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A simple method for invalid loops removal of planar offset curves

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Abstract

The function of curve offset is of importance in the process of generating a machining tool-path. The robustness of curve offset is compact with reliable invalid loops removal algorithms. The traditional method based on interference detections in searching for all contact positions is a time consuming process and prone to misunderstanding. In order to improve such removal function, a new algorithm called the forward locus tracing method (FLTM) was introduced here. The FLTM searches for all intervals split by intersections of complicated planar curves directly and transforms 2D transversal intersection problems into 1D interval identifications. This proposed mapping process in FLTM may simplify the structure of tasks and be implemented by a computer program easily for CAD systems. Some examples with multiple loops were demonstrated and the results present considerable efficiency and reliability in the offset operation.

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References

  1. Held M (1998) Voronoi diagrams and offset curves of curvilinear polygons. Comput Aided Des 30(4):287–300

    Article  MATH  Google Scholar 

  2. You CF, Sheen BT, Lin TK (2001) Robust spiral tool-path generation for arbitrary pockets. Adv Manuf Technol 17:181–188

    Article  Google Scholar 

  3. Choi BK, Kim BH (1997) Die-cavity pocketing via cutting simulation. Comput Aided Des 29:837–846

    Article  Google Scholar 

  4. Held M, Lukacs G, Andor L (1994) Pocket machining based on contour-parallel tool paths generation by means of proximity maps. Comput Aided Des 26(3):495–506

    Article  Google Scholar 

  5. Lee IK, Kim MS, Elber G (1996) Planar curve offset based on circle approximation. Comput Aided Des 28:617–630

    Article  MATH  Google Scholar 

  6. Rohmfeld RF (1998) IGB-offset for plane curves – loop removal by scanning of interval sequences. Comput Aided Geom Des 15:339–375

    Article  MATH  MathSciNet  Google Scholar 

  7. Park SC, Choi BK (2001) Uncut free pocketing tool-paths generation using pair-wise offset algorithm. Comput Aided Des 33:739–746

    Article  Google Scholar 

  8. Lee E (2003) Contour offset approach to spiral toolpath generation with constant scallop height. Comput Aided Des 35:511–518

    Article  Google Scholar 

  9. Kalmanovich G, Nisnevich G (1998) Swift and stable polygon growth and broken line offset. Comput Aided Des 30(11):847–852

    Article  MATH  Google Scholar 

  10. Kim DS (1998) Polygon offsetting using a Voronoi diagram and two stacks. Comput Aided Des 30(14):1069–1076

    Article  MATH  Google Scholar 

  11. Choi HI, Han CY, Moon HP, Roh KH, Wee NS (1999) Medial axis transform and offset curves by Minkowski Pythagorean hodograph curves. Comput Aided Des 31:59–72

    Article  MATH  Google Scholar 

  12. Shan Y, Wang S, Togn S (2000) Uneven offset method of NC tool path generation for free-form pocket machining. Comput Ind 43:97–103

    Article  Google Scholar 

  13. Choi BK, Park SC (1999) A pair-wise offset algorithm for 2D point-sequence curve. Comput Aided Des 31:735–745

    Article  MATH  Google Scholar 

  14. Maekawa T (1999) An overview of offset curves and surface. Comput Aided Des 31:165–173

    Article  MATH  Google Scholar 

  15. Seiler A, Balendran V, Sivayoganathan K (1997) Tool interference detection and avoidance based on offset nets. Int J Mach Tools Manuf 37(5):717–722

    Article  Google Scholar 

  16. Barequet G, Briggs AJ, Dickerson MT, Goodrich MT (1998) Offset-polygon annulus placement problems. Comput Geom 11:125–141

    Article  MATH  MathSciNet  Google Scholar 

  17. Jeong J, Kim K (1999) Generating tool paths for free-form pocket machining using z-buffer-based Voronoi diagrams. Int J Adv Manuf Technol 15:182–187

    Article  Google Scholar 

  18. Tawfik T, Ahmed E, Hamdy T (2002) A sweep-line algorithm and its application to spiral pocketing. Int J CAD/CAM 2:23–28

    Google Scholar 

  19. Boissonnat JD, Snoeyink J (2000) Efficient algorithms for line and curve segment intersection using restricted predicates. Comput Geom 16:35–52

    Article  MATH  MathSciNet  Google Scholar 

  20. Gavrilova M, Rokne JG (2000) Reliable line segment intersection testing. Comput Aided Geom Des 32:737–745

    Google Scholar 

  21. Hu CY, Maekawa T, Sherbrooke EC, Patrikalakis NM (1996) Robust interval algorithm for curve intersections. Comput Aided Des 28(6):495–506

    Article  Google Scholar 

  22. Manocha D, Krishnan S (1997) Algebraic pruning: a fast technique for curve and surface intersection. Comput Aided Geom Des 14:823–845

    Article  MATH  MathSciNet  Google Scholar 

  23. Gupta P, Janardan R, Smid M (1996) Algorithms for generalized halfspace range searching and other intersection searching problems. Comput Geom 6:1–19

    Article  MATH  MathSciNet  Google Scholar 

  24. Banks DC (1997) Screen-parallel determination of intersection curves. Parallel Comput 23:953–960

    Article  MATH  Google Scholar 

  25. Andersson LE, Peters TJ, Stewart NF (1998) Selfintersection of composite curves and surfaces. Comput Aided Geom Des 15:507–527

    Article  MATH  MathSciNet  Google Scholar 

  26. Hobby JD (1999) Practical segment intersection with finite precision output. Comput Geom 13:199–214

    Article  MATH  MathSciNet  Google Scholar 

  27. Chan TM (2000) Reporting curve segment intersections using restricted predicates. Comput Geom 16:245–256

    Article  MATH  MathSciNet  Google Scholar 

  28. Lai W, Faddis T, Sorem R (2000) Incremental algorithms for finding the offset distance and minimum passage width in a pocket machining toolpath using the Voronoi technique. Mater Process Technol 100:30–35

    Article  Google Scholar 

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Correspondence to Yuan-Lung Lai.

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Lai, YL., Wu, JS., Hung, JP. et al. A simple method for invalid loops removal of planar offset curves. Int J Adv Manuf Technol 27, 1153–1162 (2006). https://doi.org/10.1007/s00170-004-2318-x

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  • DOI: https://doi.org/10.1007/s00170-004-2318-x

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