Exercises
 Give a definition of an implicit surface and give three examples of
where such things might be useful.
 The marching cubes algorithm, as it applies to implicit surfaces,
is described in the Wyvill article; while Lorenson and Cline
concentrate on the algorithm as applied to voxel data. It is useful
that the same algorithm works for both types of data. Explain how
voxel data can be thought of a defining an implicit surface (or
surfaces). Explain, conversely, how the Wyvill algorithm can be
thought of as converting implicit surface data into voxel data before
producing the final surface.
 Following Section 4 of Lorenson and Cline's paper, sketch an
implementation of the twodimensional `marching squares' algorithm 
where you generate line segments in 2D rather than triangles in 3D. An
appliation of this algorithm would be the drawing of isobars on a
weather map, given pressure values at a regular (2D) grid of points.
 Medical data is captured in slices. Each slice is a 2D image of
density data. The distance between slices may be different to the
distance between the pixels within a slice (for example, see Lorenson
and Cline, Section 7.1, p. 167). What effect does this difference have
on the voxel data? What effect does it have on the marching cubes
algorithm?
 Consider Lorenson and Cline, Section 6. This research was done
about twelve years ago. Given your knowledge of processor performance,
what differences in performance would you expect to see between then
and now?
 Lorenson and Cline is an example of a graphics research
paper. Critically evaluate Lorenson and Cline. How good is this piece
of research?
 Research papers at the SIGGRAPH conference are limited in their
length. Evaluate Lorenson and Cline in terms of the following
questions. What has been left out that would have been useful? What
has been included that could have been left out? Where could the
explanation have been better? Are any of the figures extraneous? Where
would an extra figure have been helpful? List any grammatical or
spelling errors (there is at least one of each).
