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Polygonization of Implicit Surfaces
, 1988
"... 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 ..."
Abstract

Cited by 376 (3 self)
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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.
A new method for drawing Algebraic Surfaces
"... R. The program produces a model of the surface which can be viewed using a general rendering package. The program has been specially designed to draw singular surfaces accurately and find all the components of the surface. There are many programs already existing which do this to a limited extent. P ..."
Abstract
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R. The program produces a model of the surface which can be viewed using a general rendering package. The program has been specially designed to draw singular surfaces accurately and find all the components of the surface. There are many programs already existing which do this to a limited extent. Programs to draw surfaces of the type z = f(x; y) have been around for a number of years. CAD systems can draw specific types of algebraic surfaces but not normally singular ones. There are a few existing programs which draw general algebraic surfaces. Ray tracers [5] can be used to produce beautiful pictures of algebraic surface but they are slow and only gives the view from one direction. Other programs such the contour tracer written by the Geometry Supercomputer Project [2], produce good results but do not pay mush attention to singularities and may give topologically incorrect results.