Graphics Reference
In-Depth Information
constraint graphs for forces and contacts. See Chapter 35 for a discussion of
dynamics and articulation data structures and algorithms.
Spatial data structures
/scene graphs are the close analogue of general com-
puter science data structures such as lists, trees, and arrays. They divide the scene
into grids or trees that allow efficient spatial queries, such as “Which objects are
within 4 m of my avatar?” Child nodes are typically contained within the bounding
volumes of their parents. Spatial data structures are employed extensively in sim-
ulation and rendering. They are usually computed automatically. Efficient algo-
rithms for building these data structures per-frame have recently emerged and this
is an active area of research. Chapters 36 and 37 discuss modeling and interaction
data structures and algorithms.
As we said earlier, we conventionally think of objects as defined by their sur-
faces, which are the boundaries between them and other objects or the surround-
ing medium. But the solid nature of objects also has an effect on their interaction
with light. Fortunately, we can limit our consideration to the interface between
two media through which light propagates differently. That there are
two
media
involved is essential. The appearance of a surface depends on both, although we
commonly observe most objects in air, so this is not always apparent. For the
moment, let us assume that objects are rendered in air so that we can define appear-
ance using a single material parameter. We will return to the two-material case in
Section 14.10.
The interaction of light and matter is quite simple. To a first approximation,
each photon that strikes the surface has one of three fates: It is absorbed and con-
verted into heat, it passes through the surface into the medium, or it reflects. The
probability of each of these outcomes and the direction that scattered photons take
after the interaction is governed by the materials involved and the microscopic
angle of the plane of the surface near the location hit. A few simple laws from
physics can describe the entire model.
However, we use high-level models that intentionally introduce more com-
plexity than is present in these simple laws. Doing so lets us work with large num-
bers of photons in the aggregate and large (or at least, macroscopic) patches of
surface. So, in exchange for complicating the material model, we can use simpler
geometric surface models and light-sampling strategies. A more complex material
model also allows aesthetic controls instead of physical ones, enabling artists to
achieve their visions using intuition instead of measurement.
It is common practice to distinguish at least the following five artistically and
perceptually significant phenomena.
1. Sharp
specular
(mirror) reflections, as seen on glass.
2.
Glossy
highlights and reflections, like the highlights on a waxed apple.
3. Shallow subsurface scattering, which produces matte
Lambertian
shading
that is independent of the viewer's orientation, such as observed with “flat”
wall paint.
4. Deep
subsurface scattering
where light diffuses beneath the surface. This
is what makes skin and marble appear soft.
5.
Transmission,
where light passes through a mostly translucent material
such as water or fog, perhaps being slightly diffused along the way and
refracted when it enters this medium.
