Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Delaunay triangulation of arbitrarily shaped planar domains
Computer Aided Geometric Design
Journal of Computational Physics
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Numerical Conformal Mapping Using Cross-Ratios and Delaunay Triangulation
SIAM Journal on Scientific Computing
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The present work consists to elaborate a computing program able to generate a Delaunay unstructured triangular meshes around the complex configurations applied in aerodynamics, like airfoil of aircraft, multi-elements airfoils, nacelle, fuselage, etc... While basing on the Delaunay criterion, again called 'in-circle criterion' of the hollow circle that means no point is inside a circle circumscribes a triangle of the mesh. The initial mesh can be set up by joining the trailing-edge point of the airfoil to all the outer boundary points, the surface mesh points for the airfoil are then introduced one at a time, and the internal nodes of the O-mesh generated by using a sequence of conformal transformation of Von Karman Trefftz through the whole domain of the out-flow. Each time a new point is introduced, the triangles failing the 'Delaunay criterion' are located using the tree-search algorithm, forming a convex cavity named 'Delaunay cavity'. These triangles will be broken and will be replaced by new triangles while connecting this new point to each of the points at vertices of this cavity. This generated a new triangulation and the algorithm repeats this process with the next new point until succeed to a Delaunay mesh. A Laplacian filter is used to reposition the mesh points in order to have a regular mesh clever to be exploited by the numerical methods: finite volume method or finite element method.