1 / 19

The Computational Geometry Algorithm Library

The Computational Geometry Algorithm Library. Pierre Alliez. http://www.cgal.org. Goals. Promote Research in Computational Geometry (CG) “make the large body of geometric algorithms developed in the field of CG available for industrial applications” -> robust programs.

aizza
Télécharger la présentation

The Computational Geometry Algorithm Library

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Computational Geometry Algorithm Library Pierre Alliez http://www.cgal.org

  2. Goals • Promote Research in Computational Geometry (CG) • “make the large body of geometric algorithms developed in the field of CG available for industrial applications” -> robust programs

  3. CG Impact Task Force Report, 1996 Among the key recommendations: • Production and distribution of usable (and useful) geometric codes • Reward structure for implementations in academia

  4. The CGAL Project • Started in 1996 as joined project of: • ETH Zurich • INRIA • MPI für Informatik • Tel-Aviv U • Utrecht U • Trier U • FU Berlin

  5. Basic Library HalfedgeDatastructure Triangulations Arrangements Convex Hull Optimisation ... • Visualization • File I/O • Number Types • Generators • STL extensions Point, Segment,... Predicates Kernel Support Library:Configuration, Assertions Structure of CGAL

  6. The Basic Library

  7. Convex Hull • 2D Convex Hull • 5 algorithms for points • CH of a simple polyline • Convexity Test • Extremal Points • 3D Convex Hull • static, incremental, dynamic

  8. Planar Subdivisions • Framework for arrangements of 2D curves • based on planar maps • based on topological maps • Models exist for polylines, circles, conic arcs • Operations • point location, overlay, ray shooting,..

  9. Search Structures • Multi dimensional data structures • range tree, segment tree • kD tree • Operations • window queries • nearest neighbor

  10. Triangulations in 2D and 3D • Delaunay, regular, constrained, conformal Delaunay • Rich APIs • fast point location, • insertion, removal of points and constraints • traversal along a line • traversal of the triangulation

  11. Triangulations • 2D, 3D Alpha shapes • 2D, 3D Voronoi diagram, power diagram • 2D Delaunay mesh, 3D Delaunay mesh • Natural neighbors* • k-order Voronoi diagram 2* • Voronoi of segments * • Voronoi of circles (*) on-going

  12. Optimization • Based on LP/QP solvers • Smallest enclosing circle/ellipse in 2D • Smallest enclosing sphere in dD • Rectangular p center, for p = 2, 3, 4 • Polytope distances in dD • Smallest enclosing annulus in dD • Smallest enclosing sphere of spheres*

  13. Nef Polyhedra 2,3*

  14. and ... • dD Delaunay/Voronoi • Polygon decomposition • Polyhedral surfaces • Halfedge data structure

  15. Library Design Let’s play Lego

  16. Generic Programming [Musser 89] float min(float a, float b) int min(int a, int b) template < CompType> CompType min(CompType a, CompType b) { return (a<b) ? a : b; } BigInt n(9), m(8), r; r = min( n, m ); BigInt is a model for the concept CompType

  17. Point_3 Cartesian Homogeneous int double Gmpz Gmpq leda::Real core::Expr Concepts: NumberType and Kernel Parameterization of Kernel Classes

  18. Parameterization of Datastructures template < Geometry > class Delaunay_triangulation_2 { void insert(Geometry::Point t) { if(Geometry::orientation(p,q,t)==..) if(Geometry::incircle(p,q,r,t)) } }; • works with CGAL kernels • works with projections kernels • write thin glue layer for your kernel

  19. Value for Users • High quality of most components • Interoperability of components • Rich functionality • allows rapid prototyping • allows focus on application domain • Reduces time to market (publication)

More Related