The Matrix DVD contains an extensive interview with John Gaeta, the visual effects director for Manex, about how the film's bullet time sequences are composed. The movie's Web site at www.whatisthematrix.com contains a shorter synopsis. A brief walkthrough of the process:
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The entire shot is "sketched" using 3D modeling software, describing who is going to be in what position when the camera is in a certain spot.
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The "bullet time" room is set up with bright green walls, floors, and ceiling, while a series of identical digital cameras are positioned in holes behind movable bright green panels. Computer-guided lasers are used to place each camera as precisely as possible, based on the computer-generated "sketch". High-speed full-motion cameras may be placed at either end of the sequence.
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The actor or actors are rigged up with wires, if necessary, in the center of the room. The cameras are all fired in sequence by a single computer, coordinated down to the millisecond. The entire take lasts for only a couple of seconds in real time, if that.
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Now, the post-production begins. First, the wires are removed digitally.
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Since the digital cameras can only be spaced so close together, computer software is used to interpolate the missing frames to produce a smooth effect.
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3D modeling software is used to create a virtual background for the shot, based on photos of the actual room. The "sketch" is used to move a virtual camera around this room to exactly match the positions of the digital cameras.
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The background and actors are composited together, frame by frame, to produce the complete shot.
End result: a few hundred man-hours and computer hours to produce between three and fifteen seconds of eye candy. Of course, it falls to the director to make sure they were hours well-spent; special effects are only as good as the story around it.