## Conformal Geometric Algebra Package
Keywords: CGA, CGAL, CGAP, geometry, library, flags, Edelsbrunner algorithm, Voronoi diagram, Delaunay triangulation, multidimensional Contents of this website: |

CGAL (www.cgal.org) is a C++ library that provides easy access to geometric algorithms. CGAL is used in various areas needing geometric computation, such as computer graphics. By default, the geometric primitives and operations are implemented by a cartesian or homogenous kernel, based on linear algebra methods. However, it offers the possibility to implement user-defined kernels.

In this master thesis project a CGA-kernel has been modelled and partly implemented for the CGAL-library. In this CGA-kernel the advantages of CGAL and CGA have been combined. With the help of this kernel, many geometric algorithms that are present in CGAL, can be made available in CGA-language. And scientists that use CGAL, can re-implement their algorithms in the simple expressions of CGA. As an example, algorithms for Delaunay triangulations and Voronoi diagrams have been implemented in dimensions 2D, 3D and nD. This project has been called the name 'Conformal Geometric Algebra Package'.

Besides that, specific research has been done for the use of so called 'flags' in high-dimensional polytope algorithms. As an application of the CGAP-library, an example of this is given in the thesis for high dimensional Voronoi diagrams in combination with Conformal Geometric Algebra.

This package is provided "as is", and is supported.

Delaunay 2D app | Delaunay 3D app | Voronoi&CGA-Flags 2D app | Voronoi&CGA-Flags 3D app |

Masters thesis | PS | |

CGAP user & reference manual | PS | |

CGAP source code & demos & binaries Supports GCC and MS Visual Studio 2005 |
ZIP | |

Master thesis presentation |

Geometric Algebra | |

University
of Amsterdam, GA Research |
Website of Leo Dorst (University of Amsterdam) about CGA |

GAIGEN | A C++-code generator for Geometric Algebras (up to dimension 8) |

Euclidian
Geometric Algebra and Quaternions |
Geometric Algebra applied to OpenGL |

Geometric Calculus | David Hestenes' Geometric Algebra site |

Geometric Algebra research group | Geometric Algebra research group at the University of Cambridge, England. |

CGAL | |

CGAL | Computational Geometry Algorithms Library website |

CGAL Reference manual | Reference manual of CGAL |

C++-programming | |

Boost
C++-Libraries and Documentation |
The CGAL-library uses some pieces of this library. |

OpenGL | Official website OpenGL, including downloads, tutorials etc. |

OpenGL Tutorial |

Voronoi, Delaunay, Convex Hull | |

Computational Geometry: Delaunay Triagulations and Voronoi Diagrams |
Links and Java applets |

Convex hull links | Arbitrary dimensional convex hull, Voronoi diagram, Delaunay triangulation links |