Skip to main content
Top

2021 | OriginalPaper | Chapter

23. An Improved Simple Sweep Line Algorithm for Delaunay Refinement Triangulation

Authors : Normi binti Abdul Hadi, Anis Farhani, Wardiah Mohd Dahalan

Published in: Advanced Engineering for Processes and Technologies II

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This paper is focused on simple sweep line algorithms with Delaunay refinement triangulation to create 2D triangulation. A new algorithm is proposed where the main idea is to add circumcircle properties into the simple sweep line algorithm. Since the Delaunay triangulation itself still generates poor quality of triangles, this paper applies the Delaunay refinement to enhance the triangulation. Next, this paper observes the percentage of bad angles to analyze the quality of the triangles and the flipping number required for each set of points to analyze the efficiency of the algorithm. At the end of this research, all objectives are achieved where an improved simple sweep line algorithm with Delaunay refinement triangulation is obtained.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Li, X.: Anisotropic mesh adaptation for image representation. EURASIP-JVP, 26 (2016) Li, X.: Anisotropic mesh adaptation for image representation. EURASIP-JVP, 26 (2016)
2.
go back to reference Dinas, S., Banon, J.M.: A review on Delaunay triangulation with application on computer vision. Int. J. Comput. Sci. Eng. 3, 9–18 (2014) Dinas, S., Banon, J.M.: A review on Delaunay triangulation with application on computer vision. Int. J. Comput. Sci. Eng. 3, 9–18 (2014)
3.
go back to reference Fortune, S.: Voronoi diagrams and Delaunay triangulations. In: Computing in Euclidean geometry, pp. 225–265. World Scientific (1995) Fortune, S.: Voronoi diagrams and Delaunay triangulations. In: Computing in Euclidean geometry, pp. 225–265. World Scientific (1995)
4.
go back to reference Bern, M., Eppstein, D.: Mesh generation and optimal triangulation. In: Computing in Euclidean Geometry, vol. 1, pp. 23–90. World Scientific (1992) Bern, M., Eppstein, D.: Mesh generation and optimal triangulation. In: Computing in Euclidean Geometry, vol. 1, pp. 23–90. World Scientific (1992)
5.
go back to reference Van Kreveld, M., Schwarzkopf, O., de Berg, M., Overmars, M.: Computational Geometry Algorithms and Applications. Springer (2000) Van Kreveld, M., Schwarzkopf, O., de Berg, M., Overmars, M.: Computational Geometry Algorithms and Applications. Springer (2000)
6.
go back to reference Zˇalik, B., Kolingerova, I.: An incremental construction algorithm for delaunay triangulation using the nearest-point paradigm. Int. J. Geogr. Inf. Sci. 17, 119–138 (2003) Zˇalik, B., Kolingerova, I.: An incremental construction algorithm for delaunay triangulation using the nearest-point paradigm. Int. J. Geogr. Inf. Sci. 17, 119–138 (2003)
7.
go back to reference Dwyer, R.A.: A faster divide-and-conquer algorithm for constructing Delaunay triangulations. Algorithmica 2(1–4), 137–151 (1987)MathSciNetCrossRef Dwyer, R.A.: A faster divide-and-conquer algorithm for constructing Delaunay triangulations. Algorithmica 2(1–4), 137–151 (1987)MathSciNetCrossRef
8.
go back to reference Guibas, L., Stolfi, J.: Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams. ACM Trans. Graph. 4(2), 75–123 (1985)CrossRef Guibas, L., Stolfi, J.: Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams. ACM Trans. Graph. 4(2), 75–123 (1985)CrossRef
9.
go back to reference Dwyer, R.A.: Higher-dimensional Voronoi diagrams in linear expected time. Discrete Comput. Geom. 6, 343–367 (1991)MathSciNetCrossRef Dwyer, R.A.: Higher-dimensional Voronoi diagrams in linear expected time. Discrete Comput. Geom. 6, 343–367 (1991)MathSciNetCrossRef
10.
go back to reference Aurenhammer, F.: Voronoi diagrams: a survey of a fundamental geometric data structure. ACM Comput. Surv. 23(3), 345–405 (1991)CrossRef Aurenhammer, F.: Voronoi diagrams: a survey of a fundamental geometric data structure. ACM Comput. Surv. 23(3), 345–405 (1991)CrossRef
11.
go back to reference Silveira, R.I., Van Kreveld, M.: Towards a definition of higher order constrained Delaunay triangulations. Comput. Geom. 42(4), 322–337 (2009)MathSciNetCrossRef Silveira, R.I., Van Kreveld, M.: Towards a definition of higher order constrained Delaunay triangulations. Comput. Geom. 42(4), 322–337 (2009)MathSciNetCrossRef
12.
go back to reference Žalik, B.: An efficient sweep-line Delaunay triangulation algorithm. Comput. Aided Des. 37(10), 1027–1038 (2005)CrossRef Žalik, B.: An efficient sweep-line Delaunay triangulation algorithm. Comput. Aided Des. 37(10), 1027–1038 (2005)CrossRef
13.
go back to reference Biniaz, A., Dastghaibyfard, G.: A faster circle-sweep Delaunay triangulation algorithm. Adv. Eng. Softw. 43(1), 1–13 (2012)CrossRef Biniaz, A., Dastghaibyfard, G.: A faster circle-sweep Delaunay triangulation algorithm. Adv. Eng. Softw. 43(1), 1–13 (2012)CrossRef
14.
go back to reference De De Oliveira, S.L.G.: A review on delaunay refinement techniques. ICCSA, pp. 172–187 (2012, June) De De Oliveira, S.L.G.: A review on delaunay refinement techniques. ICCSA, pp. 172–187 (2012, June)
15.
go back to reference Shewchuk, J.R.: Lecture notes on Delaunay mesh generation. Department of Electrical Engineering and Computer Sciences (1999) Shewchuk, J.R.: Lecture notes on Delaunay mesh generation. Department of Electrical Engineering and Computer Sciences (1999)
Metadata
Title
An Improved Simple Sweep Line Algorithm for Delaunay Refinement Triangulation
Authors
Normi binti Abdul Hadi
Anis Farhani
Wardiah Mohd Dahalan
Copyright Year
2021
DOI
https://doi.org/10.1007/978-3-030-67307-9_23

Premium Partners