Polygonization of implicit surfaces

This paper discusses a numerical technique that approximates an implicit surface with a polygonal representation. The implicit function is adaptively sampled as it is surrounded by a spatial partitioning. The partitioning is represented by an octree, which may either converge to the surface or track it. A piecewise polygonal representation is derived from the octree.

The technique is insensitive to the complexity of the implicit function, allowing the designer great latitude. With a polygonal representation of the surface available, certain computational economies result; in particular, the roots to the function need not be solved each time the surface is rendered.