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Pocket Machining Based on Offset Curves



Voronoi Diagrams of 2D shapes are a very powerful tool which make the generation of offset tool paths for pocket machining relatively easy. My own pocketing program, which is based on (an early version of) one of my Voronoi codes,

May 16, 2000: I have finally managed to start working on WWW pages for VRONI, my newest Voronoi algorithm and code. If the theory and application of Voronoi diagrams of points and line segments in 2D is of interest to you then you may want to visit VRONI's home page. (The VD/pocketing code described on this page will be out of date once VRONI is available; please note that I won't hand out that code any longer.)


Related publications:

M. Held (1991):
``On the Computational Geometry of Pocket Machining''.
Lecture Notes in Computer Science, vol. 500, Springer-Verlag, June 1991. ISBN 3-540-54103-9.

M. Held, G. Lukács, L. Andor (1994):
``Pocket Machining Based on Contour-Parallel Tool Paths Generated by Means of Proximity Maps''.
Computer-Aided Design 26(3):189--203, March 1994.


The following images have been generated by means of the pocketing package LARK, as described in the CAD paper referenced above.


[Image of Offset Tool Path] This image shows a logo, as it is common in the sign-production business.

[Image of Offset Tool Path] This image shows the Voronoi diagram of the logo; every individual Voronoi region was assigned a random color. Note that the Voronoi regions were subdivided at the straits of the logo.

[Image of Offset Tool Path] This image shows the offset-connected subareas, which where computed by means of the Voronoi diagram. Random colors were assigned to the individual areas.



The following images show tool paths for sample pockets which were computed by means of my pocketing code. (Click on an image icon in order to see the full-size image. The full-size images have 1000x700 pixels.) Please note: all visible discontinuities are nothing but graphics artifacts - of course, the offsets represent continuous curves!


[Image of Offset Tool Path] This polygonal star consists of 320 contour segments. Computing its offset tool path (based on its Voronoi diagram) took 30 milliseconds on a Sun SPARCstation 10.

[Image of Offset Tool Path] This polygonal flower consists of 1024 contour segments. Computing its offset tool path (based on its Voronoi diagram) took 80 milliseconds on a Sun SPARCstation 10.

[Image of Offset Tool Path] This smooth polygonal shape consists of 8,192 contour segments. Computing its offset tool path (based on its Voronoi diagram) took 610 milliseconds on a Sun SPARCstation 10.

[Image of Offset Tool Path] This simplified map of Austria contains 1 hole and consists of a total of 116 contour segments. Computing its offset tool path (based on its Voronoi diagram) took 30 milliseconds on a Sun SPARCstation 10.

[Image of Offset Tool Path] The cover logo of my Habilitationsschrift contains 31 curvilinear contours and consists of a total of 189 contour segments (straight lines and circular arcs). Computing its offset tool path (based on its Voronoi diagram) took 50 milliseconds on a Sun SPARCstation 10.


[Image of CS Logo]
file last modified: Tuesday, 06-Aug-2013 11:58:51 CEST
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