A Parametrization Scheme for the Burmester Curves
Abstract The cubic representation of the Burmester curve in Cartesian coordinates has certain disadvantages when automated searches are carried out. A parametric representation of the curve would be ideal. A systematic search could then be carried out by tracking points in a continuous fashion along the curve. In addition, solution rectification methods could be applied to determine the feasible segments, and the search could be limited to those portions only. This paper presents an alternative scheme for parametrizing the Burmester curves, as opposed to the complex number approach used by Chase et al. It uses the graphical method as its basis. The final scheme is not single valued, as it involves a parameter value as well a sign variable, but otherwise fulfils the requirements for an automatic search. It is an improvement on the cubic representation as it is double valued, rather than triple valued. The basic theory associated with the parametrization and the issues arising out of it are developed.