The detection of collisions in an environment composed of two three-dimensional bodies traversing independent general three-dimensional trajectories is accomplished through the use of swept solids and solid modeling techniques. A swept solid represents the space volumetrically swept out by the motion of a given body along a given trajectory. A swept solid is created for each of the bodies in the given environment. Using the swept solids created for each body, calculations (solid modeling boolean intersections) can be performed to determine if these swept solids intersect. If the original bodies will collide while traversing their given trajectories, then their swept solids will statically interfere. Further, an object comprising the volume of the intersection can be created if the bodies do, in fact, interfere. This object can be thought of as the “volume of interference.” Enhancements to this technique provide for the formation of swept solids using relative motion. Through these enhancements, only one swept solid need be created since the absolute motions can be converted to motion of one body relative to another body. Therefore, intersection calculations may be performed between one relative swept solid and the original body.

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