Graphics Reference
In-Depth Information
Meshes
Back in Chapter 8, we introduced meshes as a way to represent shapes in com-
puter graphics. We now return to examine meshes in more detail, because they
dominate present-day graphics. The vertex-and-face-tables model we introduced
in Chapter 8 is widely used to represent triangle meshes, which are almost uni-
versally used in hardware rendering, because triangles are automatically convex
and planar and there's only one possible way to linearly interpolate values at the
three vertices of a triangle. Quad meshes, in which each face has four vertices, are
also interesting in various situations. Indexing a regular planar quad mesh is very
simple compared to indexing a regular planar triangle mesh, for instance. On the
other hand, quads are not necessarily planar, they may be nonconvex, and if we
have values at the four vertices of a quad, linear interpolation over the interior of
the quad is likely to be undefined. So almost everything that's simple for triangles
is more difficult for quads.
During geometric modeling, arbitrary polygon meshes, in which a face can
have any number of vertices, can be a real convenience. In 2D modeling, for
instance, the countries in a geography-based board game might be described by
polygons with hundreds of vertices. Expressing these as triangulated polygons
would introduce meaningless artifacts into the country descriptions. It would also
amplify the space required to store the map. In general, such unconstrained meshes
present all the problems of quad meshes, and more, but they have their place
in situations where artistic intent or natural semantic structure in a model is
important.
As we mentioned in Chapter 14, triangle strips and fans are sometimes used
as a way to reduce mesh storage or transmission costs. In a triangle mesh, instead
of having a list of vertex-index triples to represent faces, we have a sequence of
triples like
(
1, 4, 18, 9, 11,
6
4
9
5
1
11
18
2
Figure 25.1: A triangle strip
is represented by a stream of
vertex indices; every group of
three adjacent indices describes
another triangle in the strip. The
communication attributable to a
typical triangle is therefore just
a single vertex index, rather than
three vertex indices.
)
, which represents the triangles with vertices 1, 4,
and 18, the one with vertices 4, 18, and 9, the one with vertices 18, 9, and 11, etc.,
as shown in Figure 25.1.
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