COVERING A SET OF POINTS WITH A MINIMUM NUMBER OF TURNS
MICHAEL J. COLLINS · International Journal of Computational Geometry & Applications · 2004
Given a finite set of points in Euclidean space, we can ask what is the minimum number of times a piecewise-linear path must change direction in order to pass through all of them. We prove some new upper and lower bounds for the rectilinear version of this problem in which all motion is orthogonal to the coordinate axes. We also consider the more general case of arbitrary directions.