Graphics Reference
In-Depth Information
surface is computed (or perhaps a few more stages of subdivision are performed
to generate an effectively smooth mesh).
Adjusting vertex positions after a level of subdivision is acceptable because
the resultant mesh is an acceptable input to the subdivision algorithm. Indeed, one
can go further: One can actually edit the topology of a mesh, adding a hole at
some level, etc. The data that needs to be recorded for such a modeling session
consists of the original vertex positions, plus any edits made at each level. In the
event that several vertices at level three, say, were all moved in the same direction,
there may be a level-two edit that would have achieved the same effect, or most
of it. Rewriting the representation to include this level-two edit, and then smaller
level-three edits, may make the representation more compact.
This editing approach has the advantage that the user can “browse” through
different levels, adjusting the shape at higher levels and then returning to lower
levels. One problem that arises is that details added at a lower level may not make
sense after a high-level edit. In a face model, for instance, a nose might be drawn
out in the
x
-direction. If at a higher level, the face is rotated by 90
◦
in the
xy
-plane,
the low-level edit will make a nose that's dragged to the side of the face rather than
in front of it. It therefore is useful to express low-level edits in a coordinate sys-
tem that's tied to the result of higher-level subdivision so that the nose is described
as being drawn out along the normal to the face, rather than “in the
x
-direction.”
Such multiscale editing is described by Cohen et al. [MCCH99], and the conden-
sation of multiscale editing representations, together with other multiscale editing
techniques, is described by Zorin et al. [ZSS97].
As with the preceding chapter, the web material for this chapter contains a much-
expanded version of the material presented here, together with pointers to the
literature. Spline and subdivision surfaces are at the heart of most of today's CAD
packages, and CAD long ago became its own area, largely separate from computer
graphics. Introductory CAD texts will help you grasp the main ideas (and some of
the sometimes-complex indexing schemes!). Loop's Master's thesis [Loo87] is a
gentle introduction. Despite the separation of graphics and CAD, there continues
to be cross-fertilization.
