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Laser scan planning based on visibility analysis and space partitioning techniques


This paper presents a methodology to develop an automatic process planning system applied for scanning parts with free-form surfaces by using a laser stripe system mounted on a coordinate measuring machine (CMM). The part has been modelled using a STL format that permits the automatic recognition of any part surface. The valid orientations of the scanning device are obtained in order to guarantee the visibility of the zone to be scanned and also to be compatible with the constraints imposed by the process. With the aim to speed up the calculation of valid orientations, we apply different methods like space partitioning techniques base on kd-tree as well as back-face culling algorithms. Once the space occupied by the part is partitioned in regions, recursive ray traversal algorithms are used in order to exclusively check for intersection the part triangles of the STL model that can potentially be traversed by each laser beam direction. In order to reduce the scanning time related to laser orientation changes, part triangles must be classified into a set of clusters based on their common visibility orientations. Finally, the scanning paths for each cluster are generated as well as the joining paths between them by taking into consideration depth of field and laser beam width.

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  1. 1.

    Curless B, Levoy M (1995) Better Optical Triangulation through Spacetime Analysis. In: Proceedings of the 5th International Conference on Computer Vision, June 1995, Boston, MA, pp. 20–23

  2. 2.

    Hüser D, Rothe H (1998) Robust averaging of signals for triangulation sensors. Meas Sci Technol 9(7):1017–1023

  3. 3.

    Feng H-Y, Liu Y, Xi F (2001) Analysis of digitizing errors of a laser scanning system. Precis Eng 25(3):185–191

  4. 4.

    Kim K-C, Kim JA, Kim S, Kwak YK (2000) A robust signal processing algorithm for linear displacement measuring optical transmission sensors. Rev Scient Instrum 71(8):3220–3225

  5. 5.

    Harris JO, Spence AD (2004) Geometric and quasi-static thermal error compensation for a laser digitizer equipped coordinate measuring machine. Int J Mach Tools Manuf 44(1):65–77

  6. 6.

    Lai X, Lin Z, Huang T, Zeng Z (2001) A study of a reverse engineering system based on vision sensor for free-form surfaces. Comp Ind Eng 40(3):215–227

  7. 7.

    Sansoni G, Docchio F (2005) In-field performance of an optical digitizer for the reverse engineering of free-form surfaces. Int J Adv Manuf Technol 26(11-12):1353–1361

  8. 8.

    Galiò F, Moroni G, Rasella M (2003) A particular class of spline in reconstruction of revolution surfaces from 3-D data measured by CMM. Robot Comput Integr Manuf 19(1):219–224

  9. 9.

    Ueng W-D, Lai J-Y, Doong J-L (1998) Sweep-surface reconstruction from three-dimensional measured data. Comput Aided Des 30(10):791–805

  10. 10.

    Li L, Schemenauer N, Peng X, Zeng Y, Gu P (2002) A reverse engineering system for rapid manufacturing of complex objects. Robot Comput Integr Manuf 18(1):53–67

  11. 11.

    Sun W, Bradley C, Zhang YF, Loh HT (2001) Cloud data modelling employing a unified, non-redundant triangular mesh. Comp Aided Des 33(2):183–193

  12. 12.

    Tai C-C, Huang M-C (2000) The processing of data points basing on design intent in reverse engineering. Int J Mach Tools Manuf 40(13):1913–1927

  13. 13.

    Galetto M, Vezzetti E (2006) Reverse engineering of free-form surfaces: A methodology for threshold definition in selective sampling. Int J Mach Tools Manuf 46(10):1079–1086

  14. 14.

    Lee Y, Park S, Jun Y, Choi WC (2004) A robust approach to edge detection of scanned point data. Int J Adv Manuf Technol 23(3-4):263–271

  15. 15.

    Kruth J-P, Kerstens A (1998) Reverse engineering modelling of free-form surfaces from point clouds subject to boundary conditions. J Mater Process Technol 76(1):120–127

  16. 16.

    Karbacher S, Häusler G (1998) A new approach for modelling and smoothing of scattered 3D data. In: Ellson RN and Nurre JH (eds). Three-dimensional image capture and applications, The International society for optical engineering, vol. 3313, Bellingham, Washington, pp. 168–177

  17. 17.

    Yau H-T, Chen C-Y, Wilhelm RG (2000) Registration and integration of multiple laser scanned data for reverse engineering of complex 3D models. Int J Prod Res 38(2):269–285

  18. 18.

