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