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Incremental algorithms of finding offset distance and minimum passage width using Voronoi diagram technique [CAM machining]

Since some practical areas, such as computer graphics, computer-aided design, robotics, pattern recognition, and finite element methods, give rise to geometrical problems, Voronoi diagrams have broad areas of application, such as mesh generation in FEA (finite element analysis) and machining toolpath planning in CAM (computer-aided manufacturing) for NC pocket machining. When the mesh generation is applied in FEA, the information for extraction of geometric proximity is important. When the contour-parallel strategy is applied to machining toolpath planning, geometric degeneracies can occur and significantly require the performance of complicated and time-consuming computations of offset curves. The best way to deal with geometric proximity and geometric degeneracies is with Voronoi diagrams. If islands are considered in machining toolpath planning, it is necessary to calculate the minimum passage width between islands, or between islands and contour segments. This paper presents the incremental algorithms of the Voronoi diagram technique to calculate the offset distance for offset curves and the minimum passage width for pocket machining toolpath planning.