Advertisement

A Delaunay Triangulation Algorithm Based on Dual-Spatial Data Organization

  • Niantao Liu
  • Bingxian Lin
  • Guonian Lv
  • A-Xing Zhu
  • Liangchen ZhouEmail author
Original Article
  • 26 Downloads

Abstract

Existing Delaunay triangulation algorithms for LiDAR data can only guarantee the efficiency of a certain reconstruction step, but cannot guarantee the overall efficiency. This paper presents a Delaunay triangulation algorithm which integrates two existing approaches to improve the overall efficiency of LiDAR data triangulation. The proposed algorithm consists of four steps: (1) dividing a point cloud into grid cells, (2) sorting a point cloud using a KD-tree, (3) triangulating the point cloud and exporting inactive triangles in main memory, and (4) scheduling the above steps. The proposed algorithm was tested using three LiDAR data sets. The LiDAR data was used for comparing the proposed algorithm with the Streaming Delaunay algorithm with respect to both time efficiency and memory usage. Results from the experiments suggest that the proposed algorithm is three to four times faster than Streaming Delaunay while using nearly the same memory space.

Keywords

Delaunay Triangulation Grid partition KD-tree sort Pipeline scheduling 

Zusammenfassung

Bestehende Delaunay-Triangulationsalgorithmen für LiDAR-Daten können nur die Effizienz eines bestimmten Rekonstruktionsschrittes garantieren, aber nicht die Gesamteffizienz. Dieser Artikel stellt einen Delaunay Triangulationsalgorithmus vor, der zwei bestehende Ansätze zur Verbesserung der Gesamteffizienz der LiDAR-Datentriangulation integriert. Der vorgeschlagene Algorithmus besteht aus vier Schritten: (1) Teilen einer Punktwolke in Gitterzellen, (2) Sortieren einer Punktwolke mit einem KD-Baum, (3) Triangulieren der Punktwolke und Exportieren inaktiver Dreiecke in den Hauptspeicher und (4) Durchführung der obigen Schritte. Der vorgeschlagene Algorithmus wurde mit drei LiDAR-Datensätzen getestet. Die LiDAR-Daten wurden verwendet, um den vorgeschlagenen Algorithmus mit dem Streaming Delaunay-Algorithmus in Bezug auf Zeiteffizienz und Speicherauslastung zu vergleichen. Die Ergebnisse der Experimente deuten darauf hin, dass der vorgeschlagene Algorithmus drei- bis viermal schneller als der Streaming Delaunay Algorithmus bei nahezu gleichem Speicherplatzverbrauch ist.

Notes

Funding

This funding was supported by National Natural Science Foundation of China (Grant no. 41571381) and National Key Research and Development Program of China (Grant no. 2018YFB0505301).

References

  1. Agarwal PK, Arge L, Yi K (2005) I/O-efficient construction of constrained Delaunay triangulations. In: European conference on algorithms, pp 355–366Google Scholar
  2. Amenta N, Choi S (2003) Incremental constructions Con BRIO. In: Nineteenth symposium on computational geometry, pp 211–219Google Scholar
  3. Boissonnat JD, Devillers O, Hornus S (2009) Incremental construction of the Delaunay triangulation and the delaunay graph in medium dimension. In: ACM Symposium on Computational Geometry, Aarhus, Denmark, pp 208–216Google Scholar
  4. Bowyer A (1981) Computing Dirichlet tessellations. Comput J 24(2):162–166CrossRefGoogle Scholar
  5. Buchin K (2009) Constructing Delaunay triangulations along space-filling curves, algorithms—ESA 2009, European Symposium, Copenhagen, Denmark, September 7–9, pp 119–130Google Scholar
  6. Cendes Z, Shenton D, Shahnasser H (1983) Magnetic field computation using Delaunay triangulation and complementary finite element methods. IEEE Trans Magn 19(6):2551–2554CrossRefGoogle Scholar
  7. Chen L, Holst M (2011) Efficient mesh optimization schemes based on optimal Delaunay triangulations. Comput Methods Appl Mech Eng 200(9–2):967–984CrossRefGoogle Scholar
  8. Cohenor D, Levanoni Y (1996) Temporal continuity of levels of detail in Delaunay triangulated terrain, VIS ‘96. In: Proceedings of the 7th Conference on Visualization ‘96, Los Alamitos, CA, USA, pp 37–42Google Scholar
  9. Edelsbrunner H, Shah NR (1996) Incremental topological flipping works for regular triangulations. Algorithmica 15(3):223–241CrossRefGoogle Scholar
  10. Isenburg M, Liu Y, Shewchuk J, Snoeyink J (2006) Streaming computation of Delaunay triangulations, ACM SIGGRAPH, pp 1049–1056Google Scholar
  11. Jian-Fei L, Jin-Hui Y (2013) A new insertion sequence for incremental Delaunay triangulation. Acta Mech Sin 29(1):99–109CrossRefGoogle Scholar
  12. Kothuri RKV, Ravada S, Abugov D (2002) Quadtree and R-tree indexes in oracle spatial: a comparison using GIS data. In: ACM SIGMOD International Conference on Management of Data, pp 546–557Google Scholar
  13. Pajarola R, Antonijuan M, Lario R (2002) QuadTIN: quadtree based triangulated irregular networks, Visualization, 2002, Vis, pp 395–402Google Scholar
  14. Pajarola R, Antonijuan M, Lario R (2002) QuadTIN: Quadtree Based Triangulated Irregular Networks. In: Proceedings of the Conference on Visualization ‘02, Washington, DC, USA, pp 395–402Google Scholar
  15. Peters S (2013) Quadtree- and octree-based approach for point data selection in 2D or 3D. Ann GIS 19(1):37–44CrossRefGoogle Scholar
  16. Schnabel R, Klein R (2006) Octree-based point-cloud compression, Eurographics/IEEE Vgtc conference on point-based graphics, pp 111–121Google Scholar
  17. Tsai VJD (1993) Delaunay triangulations in TIN creation: an overview and a linear-time algorithm. Geogr Inf Syst 7(6):501–524Google Scholar
  18. Watson DF (1981) Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes. Comput J 24(2):167–172CrossRefGoogle Scholar
  19. Wu H, Guan X, Gong J (2011) ParaStream: a parallel streaming Delaunay triangulation algorithm for LiDAR points on multicore architectures. Comput Geosci 37(9):1355–1363CrossRefGoogle Scholar

Copyright information

© Deutsche Gesellschaft für Photogrammetrie, Fernerkundung und Geoinformation (DGPF) e.V. 2019

Authors and Affiliations

  • Niantao Liu
    • 1
    • 2
    • 3
  • Bingxian Lin
    • 1
    • 2
    • 3
  • Guonian Lv
    • 1
    • 2
    • 3
  • A-Xing Zhu
    • 1
    • 2
    • 3
  • Liangchen Zhou
    • 1
    • 2
    • 3
    Email author
  1. 1.Key Laboratory of Virtual Geographic EnvironmentNanjing Normal University, Ministry of EducationNanjingChina
  2. 2.State Key Laboratory Cultivation Base of Geographical Environment EvolutionNanjingChina
  3. 3.Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and ApplicationNanjingChina

Personalised recommendations