 
Summary: Discrete approximations to continuous curves
Sean B. Andersson
Department of Aerospace and Mechanical Engineering
Boston University, Boston, MA 02215
Email: sanderss@bu.edu
Abstract We consider the problem of approximating a con
tinuous curve by a piecewise linear one whose segments are
assumed to be connected by universal joints. Rather than taking
a leastsquares approach, we require that the endpoints of the line
segments lie on the continuous curve. We show that under these
assumptions a single rotational degree of freedom remains. An
algorithm is derived to determine the set of angles characterizing
the relative orientation of each consecutive pair of line segments
as a function of this rotational degree of freedom. Two examples
are given to illustrate the procedure. The motivating application
for this work is the control of a snakelike robot using a set of
gaits designed from shape primitives.
I. INTRODUCTION
In this paper we consider the problem of approximating a
continuous parameterized 3D curve with a piecewise linear
