We present a new method to define implicit surfaces, broadening the
scope of implicit surface modeling. The implicit surfaces usually
employed in Computer Graphics have been limited to two dimensional
manifolds. These surfaces are defined by real valued functions that
impose a binary partitioning of space (i.e., they represent solid
models that define an inside and an outside). When tiled, these surfaces
yield tessellations whose edges are all of multiplicity 2.
The method presented here allows for the definition of implicit surfaces
with borders (i.e., edges of multiplicity 1) and intersections (i.e., edges
of multiplicity 3 or more). These non-manifold implicit surfaces
are defined by a multiple (rather than binary) partitioning of space. The
object definition includes a list of those pairs of regions whose separating
surface is of interest.
We also present an implementation for a polygonizer that converts a
non-manifold implicit surface definition into a collection of polygons.
Although following the basic steps of a conventional implicit surface
polygonizer, there are several significant differences necessitated by
the multiple partitioning of space.
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