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Chapter 5
Motion simulation
The core of any animation system is the motion simulation algorithm that it uses to transform
the user's specications into detailed motion paths for the objects in a scene. For keyframe
animation systems, where the position and other state variables are given for particular
points in time, this algorithm must interpolate between these points to determine the full
paths. For physically-based animation systems, however, motion simulation is much more
involved, since the movement of the objects is a result of the physical laws that apply to the
scene.
The physical model that Asgard presents to the user is described in Chapter 3. This
chapter will rst describe the primitives that are used by the motion simulation code and how
the user-level elements are mapped onto it. Then the manner in which the resulting system
of dierential equations is handled will be discussed, with special attention to the problems
specic to interactive animation and how Asgard addresses them. Finally, a description will
be given of other alternatives for motion simulation, and they will be compared to Asgard's
approach.
5.1 Problem formulation and primitives
The model of the animated scene that Asgard presents to the user is in terms of high level
concepts: rigid bodies with user-specied shapes, forces, links, and constraints. At the lowest
level, however, the primitives are dierential equations and piecewise-linear functions of time,
and the high-level concepts must be mapped into these primitives. This section describes
how this mapping is performed.
5.1.1 Objects and forces
Articulated bodies are composed of components, which are rigid bodies, connected by links.
A link can be thought of as a connection between a point on one component and a point
on another. For the rest of this chapter, the term \object" will be used to refer to these
components, since internally all the components of a body are treated as separate entities,
except for the purpose of collision detection.
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