Graphics Reference
In-Depth Information
has not been formally explored. Numerical integration is essential to other fields
and is an area of constant scientific advance. We are not aware of experiments with
various newer integration methods, particularly adaptive step-size ones, in dynam-
ics simulation for computer graphics. Thus, it is an open question where the best
tradeoff lies between per-step cost and steps per frame. Recall that the benefits of
higher-order integration are only justified if they result in fewer steps and implic-
itly conserve precision. Taking more low-order steps, especially on massively par-
allel processors, could be preferable in some systems. Alternatively, taking very
few high-order steps could be preferable. Thus, experimentation with the core
numerical integration scheme is another area that may yield interesting results.
Our understanding is that physical simulation for nongraphics engineering and
science applications has been proceeding in this direction and we encourage its
development within graphics as well.
We've explained in this chapter how physically based animation can be described
by differential equations whose solutions present various challenges, depending
on context. The other kind of animation, which one might call “fine-art anima-
tion,” and which involves human animators, is a separate discipline. Nonetheless,
physically based animation and algorithmic animation are being used more and
more, even within fine-art animation. This presents challenges and opportunities
in designing comprehensible interfaces for artists who must interact with physics
and try to control it to achieve certain artistic goals.
