An Experimental Assessment of Three Point-Insertion Sequences for 3-D Incremental Delaunay Tessellations

  • Sanderson L. Gonzaga de Oliveira
  • Diogo T. Robaina
  • Diego N. Brandão
  • Mauricio Kischinhevsky
  • Gabriel Oliveira
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10860)


Currently, state-of-the-art algorithms for building 3-D Delaunay tessellations are incremental. Thus, their execution costs depend on the order of point insertion. This work evaluates three point-insertion sequences in incremental algorithms for building 3-D Delaunay tessellations. An incremental algorithm with point-insertion sequence provided by the cut-longest-edge kd–tree is evaluated against the BRIO–Hilbert order in conjunction with spatial middle and median policies employed in the 4.11 version of the Computational Geometry Algorithms Library. The results of computational costs (time and space) of these three algorithms are evaluated experimentally. Extensive results show that the incremental algorithm with a point-insertion sequence provided by the BRIO–Hilbert order with spatial middle policy employed in the latest version of the Computational Geometry Algorithms Library shows lower execution and storage costs than the two other algorithms evaluated.



We are grateful to Prof. Dr. Jianfei Liu, from the Department of Mechanics and Engineering Science, College of Engineering, Peking University, for sharing his program code and for his helpful comments.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Sanderson L. Gonzaga de Oliveira
    • 1
  • Diogo T. Robaina
    • 2
  • Diego N. Brandão
    • 3
  • Mauricio Kischinhevsky
    • 2
  • Gabriel Oliveira
    • 1
  1. 1.Universidade Federal de LavrasLavrasBrazil
  2. 2.Universidade Federal FluminenseNiteróiBrazil
  3. 3.CEFET-RJRio de JaneiroBrazil

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