Computational Geometry Toolbox

Convex hull, mesh generation, Delaunay triangulation, Voronoi diagram and other algorithms.

In this submission, finite element mesh, Delaunay triangulations and Voronoi diagrams are generated through the use of the convex hull algorithm, which is implemented in an optimized way that maximizes speed and performance. The Delaynay triangulation and Voronoi diagram algorithms are essentially based on the convex hull algorithm. Information about the code and the ways to be used is shown in 'Theory of convex hulls, Delaunay triangulations and Voronoi diagrams'. The convex hull algorithm is applied by the function 'convhull_nd', the Delaunay triangulation by the function 'delaunay_nd' and the Voronoi diagram by the function 'voronoi_nd'. All functions included in this package can be used for any dimension n. The use of the three aforementioned functions is illustrated by many examples, included in the file 'Contents'.
The functions included in this submission can be used for the generation of finite element and boundary element meshes, which are utilized for discretization of various media, structural or not, to be numerically analysed.
Apart from this, they can be used to solve various problems of computational geometry, such as:
- convex hulls
- intersections
- triangulation and partitioning
- line arrangements and duality
- Voronoi diagrams and Delaunay triangulations
- Point in polygon, etc.
It has to be noted that most of these problems (many of which are included in this package as solved examples) are solved using essentially the convex hull algorithm.
References:
[1] The Quickhull Algorithm for Convex Hull, C. Bradford Barber, David P. Dobkin and Hannu Huhdanpaa, Geometry Center Technical Report GCG53, July 30, 1993.
[2] Voronoi Diagrams from Convex Hulls, Kevin Q. Brown, Information Processing Letters, Vol.9, No.5, December 16, 1979
[3] Voronoi Diagrams and Arrangements, Herbert Edelsbrunner and Raimund Seidel, Discrete & Computational Geometry 1:25-44, 1986