Merging and smoothing machining boundaries on cutter location surfaces

ABSTRACT

In region machining, neighbouring regions may be close together, but disconnected. Boundary curves may also have unwanted geometric artifacts caused by approximation and discretisation. We present a strategy to improve the topology and geometry of such boundary curves, allowing the generation of better tool paths, and in turn, improved tool wear and surface quality of the machined part. We make such improvements in three steps: firstly, disconnected regions are merged where appropriate, using a method based on morphological operations from image processing. Secondly, boundary segments with undesirable geometric properties are identified and replaced by simpler segments, using a vertex deletion operation. Finally, flaws at a smaller geometric scale are removed, using a curve shortening algorithm. Experimental results are given to illustrate our algorithm.

References

1. A M Bruckstein, G Sapiro, and D Shaked. Evolutions of planar polygons. International Journal of Pattern Recognition and Artificial Intelligence, 9(6):991--1014, 1995.
2. B K Choi, B H Kim, and R B Jerard. Sculptured surface nc machining. In G Farin, J Hoschek, and M-S Kim, editors, Handbook of Computer Aided Geometric Design, pages 543--574. Elsevier, 2002.
3. F Duguet and G Drettakis. Robust epsilon visibility. ACM Transactions on Graphics, 21(3):567--575, 2002.
4. M Eck and R Jaspert. Automatic fairing of point sets. In N S Sapidis, editor, Designing fair curves and surfaces, pages 44--60. SIAM, 1994.
5. A Flutter and J Todd. A machining strategy for toolmaking. Computer-Aided Design, 33(13):1009--1022, 2001.
6. Steve Hobbs. Personal communication, 2007.
7. M Hofer and H Pottmann. Energy-minimizing splines in manifolds. ACM Transactions on Graphics, 23(3):284--293, 2004.
8. G Mullineux and S T Robinsona. Fairing point sets using curvature. Computer-Aided Design, 39(1):27--34, 2007.
9. S C Park and B K Choi. Boundary extraction algorithm for cutting area detection. Computer-Aided Design, 33(8):571--579, 2001.
10. S P Radzevich. A cutting-tool-dependent approach for partitioning of sculptured surface. Computer-Aided Design, 37(7):767--778, 2005.
11. Y F Ren, W H Zhu, and Y-S Le. Material side tracing and curve refinement for pencil-cut machining of complex polyhedral models. Computer-Aided Design, 37(10):1015--1026, 2005.
12. W Renz. Interactive smoothing of digitized point data. Computer-Aided Design, 14(5):267--269, 1982.
13. P Soille. Morphological Image Analysis: Principles and Applications. Springer, 1999.
14. X N Yang and G Z Wang. Planar point set fairing and fitting by arc splines. Computer-Aided Design, 33(1):35--43, 2001.

Index Terms

• Applied computing

  • Arts and humanities

    • Architecture (buildings)

      • Computer-aided design

  • Operations research

    • Computer-aided manufacturing

  • Physical sciences and engineering

    • Engineering

      • Computer-aided design

• Computing methodologies

  • Computer graphics

    • Shape modeling

• Theory of computation

  • Randomness, geometry and discrete structures