title: The measurement of distortion: mathematical considerations.
abstract: The proposed method for accurately determining the coordinates of given points in a three-dimensional space, along with the mathematical rigid body displacements to move these points into some predefined reference position, builds a complete model of the positional relationships of these points. On this basis additional information can easily be extracted, e.g., the distance between any two given points or the angle in degrees between any two given points or the angle in degrees between any three given points. An important advantage of the procedure is that the normally tedious calculations involved with distortions have been computerized, thus eliminating the tedium of repeated calculations. The possibility of calculation error is also reduced. Perhaps the greatest advantage to the investigator arises from the fact that once the procedural routine has been established and the computer programs written, the entire procedure can be done by technical personnel and does not necessarily require a large time committment from the principal researcher. Also, because of the normally small amount of time needed to read the coordinates and compute the inherent distortions, a set of computed distortions which appear unreasonable may be checked by repeating the entire set of coordinate readings and distortion calculations in a relatively short time.
mesh_terms: D000703:Analog-Digital Conversion; D003748:Dental Equipment; D008433:Mathematics; D008962:Models, Theoretical; D013499:Surface Properties