Appendix : Class Hierarchy ( Core Classes Only )

Modeling and animating three-dimensional scenes involves inherent difficulties both in the specification of scenes and in the implementation of computer animation systems. We present an objectoriented methodology for the integrated modeling of geometry, time, and behavior. Models are defined by two directed acyclic graphs and a set of constraints: the geometry graph is used to specify hierarchically composed objects and their attributes, the behavior graph specifies time-dependent behaviors, and the set of constraints is applied to both the geometry graph and the behavior graph. Time, behavior, and constraints are represented as objects, i.e. similar to geometric primitives they are implemented as polymorphic basic building blocks. These blocks are lightweight, share a common communication protocol and can be composed in almost arbitrary manner leading to simple and elegant construction techniques as well as to efficient implementations. We have implemented our methodology in MAM, the Modeling and Animation Machine. MAM is an extensible and portable C++ toolkit which offers a rich set of modeling, animation and interaction classes. It separates rendering and modeling and therefore allows easy integration of new modeling, rendering, and interaction techniques.