SECRETS OF A HOMICIDE: Science of Motion

Aligning 3D models with the Zapruder film

To begin the process of recreating the assassination sequence, it was necessary to position the virtual camera at the exact location occupied by Zapruder's original camera. It's possible to determine a camera's location in three-space by triangulating three or more fixed points visible in its field of view.

Triangulation is a highly accurate way of computing the six degrees of a camera's freedom - X, Y, Z, heading, pitch, and bank - based on camera footage. This technique is used by many of the world's best special effects masters to seamlessly match computer generated imagery with live action footage without the use of a motion control rig.

To avoid errors in camera placement, triangulation points were not selected from any cosmetic portions of the 3D models - road stripes, trees, or traffic signs. Only fixed triangulation points - monuments, buildings, roadways, curbs and sidewalks - were used to position the camera.

Once the camera position was determined, the location of the Stemmons freeway sign was triangulated using the same fixed points.

The resulting position was then compared with virtual recreations of many other assassination photographers including Phil Willis, Wilma Bond, Hugh Betzner, Jr., and Charles Bronson. This method insured the proper placement of the sign as it appeared at the time of the shooting.

The same method was employed to position both the R.L. Thornton Freeway and the Ft. Worth Turnpike road signs. In addition, trees, lampposts and other decorative objects were added to the scene using triangulation.

Once the virtual model of Dealey Plaza was completed, the process of recreating the path and motion of the presidential limousine and its occupants began. The first issue to deal with was one of timing. Zapruder's Bell & Howell Zoomatic camera operated at an average speed of 18.3 frames per second. The final animated recreation was intended to be rendered and displayed in a digital video format, which is timed at 29.97 (30) frames per second. (To simplify the process, 30 frames were produced to represent each second of motion.) Producing the final animation in a digital video format would provide a sample rate that is nearly twice that of the original recording - providing a smoother, higher quality motion sequence. A simple math formula provides the necessary conversion rate: 30 (fps) divided by 18.3 (fps) = 1.6393442 digital animation frames exposed for every Zapruder frame.

Since the computer program used for the recreation, LightWave 3D, allows frame rate conversions to be made after the animation process, it was decided that the simplest approach would be to produce a frame-for-frame match of the Zapruder film (18.3 fps), then, convert to the higher sample rate (30 fps) at render time. (The consequence of this process is that none of the final animation frames will exactly match any given frame of the Zapruder film. That's because the sample rate of the Zapruder film (18.3 fps) will never exactly coincide with the animation frame rate (30 fps). [i.e., the moments in time recorded by Zapruder's camera (1/18.3 of second intervals) are different than those rendered by the computer (1/30 of second intervals)] In short, the animated recreation can be better thought of as a re-photographing of the assassination sequence as recorded by Zapruder's camera.)

Before proceeding, it's necessary to understand how motion paths are created within computer environments. There are two kinds of basic motion paths that objects can follow in computer animation: linear and spline based.

Linear-based motion paths represent constant velocity. For example, if an object moved from point-A to point-B and the time it took to traverse this distance was 1-second, at 30 frames-per-second, the computer would calculate the motion path as 30 equal divisions between point-A and point-B.

Linear-based motion paths are not quite as realistic as spline-based motion paths, since physical objects of any mass never follow constant velocities.

Spline-based motion paths, on the other hand, allow for the slowing down and speeding up of objects as they change velocity. The speed at which these ease-ins and ease-outs occur is under the control of the animator using spline curves. A spline-based motion path created between the same two points mentioned above, over an equal time period, would not contain 30 equal divisions. Instead, an object which began at point-A, gradually picked up speed, and then slowed to a stop at point-B would reveal a spline curve that had small divisions at the beginning, grew to longer divisions, then settled back into shorter divisions.

This concept of motion is important because it is the backbone of numeric interpolation. An object of a given mass moving from point-A to point-B at a given velocity follows a predictable path. The shorter the distance between point-A and point-B, the more accurate the interpolation - or, if you will, prediction.

Distances covered by an object in less than a second are free from interpolation error as long as the rate of change in velocity is small, hence, the ability of the computer to predict where an object is when it is obscured from view for short periods of time.

[BACK][TOP][NEXT]