Skip to main content
Log in

Real-time triangulation of point streams

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

Hand-held laser scanners are commonly used in industry for reverse engineering and quality measurements. In this process, it is difficult for the human operator to scan the target object completely and uniformly. Therefore, an interactive triangulation of the scanned points can assist the operator in this task. In this paper, we describe the technical and implementational details of our real-time triangulation approach for point streams, presented at the 17th International Meshing Roundtable. Our method computes a triangulation of the point stream generated by the laser scanner online, i.e., the data points are added to the triangulation as they are received from the scanner. Multiple scanned areas and areas with a higher point density result in a finer mesh and a higher accuracy. On the other hand, the vertex density adapts to the estimated surface curvature. To guide the operator, the resulting triangulation is rendered with a visualization of its uncertainty and the display of an optimal scanning direction.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Akkiraju N, Edelsbrunner H, Facello M, Fu P, Mücke E, Varela C (1995) Alpha shapes: definition and software. In: 1st International computational geometry software workshop, pp 63–66

  2. Alexa M, Behr J, Cohen-Or D, Fleishman S, Levin D, Silva C (2003) Computing and rendering point set surfaces. IEEE Trans Vis Comput Graphics 9(1):3–15

    Article  Google Scholar 

  3. Allègre R, Chaine R, Akkouche S (2007) A streaming algorithm for surface reconstruction. In: Symposium on Geometry Processing, pp 79–88

  4. Amenta N, Choi S, Kolluri R (2001) The power crust. In: 6th ACM symposium on solid modeling and applications, pp 249–266

  5. de Berg M, van Kreveld M, Overmars M, Schwarzkopf O (2000) Computational geometry. Springer, Berlin

  6. Bodenmüller T, Hirzinger G (2004) Online surface reconstruction from unorganized 3d-points for the DLR hand-guided scanner system. In: 2nd Symposium on 3D data processing, visualization and transmission, pp 285–292

  7. Chaine R (2003) A geometric convection approach of 3-d reconstruction. In: Sympoisum on geometry processing, pp 218–229

  8. Denker K, Lehner B, Umlauf G (2008) Live scanning video. http://cg.cs.uni-kl.de/denker/scanning.avi

  9. Denker K, Lehner B, Umlauf G (2008) Online triangulation of laser-scan data. In: Garimella R (ed) 17th International Meshing Roundtable, pp 415–432

  10. Dyer R, Zhang H, Möller T (2007) Delaunay mesh construction. In: Symposium on geometry processing, pp 273–282

  11. Edelsbrunner H, Kirkpatrick D, Seidel R (1983) On the shape of a set of points in the plane. IEEE Trans Inf Theory 29(4):551–559

    Article  MathSciNet  MATH  Google Scholar 

  12. Edelsbrunner H, Mücke E (1994) Three-dimensional alpha shapes. ACM Trans Graph 13(1):43–72

    Article  Google Scholar 

  13. Faro Europe GmbH & Co. KG (2008) http://www.faro.com

  14. Hjelle Ø, Dæhlen M (2006) Triangulations and applications. Springer, Berlin

  15. Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W (1992) Surface reconstruction from unorganized points. Comput Graph 26(2):71–78

    Article  Google Scholar 

  16. Jolliffe I (2002) Principal component analysis. Springer, Berlin

  17. Kolluri R, Shewchuk JR, O’Brien J (2004) Spectral surface reconstruction from noisy point clouds. In: Symposium on geometry processing, pp 11–21

  18. Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3d surface construction algorithm. SIGGRAPH Comput Graph 21(4):163–169

    Article  Google Scholar 

  19. Marcks G (1952) Bildnis Theodor Heuss. In: “Pfalzgalerie Kaiserslautern”, permanent loan from “Vereinigung Pfälzer Kunstfreunde” (VPK). Bronze sculpture, 31.5 × 21 × 23.5 cm

  20. Prautzsch H, Boehm W, Paluszny M (2002) Bezier and B-spline techniques. Springer, Berlin

  21. Schneider J, Scheidegger CE, Fleishman S, Silva CT (2006) Direct (re)meshing for efficient surface processing. Comp Graph Forum 25(3):527–536

    Article  Google Scholar 

  22. Smith O (1961) Eigenvalues of a symmetric 3 × 3 matrix. Comm ACM 4:168

    Article  MathSciNet  Google Scholar 

  23. Teichmann M, Capps M (1998) Surface reconstruction with anisotropic density-scaled alpha shapes. In: IEEE conference on visualization, pp 67–72

Download references

Acknowledgments

This work was supported by DFG IRTG 1131 “Visualization of large and unstructured data sets.” We also thank Faro Europe for lending out their “Laser ScanArm” and “Pfalzgalerie Kaiserslautern” and “Vereinigung Pfälzer Kunstfreunde (VKP)” for their generous support with the sculpture [19]. In particular, we thank Peter Salz for his help on the implementation of the visualizations of the optimal scanning direction.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Klaus Denker.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Denker, K., Lehner, B. & Umlauf, G. Real-time triangulation of point streams. Engineering with Computers 27, 67–80 (2011). https://doi.org/10.1007/s00366-010-0181-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-010-0181-y

Keywords

Navigation