar set of points for which f(p) = c, where c is the iso-contour value of the surface. The function f is sometimes called the implicit function, although we prefer implicit surface function. A review of the salient properties of implicit surfaces may be found in [Hoffmann 1989].
