## CGAL - The Computational Geometry Algorithm Library (2001)

Venue: | Sandia National Laboratory |

Citations: | 15 - 0 self |

### BibTeX

@INPROCEEDINGS{Fabri01cgal-,

author = {Andreas Fabri},

title = {CGAL - The Computational Geometry Algorithm Library},

booktitle = {Sandia National Laboratory},

year = {2001},

pages = {137--142}

}

### OpenURL

### Abstract

The Cgal project (www.cgal.org) is a collaborative e#ort of several research institutes in Europe. The mission of the project is to make the most important of the solutions and methods developed in computational geometry available to users in industry and academia.

### Citations

1843 |
Computational Geometry: An Introduction
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- 1985
(Show Context)
Citation Context ...geometry is a research area in data structures and algorithm design which is a branch of theoretical computer science. In the seventies the term was coined, Preparata/Shamos wrote the first text book =-=[20]-=-, the eighties brought theoretically optimal, but unimplementable algorithms, the nineties saw a renaissance of simple algorithms, partially due to new complexitiy analysis methods 1 . The Cgal projec... |

145 | Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates
- Shewchuk
- 1997
(Show Context)
Citation Context ...eved straightforwardly by relying on an exact number type, this is not the most efficient approach, and the idea of so-called filters has been developed to speed up the exact evaluation of predicates =-=[4, 11, 24]-=-. The basic idea is to use a filtering step before the costly computation with an exact number type. The filter step evaluates quickly and approximately the result of the predicate, but is also able t... |

125 | Computational Geometry Algorithms Library. http://www.cgal.org - CGAL |

110 |
The C++ Programming Language(3rd edition
- Stroustrup
- 1997
(Show Context)
Citation Context ...tructure, as the triangulation may be a single step in an application pipeline, or in an application loop, so that converting forth and back between different representations is no option. Stroustrup =-=[26]-=- provides a general introduction to C++ template programming. Austern [1] provides a good reference for generic programming and the Stl, and a good reference for the C++ Standard Library is the book o... |

96 | The exact computation paradigm
- Yap, Dube
- 1995
(Show Context)
Citation Context ...on speed for only getting aesthetically or software engineering wise better code. 2.3 Exact Computing The established approach for robust geometric algorithms following the exact computation paradigm =-=[28]-=- requires the exact evaluation of geometric predicates, i.e., decisions derived from geometric computations have to be correct. While this can be achieved straightforwardly by relying on an exact numb... |

95 | On the design of cgal, a computational geometry algorithms library - Fabri, Giezeman, et al. |

73 | Generic Programming
- Musser, Stepanov
(Show Context)
Citation Context ...lean separation of specification and implementation. It supports polymorphism, and most importantly for Cgal, it supports the generic programming paradigm. 2.2 Generic Programming Generic programming =-=[18]-=- gives a tremendous flexibility during development, and efficient code at run time of a program. Its power became apparent with the Stl, the Standard Template Library, which is now part of the Iso C++... |

63 | Static analysis yields efficient exact integer arithmetic for computational geometry
- Fortune, Wyk
- 1996
(Show Context)
Citation Context ...eved straightforwardly by relying on an exact number type, this is not the most efficient approach, and the idea of so-called filters has been developed to speed up the exact evaluation of predicates =-=[4, 11, 24]-=-. The basic idea is to use a filtering step before the costly computation with an exact number type. The filter step evaluates quickly and approximately the result of the predicate, but is also able t... |

58 | Interval arithmetic yields efficient dynamic filters for computational geometry
- Brönnimann, Burnikel, et al.
(Show Context)
Citation Context ...eved straightforwardly by relying on an exact number type, this is not the most efficient approach, and the idea of so-called filters has been developed to speed up the exact evaluation of predicates =-=[4, 11, 24]-=-. The basic idea is to use a filtering step before the costly computation with an exact number type. The filter step evaluates quickly and approximately the result of the predicate, but is also able t... |

53 | Delaunay based shape reconstruction from large data, in
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(Show Context)
Citation Context ...res get used: 3D regular triangulation for transition mesh generation in geological modelling [2], 3D Delaunay triangulation for coarse grained molecular dynamics [10], and for surface reconstruction =-=[8]-=-, 2D Delaunay triangulations for cell decomposition in air traffic control, polyhedral surfaces for surface extraction from Mris, smallest enclosing spheres for fast collision detection in games, bool... |

43 | Improved incremental randomized Delaunay triangulation, in
- Devillers
- 1998
(Show Context)
Citation Context ...eding triangulation, the data structure remains small and achieves fast point location queries on real data. This structure has an optimal behaviour when it is built for 2D/3D Delaunay triangulations =-=[7]-=-. Because in practice it also works well for other types of triangulations, it is parameterized with a triangulation class.sEfficiency is a must in order to be of practical relevance. For example the ... |

