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Although the scene is decomposed naturally into components, some global objects remain. One of them is the constraint handler, which maintains a list of all constraints and observes deviations from the specified constraints (an object moving out of its joint, etc.). Then a numerical solver is called to compute forces that correct this deviation.
It is difficult to decompose this process into separate objects, since, potentially, arbitrary interactions exist. E.g., when two objects collide, interactions between their parts have to be computed. This is initiated by the collision detector, which creates a new constraint object when it signals a collision. This contraint object contains references to the colliding objects and represents the physical interaction between them. Again, the collision detector is a typical global object. It is a topic of active research to decompose the activity of the collision detector, especially in order to improve performance.