Efi Fogel
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Arrangements on Spheres

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We have developed a toolkit that constructs and maintains 3-dimensional scenes. The toolkit consists of a couple of libraries and an interactive 3D application named player that renders 3D scenes stored in an extended VRML format. The format was extended with several geometry modes, which describe models represented with CGAL data structures. Some of the new nodes are listed below. The player application is linked with:
  1. SCGAL - an internal library that constructs and maintains geometry nodes, which describe models represented with CGAL data structures.
  2. SGAL - an internal library that constructs and maintains 3D scene-graphs, written in C++, and built on top of OpenGL.
  3. ImageMagick and magick++
  4. CGAL
  5. boost
  6. GMP - a library that provides the exact rational number-type
New geometry nodes:
ArrangementOnSphere
describes a model represented by an arrangement of geodesic arcs embedded on the sphere.
VoronoiDiagramOnSphere
describes a Voronoi diagram of points on the sphere.
PowerDiagramOnSphere
describes a Power diagram of circles on the sphere.
ExactPolyhedron
describes a model represented by the CGAL Polyhedron_3 data structure.
SphericalGaussianMap
describes a polytope represented by its spherical Gaussinal map, which in turn is represented by the CGAL Arrangement_on_surface_2 data structure.
CubicalGaussianMap
describes a polytope represented by the CGM data structure, which in turn is represented by six planar maps among the other.
NefGaussianMap
describes a polytope represented by Nef polyhedra embedded on the sphere.

Last modified: February 12 2008.
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