Graphics Reference
In-Depth Information
describes individual bricks and window casings, and bidirectional scattering
distribution functions (BSDFs) that describe the microscopic roughness that
makes the brick appear matte and the flower boxes appear shiny.
Switching to a less complex object representation is a way to reduce the num-
ber of independent (scalar) state variables in a physical system, also known as the
number of
degrees of freedom
of a system. For example, a dot on a piece of paper
has two degrees of freedom—its
x
- and
y
-positions. A square drawn on the paper
has four degrees of freedom—the position of the center along horizontal and ver-
tical axes, the length of the side, and the angle to the edge of the page. A 3D rigid
body has trillions of degrees of freedom if the underlying atoms are considered,
but only six degrees of freedom (3D position and orientation) if taken as a whole.
Simulating the root positions of the characters in a crowd is a reduction of the
number of degrees of freedom from simulating the muscles of every individual
character.
Furthermore, an object may be modeled for rendering purposes with much
higher detail than is present for simulation. For example, a space ship can be
modeled as a cylinder for inertia and collision purposes but rendered with fins, a
cockpit, and rotating radar dishes without the viewer perceiving the difference.
Separating the rendering representation, motion control scheme, and object
representation introduces error into the simulation of a virtual world. This may or
may not be perceptually significant. From a system design perspective, error is not
always bad. In fact, acceptable error can be your friend: It provides room to tweak
and choose where to put simulation (and therefore development) effort.
In a
key pose
animation scheme (a.k.a. key frame, interpolation-based animation),
an animation artist (
animator
) specifies the poses to hit at specific times, and an
algorithm computes the intermediate poses, usually in the absence of full physics.
The challenges in key pose animation are creating suitable authoring envi-
ronments for the animators and performing interpolation that conserves impor-
tant properties, such as momentum or volume. Because an animator's creation is
expressive and not necessarily realistic or algorithmic, perfect key pose anima-
tion is ultimately an artificial intelligence problem: Guess the intermediate pose
a human animator would have chosen. Nonetheless, this is the most popular con-
trol scheme for character performances, and for sufficiently dense key poses it is
considered a solved problem with many suitable algorithms.
In a
dynamics
(a.k.a. physically based animation, simulation) scheme, objects are
represented by positions and velocities and physical laws are applied to advance
this state between frames. The laws need not be those of real-world physics.
The laws of mechanics from physics are well understood, but generally admit
only numerical solutions. Two challenges in dynamics are stability and artistic
control. It is hard to make numerical methods efficient while preserving stability,
that is, conserving energy, or at least not increasing energy and “exploding.” It
is also hard to make realistic physics act the way that an art director might want
(e.g., a film explosion blowing a door directly into the camera or a video game car
that skids around corners without spinning out).
