UNIQUELY REPRESENTING POINT PATTERNS WITH MINIMAL INFORMATION

As an alternative to coordinate locations, patterns of points can be represented using interpoint distances. In certain applications, such as dimensioning and multidimensional scaling, interpoint distances have traditionally been used. In other applications, such as radar location, interpoint distance information is readily obtained. This paper utilizes kinematics, rigidity theory, and graph algorithms to determine the theoretical minimum interpoint distance information adequate for uniquely representing point patterns. It is shown that this theoretical minimum is comparable to that amount of information required by coordinate descriptions.