skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: An evaluation of point-insertion sequences for incremental Delaunay tessellations

Abstract

Currently, incremental algorithms may be seen as the lowest-cost computational methods to generate Delaunay tessellations in several point distributions. In this work, eight point-insertion sequences in incremental algorithms for generating Delaunay tessellations are evaluated. More specifically, four point-insertion sequences in incremental algorithms for generating Delaunay tessellations are proposed: with orders given by the red–black tree with in-order and level-order traversals, spiral ordering, and H-indexing. These four incremental algorithms with such sequences are compared with four incremental algorithms with point-insertion orders given by the following sequences: the Hilbert and Lebesgue curves, cut-longest-edge kd-tree, and random order. Six 2-D and seven 3-D point distributions are tested, with sets ranging from 25,000 to 8,000,000 points. The results of computational and storage costs of these eight algorithms are analyzed. It follows that the incremental algorithm with a point-insertion sequence in the order given by the cut-longest-edge kd-tree shows the lowest computational and storage costs of the sequences tested.

Authors:
 [1];  [2]
  1. Universidade Federal de Lavras (Brazil)
  2. Ciência e Tecnologia do Sul de Minas Gerais/Campus Passos, Instituto Federal de Educação (Brazil)
Publication Date:
OSTI Identifier:
22769375
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 1; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; COMPUTER-AIDED DESIGN; MESH GENERATION

Citation Formats

Gonzaga de Oliveira, Sanderson L., E-mail: sanderson@dcc.ufla.br, and Nogueira, Jéssica Renata, E-mail: jessica.nogueira@ifsuldeminas.edu.br. An evaluation of point-insertion sequences for incremental Delaunay tessellations. United States: N. p., 2018. Web. doi:10.1007/S40314-016-0358-0.
Gonzaga de Oliveira, Sanderson L., E-mail: sanderson@dcc.ufla.br, & Nogueira, Jéssica Renata, E-mail: jessica.nogueira@ifsuldeminas.edu.br. An evaluation of point-insertion sequences for incremental Delaunay tessellations. United States. doi:10.1007/S40314-016-0358-0.
Gonzaga de Oliveira, Sanderson L., E-mail: sanderson@dcc.ufla.br, and Nogueira, Jéssica Renata, E-mail: jessica.nogueira@ifsuldeminas.edu.br. Thu . "An evaluation of point-insertion sequences for incremental Delaunay tessellations". United States. doi:10.1007/S40314-016-0358-0.
@article{osti_22769375,
title = {An evaluation of point-insertion sequences for incremental Delaunay tessellations},
author = {Gonzaga de Oliveira, Sanderson L., E-mail: sanderson@dcc.ufla.br and Nogueira, Jéssica Renata, E-mail: jessica.nogueira@ifsuldeminas.edu.br},
abstractNote = {Currently, incremental algorithms may be seen as the lowest-cost computational methods to generate Delaunay tessellations in several point distributions. In this work, eight point-insertion sequences in incremental algorithms for generating Delaunay tessellations are evaluated. More specifically, four point-insertion sequences in incremental algorithms for generating Delaunay tessellations are proposed: with orders given by the red–black tree with in-order and level-order traversals, spiral ordering, and H-indexing. These four incremental algorithms with such sequences are compared with four incremental algorithms with point-insertion orders given by the following sequences: the Hilbert and Lebesgue curves, cut-longest-edge kd-tree, and random order. Six 2-D and seven 3-D point distributions are tested, with sets ranging from 25,000 to 8,000,000 points. The results of computational and storage costs of these eight algorithms are analyzed. It follows that the incremental algorithm with a point-insertion sequence in the order given by the cut-longest-edge kd-tree shows the lowest computational and storage costs of the sequences tested.},
doi = {10.1007/S40314-016-0358-0},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 1,
volume = 37,
place = {United States},
year = {2018},
month = {3}
}