Report Number: CS-TR-71-229
Institution: Stanford University, Department of Computer Science
Title: Variational study of nonlinear spline curves
Author: Lee, Erastus H.
Author: Forsythe, George E.
Date: August 1971
Abstract: This is an exposition of the variational and differential properties of nonlinear spline curves, based on the Euler-Bernoulli theory for the bending of thin beams or elastica. For both open and closed splines through prescribed nodal points in the euclidean plane, various types of nodal constraints are considered, and the corresponding algebraic and differential equations relating curvature, angle, arc length, and tangential force are derived in a simple manner. The results for closed splines are apparently new, and they cannot be derived by the consideration of a constrained conservative system. There is a survey of the scanty recent literature.