Polyline defined NC trajectories parametrization. A compact analysis and solution focused on 3D Printing

This paper consists of a formal analysis and one solid solution to the knot finding problem given a source polyline and a parametric curve (e.g. circular arc, ellipse or biarc). We solve the problem using both a greedy algorithm to collect possible arc candidates and a simple algorithm to decide their combination. The rise of 3D printing technology has made it necessary to gain control over how we describe trajectories to our machines. The common method to define paths on 3D printers is describing complex trajectories with high-density polylines. This is computationally expensive and establishes a limit to the greatest accuracy for a given moving speed. This work provides an analysis and a method to fit those polylines with a near-optimal distribution of circular arcs and straight segments.