Pocket machining based on contour-parallel tool paths generated by means of proximity maps

Held, Martin; Lukács, Gábor; Andor, László

doi:10.1016/0010-4485(94)90042-6

Cited by 153 publications

(50 citation statements)

References 15 publications

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“…(Voronoi edges that meet reflex vertices of the polygon are technically not part of the medial axis.) Medial axes are used in several applications, including shape recognition and reconstruction [16], [18], [64], mesh generation [40], [58], [61], [62], motion planning [55], [60], and computer-aided manufacturing [41], [42], [61]. Despite these many uses of medial axes, their curved arcs have been considered a shortcoming and have led several researchers to form piecewise-linear approximations by sampling the input [61], rectilinear Voronoi diagrams [61], or other techniques [17], [51].…”

Section: Introductionmentioning

confidence: 99%

Raising Roofs, Crashing Cycles, and Playing Pool: Applications of a Data Structure for Finding Pairwise Interactions

Eppstein¹,

Erickson²

1999

Discrete Comput Geom

144

165

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The straight skeleton of a polygon is a variant of the medial axis introduced by Aichholzer et al., defined by a shrinking process in which each edge of the polygon moves inward at a fixed rate. We construct the straight skeleton of an n-gon with r reflex vertices in time O(n 1+ε + n 8/11+ε r 9/11+ε ), for any fixed ε > 0, improving the previous best upper bound of O(nr log n). Our algorithm simulates the sequence of collisions between edges and vertices during the shrinking process, using a technique of Eppstein for maintaining extrema of binary functions to reduce the problem of finding successive interactions to two dynamic range query problems: (1) maintain a changing set of triangles in R 3 and answer queries asking which triangle is first hit by a query ray, and (2) maintain a changing set of rays in R 3 and answer queries asking for the lowest intersection of any ray with a query triangle. We also exploit a novel characterization of the straight skeleton as a lower envelope of triangles in R 3 . The same time bounds apply to constructing non-self-intersecting offset curves with mitered or beveled corners, and similar methods extend to other problems of simulating collisions and other pairwise interactions among sets of moving objects.

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Section: Introductionmentioning

confidence: 99%

Raising Roofs, Crashing Cycles, and Playing Pool: Applications of a Data Structure for Finding Pairwise Interactions

Eppstein¹,

Erickson²

1999

Discrete Comput Geom

144

165

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show abstract

“…Offsetting is a fundamental operation for planar shapes, and it is needed frequently, e.g., in computer-aided manufacturing [16,26]. Several authors base their offsetting algorithms on the Voronoi diagram or the medial axis [16,13,4].…”

Section: Trimmed Offsetsmentioning

confidence: 99%

“…Several authors base their offsetting algorithms on the Voronoi diagram or the medial axis [16,13,4]. Once more, a PC-representation of the input shape is advantageous, because the class of such shapes is closed under offsetting operations.…”

Section: Trimmed Offsetsmentioning

confidence: 99%

Divide-and-conquer for Voronoi diagrams revisited

Aichholzer

Aigner

Aurenhammer

et al. 2009

Proceedings of the Twenty-Fifth Annual Symposium on Computational Geometry

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We show how to divide the edge graph of a Voronoi diagram into a tree that corresponds to the medial axis of an (augmented) planar domain. Division into base cases is then possible, which, in the bottom-up phase, can be merged by trivial concatenation. The resulting construction algorithm-similar to Delaunay triangulation methods-is not bisector-based and merely computes dual links between the sites, its atomic steps being inclusion tests for sites in circles. This guarantees computational simplicity and numerical stability. Moreover, no part of the Voronoi diagram, once constructed, has to be discarded again. The algorithm works for polygonal and curved objects as sites and, in particular, for circular arcs which allows its extension to general free-form objects by Voronoi diagram preserving and data saving biarc approximations. The algorithm is randomized, with expected runtime O(n log n) under certain assumptions on the input data. Experiments substantiate an efficient behavior even when these assumptions are not met. Applications to offset computations and motion planning for general objects are described.

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“…NC machining is one of the most common manufacturing scheme available nowadays [1][2][3], [10][11][12], [15], [17][18], [20]. For example, forming die-cavities [2] is one such application.…”

Section: Introductionmentioning

confidence: 99%

C¹Continuous Toolpath Generation Toward 5-axis High Speed Machining

Elber

Cohen

Drake

2006

Computer-Aided Design and Applications

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We present a scheme to construct C 1 continuous toolpath for 5-axis pocketing of high speed machining. A continuous toolpath synthesis is proposed, that forms out circular segments of maximally inscribed sizes and linear segments connecting these circular segments. Extending earlier work that employed the Medial Axis Transform to compute these maximally inscribed circles for 2D planar pockets, this work examines general pockets in ℜ 3 represented as NURBS surfaces, and in 5-axis machining setup. Results are demonstrated by employing t he proposed scheme toward the machining of impellers. Possible extensions toward a C 2 continuous toolpath is discussed as well.

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Pocket machining based on contour-parallel tool paths generated by means of proximity maps

Cited by 153 publications

References 15 publications

Raising Roofs, Crashing Cycles, and Playing Pool: Applications of a Data Structure for Finding Pairwise Interactions

Raising Roofs, Crashing Cycles, and Playing Pool: Applications of a Data Structure for Finding Pairwise Interactions

Divide-and-conquer for Voronoi diagrams revisited

C¹Continuous Toolpath Generation Toward 5-axis High Speed Machining

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Pocket machining based on contour-parallel tool paths generated by means of proximity maps

Cited by 153 publications

References 15 publications

Raising Roofs, Crashing Cycles, and Playing Pool: Applications of a Data Structure for Finding Pairwise Interactions

Raising Roofs, Crashing Cycles, and Playing Pool: Applications of a Data Structure for Finding Pairwise Interactions

Divide-and-conquer for Voronoi diagrams revisited

C1Continuous Toolpath Generation Toward 5-axis High Speed Machining

Contact Info

Product

Resources

About

C¹Continuous Toolpath Generation Toward 5-axis High Speed Machining