VRONI: An engineering approach to the reliable and efficient computation of Voronoi diagrams of points and line segments

In pocketing with contour parallel (CP) paths, the cutter encounters a varying engagement with the workpiece, which causes variation in chip load and cutting forces. This varying cutting force naturally leads to the variation of tool deflection, hence impairing machined surface accuracy. This paper presents a new tool path modification scheme, which regulates a constant cutting engagement with workpiece in 2.5D end milling. The semi-finishing path, the path prior to the finishing path, is modified by the proposed scheme such that the engagement angle along the finishing path is regulated at a desired level. By maintaining cutting engagement constant, the cutting force can be regulated approximately constant, thus minimizing the variation of tool deflection, and improving machining accuracy. The improvement of machining accuracy by applying the new tool path modification scheme is experimentally validated for the case where the proposed scheme is applied to pocketing. The machining results are analyzed and compared with the cases with conventional contour parallel path and the feed rate control scheme applied in pocketing.

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“…In this paper, we adopt the algorithm developed by Held (9) to compute parallel offsets based on the Voronoi diagram.…”

Section: Algorithm For Modified Constant Engagement (Ce) Tool Path Gementioning

confidence: 99%

Constant Engagement Tool Path Generation to Enhance Machining Accuracy in End Milling

Uddin

Ibaraki

Matsubara

et al. 2006

JSME Int. J., Ser. C

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“…A common approach is to rely on arbitrary precision representation and on exact geometric predicates [Shewchuk 1997;Devillers and Pion 2003], however imposing a significant performance penalty on the final system. Similarly to Held [2001], the presented approach provides a solution favoring speed of computation over accuracy. The presented solution is based on floating point arithmetic and relies on a carefully designed combination of robustness tests and one exact geometric predicate.…”

Section: Triangulationsmentioning

confidence: 99%

Dynamic and Robust Local Clearance Triangulations

Kallmann

2014

ACM Trans. Graph.

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The Local Clearance Triangulation (LCT) of polygonal obstacles is a cell decomposition designed for the efficient computation of locally shortest paths with clearance. This paper presents a revised definition of LCTs, new theoretical results and optimizations, and new algorithms introducing dynamic updates and robustness. Given an input obstacle set with n vertices, a theoretical analysis is proposed showing that LCTs generate a triangular decomposition of O(n) cells, guaranteeing that discrete search algorithms can compute paths in optimal times. In addition, several examples are presented indicating that the number of triangles is low in practice, close to 2n, and a new technique is described for reducing the number of triangles when the maximum query clearance is known in advance. Algorithms for repairing the local clearance property dynamically are also introduced, leading to efficient LCT updates for addressing dynamic changes in the obstacle set. Dynamic updates automatically handle intersecting and overlapping segments with guaranteed robustness, using techniques that combine one exact geometric predicate with adjustment of illegal floating point coordinates. The presented results demonstrate that LCTs are efficient and highly flexible for representing dynamic polygonal environments with clearance information.

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“…(Geometrically it falls precisely on the common end-point, but topologically it must be associated with the correct side.) This has proved difficult to achieve, and workers have spent a great deal of time attempting to construct robust algorithms (e.g [12], [13], [23]). …”

Section: The Kinetic Line-segment Vdmentioning

confidence: 99%