    Bradley C (2001) Rapid prototyping models generated from machine vision data. Comput Ind 44(2):159–173

  19. 19.

    Cheng WL, Cheng, Menq CH (1995) Integrated laser/CMM system for the dimensional inspection of objects made of soft material. Int J Adv Manuf Technol 5(10):36–45

  20. 20.

    Xi F, Shu C (1999) CAD-based path planning for 3-D line laser scanning. Comp Aided Des 31(7):473–479

  21. 21.

    Lee KH, Park H-P (2000) Automated inspection planning of free-from shape parts by laser scanning. Robot Comput Integr Manuf 16(4):201–210

  22. 22.

    Zussman E, Schuler H, Seliger G (1994) Analysis of the geometrical feature detectability constraints for laser-scanner sensor planning. Int J Adv Manuf Technol 9(1):56–64

  23. 23.

    Trucco E, Wallace AM, Roberto V (1997) Model-based planning of optimal sensor placements for inspection. IEEE Trans Robot Autom 13(2):182–194

  24. 24.

    Mahmud M, Joannic D, Fontaine J-F, Gonnet J-P (2005) Analyse de processus de numérisation de pièces tridimensionnelles complexes. In: 4th International conference of integrated design and production, Casablanca (Morocco), November, pp. 132–147

  25. 25.

    Elber G, Zussman E (1998) Cone visibility decomposition of freeform surfaces. Comp Aided Des 30(4):315–320

  26. 26.

    Son S, Park H-P, Lee KH (2002) Automated laser scanning system for reverse engineering and inspection. Int J Mach Tools Manuf 42(8):889–897

  27. 27.

    Son S, Kim S, Lee KH (2003) Path planning of multi-patched freeform surfaces for laser scanning. Int J Adv Manuf Technol 22(5):424–435

  28. 28.

    Milroy MJ, Bradley C, Vickers GW (1996) Automated laser scanning based on orthogonal cross sections. Mach Vis Appl 9(3):106–118

  29. 29.

    Fuchs H, Kedem ZM, Naylor BF (1980) On visible surface generation by a priori tree structures. In: Proceedings of the 7th annual conference on Computer graphics and interactive techniques (SIGGRAPH’80), ACM Press, Seattle, Washington, USA, 14(3) pp. 124–133

  30. 30.

    Kaplan M (1985) Space-tracing: A constant time ray-tracer. In State of the Art in Image Synthesis (SIGGRAPH’85), ACM Press, San Francisco, CA, USA, 18(3), pp. 149–158

  31. 31.

    Jansen FW (1986) Data structures for Ray Tracing. In: Kessener LRA et al (eds) Data structures for raster graphics, Springer-Verlag, Berlin, Germany, pp 57–73

  32. 32.

    Havran V (2000) Heuristic ray shooting algorithms. Ph. D. dissertation, Czech Technical University

  33. 33.

    Foley JD, van Dam A, Feiner SK, Hughes JF (1997) Visible-surface determination. In: Gordon PS (eds) Computer graphics, principles and practice, Addison-Wesley, Cornell, USA, pp 663–664

  34. 34.

    Möller TA, Trumbore B (1997) Fast, minimum storage ray/triangle intersection. J Graphics Tools 2(1):21–28

  35. 35.

    Gottschalk S, Lin MC, Manocha D (1996) OBBTree: a hierarchical structure for rapid interference detection. In: Proceedings of the 23rd Annual Conference on Computer Graphics (SIGGRAPH’96), ACM Press, New Orleans, LA, USA, 30, pp. 171–180

  36. 36.

    Eberly DH (2000) Geometrical methods. In: Cox T et al (eds) 3D Game engine design. A practical approach to real-time computer graphics, Morgan Kaufmann Publishers, San Diego, USA, pp 38–73

  37. 37.

    Schneider PJ, Eberly DH (2003) Distance in 3D. In: Cerra D et al (eds) Geometrical Tools for computer graphics, Morgan Kaufmann Publishers, San Francisco, USA, pp 365–477

  38. 38.

    Vafaeesefat A, ElMaraghy HA (2000) Automated accessibility analysis and measurement clustering for CMMs. Int J Prod Res 38(10):2215–2231

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Correspondence to J. Carlos Rico.

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Fernández, P., Rico, J.C., Álvarez, B.J. et al. Laser scan planning based on visibility analysis and space partitioning techniques. Int J Adv Manuf Technol 39, 699–715 (2008).

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  • Scanning
  • Laser stripe
  • Planning
  • Visibility
  • Space partitioning
  • CMM