Since some practical areas of computer science, such as computer graphics, computeraided design, robotics, and pattern recognition, give rise to geometrical problems, Voronoi diagrams have broad areas of application. Voronoi diagrams also have popular application in machining toolpath planning, using a contour-parallel strategy. When the contour-parallel strategy is applied to the machining toolpath planning, geometric degeneracies can occur and significantly require complicated and time-consuming computations of offset curves. The best way to deal with geometric degeneracies is with the bisector on each endpoint of the contour segment of the Voronoi diagrams. If islands are considered in the toolpath planning, it is essential to calculate the minimum passage width between islands, or between islands and contour segments. Furthermore, if the machining process is taken into account, it is also important to detect the location and thickness of thin walls in a pocket to avoid the machining damage on the working material. This paper presents the incremental algorithms based on the computations of offset curves to calculate the minimum passage width and to detect thin walls in pocket machining toolpath planning.
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