EQUILIBRIA OF THE CURVATURE FUNCTIONAL AND MANIFOLDS OF NONLINEAR INTERPOLATING SPLINE CURVES

摘要

The mathematical formulation of curve fitting by mechanical splines, i.e. thin, flexible, elastic beams passing through freely rotating sleeves anchored at fixed locations, is studied in this report. These are called elastica or nonlinear spline curves. As contrasted with the mathematically idealized splines, which have proven to be of considerable utility and concerning which much information is available, the nonlinear splines are relatively poorly understood. The writers are attempting to understand and systematically construct these curves. Computer graphics obtained by other workers suggest remarkable efficiency of the elastica for curve fitting. This is perhaps not too surprising since the nonlinear spline represents an equilibrium position of a thin beam.