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Updated: Jan 19, 2026

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New approaches for Delaunay triangulation and optimisation.

Logah Perumal1

  • 1Faculty of Engineering and Technology, Multimedia University, Jalan Ayer Keroh Lama, Bukit Beruang, 75450, Melaka, Malaysia.

Heliyon
|September 14, 2019
PubMed
Summary

New techniques improve Delaunay triangulation for generating high-quality triangular meshes. This method optimizes elements for better aspect ratio and skewness in mesh generation.

Keywords:
Aspect ratioComputer simulationComputing methodologyDelaunay triangulationElement skewnessFinite element methodsGeneralised equationGeometryMappingMathematical modelingMechanical engineeringMesh optimisationSample points

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Area of Science:

  • Computational geometry
  • Computer-aided design (CAD)
  • Finite element analysis (FEA)

Background:

  • Delaunay triangulation is a fundamental algorithm for mesh generation.
  • Optimizing mesh quality is crucial for accuracy in simulations.
  • Existing methods for sample point generation can be inefficient.

Purpose of the Study:

  • To introduce novel techniques for Delaunay triangular mesh generation.
  • To enhance mesh element optimization through node manipulation.
  • To demonstrate the efficacy of these techniques using simulation.

Main Methods:

  • Generating sample points for triangulation via a new mapping approach.
  • Applying the conventional Delaunay method for triangulation.
  • Optimizing triangular elements by adding, removing, and relocating sample points (nodes).
  • Utilizing Mathematica software for implementation and demonstration.

Main Results:

  • The proposed techniques successfully generate triangular meshes.
  • Achieved meshes consist of elements with an aspect ratio below 2.
  • The minimum element skewness achieved is greater than 45°.

Conclusions:

  • The novel mapping-based sample point generation enhances Delaunay triangulation.
  • The mesh optimization technique effectively improves element quality.
  • The presented methods offer a viable approach for generating high-quality triangular meshes.