A robust 2D point-sequence curve offset algorithm with multiple islands for contour-parallel tool path

An offset algorithm is important to the contour-parallel tool path generation process. Usually, it is necessary to offset with islands. In this paper a new offset algorithm for a 2D point-sequence curve (PS-curve) with multiple islands is presented. The algorithm consists of three sub-processes, the islands bridging process, the raw offset curve generation and the global invalid loops removal. The input of the algorithm is a set of PS-curves, in which one of them is the outer profile and the others are islands. The bridging process bridges all the islands to the outer profile with the Delaunay triangulation method, forming a single linked PS-curve. With the fact that local problems are caused by intersections of adjacent bisectors, the concept of stuck circle is proposed. Based on stuck circle, local problems are fixed by updating the original profile with the proposed basic rule and append rule, so that a raw offset curve can be generated. The last process first reports all the self-intersections on the raw offset PS-curve, and then a procedure called tree analysis puts all the self-intersections into a tree. All the points between the nodes in even depth and its immediate children are collected using the collecting rule. The collected points form the valid loops, which is the output of the proposed algorithm. Each sub-process can be complete in near linear time, so the whole algorithm has a near linear time complexity. This can be proved by the examples tested in the paper.

► Islands are bridged to the outer profile in near linear time.
► The concept of a stuck circle is proposed.
► Two profile updating rules are proposed, the basic rule and the append rule.
► A tree analysis (TA) procedure is proposed to remove global invalid loops.