Slicing point cloud incrementally for Additive Manufacturing via online learning


This paper reports an algorithm to chop point cloud into layer-wise slices for additive manufacturing. It starts with intersecting slicing plane with the 3D input points, generating planar samples. Then, an online learning model, known as competitive segments representation (CSR), extracts their implicit topology and distribution. CSR structure is a restricted graph that equals to multiple polylines, which are meanwhile piecewise linear approximation to the principal curves of samples. Edge segments of CSR compete with each other for representing consecutively given samples. They dynamically move, grow, shrink or rewire subject to several heuristic rules. Those rules are designed to depress abnormal data, enable lifelong learning, recover salient feature and ensure correct topology. Assembling them together allows online tracking of changing curves. Once CSR converges on one slice, learnt curves are reused as initial estimation for the next. By this practice, shape coherence of successive slices is efficiently utilized, and the ongoing learning output all subsequent slices incrementally. We have verified the feasibility of proposed algorithm both on synthesized data and scanned points.

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

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
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22


  1. 1.

    Zhang L, Dong H, Saddik AE (2016) From 3d sensing to printing: a survey. ACM Trans Multimed Comput Commun Appl 12(2):27

    Article  Google Scholar 

  2. 2.

    Gao W, Zhang Y, Ramanujan D et al (2015) The status, challenges, and future of additive manufacturing in engineering. Comput Aided Des 69:65–89

    Article  Google Scholar 

  3. 3.

    Mohan Pandey P, Venkata Reddy N, Dhande SG (2003) Slicing procedures in layered manufacturing: a review. Rapid Prototyp J 9(5):274–288

    Article  Google Scholar 

  4. 4.

    Hastie T, Stuetzle W (1989) Principal curves. J Am Stat Assoc 84(406):502–516

    MathSciNet  MATH  Article  Google Scholar 

  5. 5.

    Fritzke B (1994) A growing neural gas network learns topologies. In: Proceedings of the 7th international conference on neural information processing systems. MIT Press, Cambridge, MA, USA, pp 625–632

    Google Scholar 

  6. 6.

    Lee KH, Woo H (2000) Direct integration of reverse engineering and rapid prototyping. Comput Ind Eng 38(1):21–38

    MathSciNet  Article  Google Scholar 

  7. 7.

    Liu G, Wong Y, Zhang Y, Loh H (2003) Modelling cloud data for prototype manufacturing. J Mater Process Technol 138(1–3):53–57

    Article  Google Scholar 

  8. 8.

    Wu Y, Wong Y, Loh H, Zhang Y (2004) Modelling cloud data using an adaptive slicing approach. Comput Aided Des 36(3):231–240

    Article  Google Scholar 

  9. 9.

    Wang J, Yu Z, Zhang W et al (2014) Robust reconstruction of 2d curves from scattered noisy point data. Comput Aided Des 50(3):27–40

    Article  Google Scholar 

  10. 10.

    Goes Fd, Cohen-Steiner D, Alliez P, Desbrun M (2011) An optimal transport approach to robust reconstruction and simplification of 2d shapes. Comput Graph Forum 30(5):1593–1602

    Article  Google Scholar 

  11. 11.

    Chen JSS, Feng HY (2011) Contour generation for layered manufacturing with reduced part distortion. Int J Adv Manuf Technol 53(9–12):1103–1113

    Article  Google Scholar 

  12. 12.

    Javidrad F, Pourmoayed AR (2011) Contour curve reconstruction from cloud data for rapid prototyping. Robot Comput Integr Manuf 27(2):397–404

    Article  Google Scholar 

  13. 13.

    Xu J, Hou W, Sun Y, Lee YS (2018) Plsp based layered contour generation from point cloud for additive manufacturing. Robot Comput Integr Manuf 49:1–12

    Article  Google Scholar 

  14. 14.

    Sun Y, Guo D, Jia Z, Liu W (2006) B-spline surface reconstruction and direct slicing from point clouds. Int J Adv Manuf Technol 27(9–10):918–924

    Google Scholar 

  15. 15.

    Khameneifar F, Feng HY (2017) Extracting sectional contours from scanned point clouds via adaptive surface projection. Int J Prod Res 55(15):1–15

    Article  Google Scholar 

  16. 16.

    Liu GH, Wong YS, Zhang YF, Loh HT (2003) Error-based segmentation of cloud data for direct rapid prototyping. Comput Aided Des 35(7):633–645

    Article  Google Scholar 

  17. 17.

    Percoco G, Galantucci LM (2008) Local-genetic slicing of point clouds for rapid prototyping. Rapid Prototyp J 14(3):161–166

    Article  Google Scholar 

  18. 18.

