Hierarchical Geometric Models for Visible Surface Algorithms
The geometric structure inherent in the definition
of the shapes of three-dimensional objects 
and environments is used not just to define their relative
motion and placement, but also to assist in 
solving many other problems of systems for producing
pictures by computer.  By using an extension of 
traditional structure information, or a geometric hierarchy,
five significant improvements to current 
techniques are possible.  First, the range of complexity
of an environment is greatly increased while 
the visible complexity of any given scene is kept within
a fixed upper limit.  Second, a meaningful way 
is provided to vary the amount of detail presented in
a scene.  Third, "clipping" becomes a very fast 
logarithmic search for the resolvable parts of the environment
within the field of view.  Fourth, frame 
to frame coherence and clipping define a graphical
"working set," or fraction of the total structure 
that should be present in primary store for immediate
access by the visible surface algorithm.  Finally, 
the geometric structure suggests a recursive descent,
visible surface algorithm in which the computation 
time potentially grows linearly with the visible complexity of the scene.
CACM October, 1976
Clark, J. H.
