An algorithm is given for
calculating the curvature of 3-dimensional curves from measurements made along
the curve by a robot desiring to determine the curve. It is well known that such curves are
fixed by their curvature and torsion parameters measured in terms of the arc
length along the curve. We have shown [1] that these parameters form a
convenient characterization for use by robots, especially since the curvature
and torsion can nicely be evaluated in terms of local Euler angles. However, in
making such evaluations it becomes necessary to correctly position the normal
vector which in turn determines the curvature, the latter being the reciprocal
of the radius of the oscillating circle at a given point [2, p. 101]. In this paper
we develop an algorithm for positioning this normal and for evaluating the
oscillating circle's radius using the vector analysis formulation developed in
[2].
[1] R. W. Newcomb and D.
Panagiotopoulos, "Equations for Robot 3D Curve Determination Decisions,"
Proceedings of the 22nd IEEE Conference on Decision & Control, Vol. 3,San
Antonio, December 16, 1983, pp. 1222 - 1223.
[2] I. D. Faux and M. J. Pratt,
"Computational Geometry for Design and Manufacture," Ellis Horwood
Ltd, Chichester, 1979.