    Kumbhar VK, Pandey PM, Rao PVM (2008) Improved intermediate point curve model for integrating reverse engineering and rapid prototyping. Int J Adv Manuf Technol 37(5–6):553–562

    Article  Google Scholar 

  19. 19.

    Yang P, Qian X (2007) Adaptive slicing of moving least squares surfaces: toward direct manufacturing of point set surfaces. J Manuf Sci Eng Trans ASME 8(3):433–442

    Google Scholar 

  20. 20.

    Qiu Y, Zhou X, Qian X (2011) Direct slicing of cloud data with guaranteed topology for rapid prototyping. Int J Adv Manuf Technol 53(1–4):255–265

    Article  Google Scholar 

  21. 21.

    Chen Y, Li K, Qian X (2013) Direct geometry processing for telefabrication. J Comput Inf Sci Eng 13(4):041002

    Article  Google Scholar 

  22. 22.

    Yang P, Li K, Qian X (2011) Topologically enhanced slicing of mls surfaces. J Comput Inf Sci Eng 11(3):031003

    Article  Google Scholar 

  23. 23.

    McMains S, Séquin C (1999) A coherent sweep plane slicer for layered manufacturing. In: Proceedings of the fifth ACM symposium on solid modeling and applications, pp 285–295

  24. 24.

    Minetto R, Volpato N, Stolfi J et al (2017) An optimal algorithm for 3d triangle mesh slicing. Comput Aided Des 92:1–10

    Article  Google Scholar 

  25. 25.

    Yaman U, Butt N, Sacks E, Hoffmann C (2016) Slice coherence in a query-based architecture for 3d heterogeneous printing. Comput Aided Des 75(C):27–38

    Article  Google Scholar 

  26. 26.

    Fritzke B (1997) A self-organizing network that can follow non-stationary distributions. In: Artificial neural networks—ICANN’97, pp 613–618

  27. 27.

    Araujo AFR, Rego RLME (2013) Self-organizing maps with a time-varying structure. ACM Comput Surv 46(1):1–38

    MATH  Article  Google Scholar 

  28. 28.

    López-Rubio E (2010) Probabilistic self-organizing maps for continuous data. IEEE Trans Neural Netw 21(10):1543–1554

    Article  Google Scholar 

  29. 29.

    Xing Y, Shi X, Shen F et al (2016) A self-organizing incremental neural network based on local distribution learning. Neural Netw 84:143–160

    Article  Google Scholar 

  30. 30.

    Vaswani N, Bouwmans T, Javed S, Narayanamurthy P (2018) Robust subspace learning: robust PCA, robust subspace tracking and robust subspace recovery. IEEE Signal Process Mag 35(4):32–55

    Article  Google Scholar 

  31. 31.

    López-Rubio E, Palomo EJ, Domínguez E (2015) Robust self-organization with m-estimators. Neurocomputing 151:408–423

    Article  Google Scholar 

  32. 32.

    Angelopoulou A, Rodriguez JG, Orts-Escolano S et al (2018) Fast 2d/3d object representation with growing neural gas. Neural Comput Appl 29(10):903–919

    Article  Google Scholar 

  33. 33.

    Löffler M, Kaiser M, van Kapel T et al (2014) The connect-the-dots family of puzzles: design and automatic generation. ACM Trans Graph 33(4):1–10

    Article  Google Scholar 

  34. 34.

    Ohrhallinger S, Mitchell SA, Wimmer M (2016) Curve reconstruction with many fewer samples. Comput Graph Forum 35(5):167–176

    Article  Google Scholar 

  35. 35.

    Fišer D, Faigl J, Kulich M (2013) Growing neural gas efficiently. Neurocomputing 104:72–82

    Article  Google Scholar 

  36. 36.

    Orts-Escolano S, Garcia-Rodriguez J, Cazorla M et al (2018) Bioinspired point cloud representation: 3d object tracking. Neural Comput Appl 29:1–10

    Article  Google Scholar 

Download references


This work was supported by the National High Technology Research and Development Program of China (Grant No. 2015AA042502). We are grateful to Xu Jinting for providing the PLSP implementation.

Author information



Corresponding author

Correspondence to Kaihua Xue.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Yang, T., Yao, S. & Xue, K. Slicing point cloud incrementally for Additive Manufacturing via online learning. Neural Comput & Applic 32, 11521–11541 (2020).

Download citation


  • Additive Manufacturing
  • Curve reconstruction
  • Topology learning
  • Principal curve