| Traditionally, cinematrographic analyses of motion have been performed using the so-called 'multiplier' technique. This is a planar technique in which the loci of the points under examination must be confined to a unique plane, the plane of motion. In this technique, a single camera is positioned at a convenient distance from the subject, with its film plane aligned parallel to the plane of motion. During data reduction, an image of known length, held in the plane of motion, is used to obtain a single scaling coefficient for converting image-displacements to real-scale, relative displacements in the plane of motion.;The techniques described are similar to those employed in analytical photogrammetry. They do not limit the investigator to particular camera configurations. Applications of the generalized three-dimensional technique require information from a minimum of two distinct views, but information from any number of views can be treated in a unified fashion to improve the final estimate for the required object-coordinates. Applications of the generalized planar technique can be made using information from a single camera. In this case, the motion under investigation must be confined to a single plane, but the film plane(s) of the camera(s) need not be aligned parallel to this plane. A refined version of the generalized three-dimensional technique is also described. This corrects for lens distortions and linear film deformations. The analytical basis for the new techniques is developed from elementary principles, and successive reductions of the generalized three-dimensional model are used to show the underlying assumptions associated with the 'multiplier' technique.;Although analytical details are provided, the development of a research tool which can be applied with a minimal comprehension of the associated theory is emphasized, and an entire chapter is devoted to the practical aspects of the new techniques. Included here are discussions of timing devices, time-matching techniques, methods for providing control information, and ways to perform numerical checks. The latter can be done by manipulating the calibration data to produce estimates for the camera position, and other values which can be measured during data collection and data reduction. An extensive glossary and a comprehensive bibliography are also included.;Four, well-documented computer programs, written in ANS FORTRAN, are contained in an appendix. The first of these programs, TMATCH, time-matches data recovered from different views using linear interpolation. The output produced by TMATCH can be fed directly into JSW2D or JSW3D. These programs perform the analytical reconstruction of the object-coordinates for planar or three-dimensional trajectories, respectively. Finally, the output from either of these programs can be fed into FILTER, which reduces noise in the reconstructed loci by applying a low-pass, Butterworth filter to contiguous blocks of coordinates.;New cinematographic techniques for performing two and three-dimensional analyses are described. Transformations between-object-coordinates and image-coordinates are developed. These, in conjunction with a number of control points--with known locations--are used to calibrate the various image-spaces. (Image space: a sequence of images which have undergone the same optical transformations.) The calibration data, together with the image-coordinates of a moving target, are used to generate the object-coordinates of the target for a particular instant.;Validations of the new techniques show that, using object-distances of approximately 35 feet, the center of a golf ball can be located to within .1 inch of its true, three-dimensional location. The acceleration of the center of mass of a spinning, yet freely falling trampolinist is determined and compared with the acceleration due to gravity. A maximum deviation of 1.5% is recorded over three replications. |
