Incremental algorithms for finding the offset distance and minimum passage width in a pocket machining toolpath using the Voronoi technique

Some practical areas of computer science, such as computer graphics, computer-aided design, robotics, and pattern recognition, give rise to geometrical problems. Voronoi diagrams are useful in those cases. Another popular application is in machining toolpath planning, using a contour-parallel strategy. When the contour-parallel strategy is applied to machining toolpath planning, geometric degeneracies can occur and require the performance of complicated and significantly time-consuming computations of offset curves. The best way to deal with geometric degeneracies is with the bisector on each end-point of the contour segment of the Voronoi diagrams. Furthermore, if islands are considered in the toolpath planning, it is essential to calculate the minimum passage width between the islands, or between the islands and contour segments. The best way to deal with the minimum passage width is with the offset curves. This paper presents the incremental algorithms of the Voronoi diagram technique to calculate the offset distance and minimum passage width for toolpath planning.