Implicit Surfaces are a very interesting research area.
While still not supported by any hardware, useful rendering and visualization techniques are required to be able to work with Implicit Surfaces in real time. Among other things areas of Mathematical Analysis, Linear Algebra, Physics, Algorithms, and Performance Engineering are all concerned with the study of Implicit Surfaces.
Back in 2002 I earned my Bachelor degree in Computer Science working with Sampling and Visualization of Implicit Surfaces, together with N. Gulzar. There're several ways of rendering these incredible surfaces, but my approach uses particles to sample and control the surfaces.
The thesis about my work can be downloaded here:
Sampling and Visualization of Implicit Surfaces (2.8mb)
The application I implemented during my work can be downloaded here:
I've later extended my work to use new kinds of implicit objects other than Blobby Spheres, and other kinds of rendering methods. The ladder includes Marching Cubes and Marching Triangles. No paper on my work with Maching Cubes/Triangles does yet exist.
A primitive test demo of the Marching Cubes algorithm can be downloaded here:
A small video clip (6 sec.) of the my Marching Cubes algorithm, rendered using a sub division of 5, is avaible here:
MC Example (650k)
Micky K. Christensen