28 | Techniques for scientific C
- Veldhuizen
- 1999
(Show Context)
Citation Context ...ry which has adopted this paradigm. It is used by the Matrix Template Library [22], by the Boost Graph Library [23], by the Grid Algorithm Library [3], in the oonumerics [19], and the Blitz++ project =-=[27]-=-. Note that it is an explicit goal of the two scientific computing projects to offer solutions that are as fast as Fortran code. They know that their community cannot make any compromise on speed for ... |

25 | An adaptable and extensible geometry kernel
- Hert, Hoffman, et al.
- 2001
(Show Context)
Citation Context ...als Cartesian<leda_real> // real numbers Cartesian<Filtered_exact<double, leda_real> > This parameterization is only the tip of the iceberg concerning the adaptability and extensibility of the kernel =-=[13]-=-. As stated earlier the basic library is independent from the kernel. All data structures in the basic library are parameterised with a class that provides all the geometric primitives the data struct... |

25 |
The Matrix Template Library: Generic Components for HighPerformance Scientific Computing
- Siek, Lumsdaine
- 1999
(Show Context)
Citation Context ...ng and the Stl, and a good reference for the C++ Standard Library is the book of Josuttis [14]. Cgal is not the only library which has adopted this paradigm. It is used by the Matrix Template Library =-=[22]-=-, by the Boost Graph Library [23], by the Grid Algorithm Library [3], in the oonumerics [19], and the Blitz++ project [27]. Note that it is an explicit goal of the two scientific computing projects to... |

16 | The LEDA class real number
- Burnikel, Mehlhorn, et al.
- 1996
(Show Context)
Citation Context ...uding geometric predicates. The generic programming approach allows to plug in arbitrary precision number types for integers and rationals (Gmp [12]), and approximations of reals (Core [16], and Leda =-=[5]-=-). 3. APPLICATION AREAS Cgal is enabling technology, that is it does not provide a vertical solution in one application area, but provides geometric primitives for many very different application area... |

6 |
The XYZ GeoBench for the Experimental Evaluation of Geometric Algorithms
- Schorn
- 1992
(Show Context)
Citation Context ...e software design, where we did not reinvent the wheel, but followed best practice. 2.1 C++ Cgal is implemented in C++ [15]. There were similar efforts for making geometry libraries: the Xyz Geobench =-=[21]-=- was written in Pascal and the Geometry Workbench [17] was written in Smalltalk. Because these language disappeared or were never widely accepted these efforts were deemed to fail. Being as mainstream... |

6 | Chazelle et al. Application challenges to computational geometry: CG impact task force report - Bernard - 1999 |

5 |
Austern Generic programming and the STL
- H
- 2001
(Show Context)
Citation Context ...line, or in an application loop, so that converting forth and back between different representations is no option. Stroustrup [26] provides a general introduction to C++ template programming. Austern =-=[1]-=- provides a good reference for generic programming and the Stl, and a good reference for the C++ Standard Library is the book of Josuttis [14]. Cgal is not the only library which has adopted this para... |

2 |
Generation of hybrid grids using power diagrams
- Balaven, Bennis, et al.
- 2000
(Show Context)
Citation Context ...ric primitives for many very different application areas. Here are some examples for how Cgal data structures get used: 3D regular triangulation for transition mesh generation in geological modelling =-=[2]-=-, 3D Delaunay triangulation for coarse grained molecular dynamics [10], and for surface reconstruction [8], 2D Delaunay triangulations for cell decomposition in air traffic control, polyhedral surface... |

2 |
A Generic Toolbox for the Grid Craftsman. 17th GAMM-Seminar Leipzig on “Construction of Grid Generation Algorithms
- Berti
- 2001
(Show Context)
Citation Context ...the book of Josuttis [14]. Cgal is not the only library which has adopted this paradigm. It is used by the Matrix Template Library [22], by the Boost Graph Library [23], by the Grid Algorithm Library =-=[3]-=-, in the oonumerics [19], and the Blitz++ project [27]. Note that it is an explicit goal of the two scientific computing projects to offer solutions that are as fast as Fortran code. They know that th... |

2 |
The Boost Graph Library. www.boost.org/libs/libraries.htm
- Siek, Lumsdaine
(Show Context)
Citation Context ...nce for the C++ Standard Library is the book of Josuttis [14]. Cgal is not the only library which has adopted this paradigm. It is used by the Matrix Template Library [22], by the Boost Graph Library =-=[23]-=-, by the Grid Algorithm Library [3], in the oonumerics [19], and the Blitz++ project [27]. Note that it is an explicit goal of the two scientific computing projects to offer solutions that are as fast... |

1 |
Coveney & E.G. Flekkoy Multiscale modelling of complex fluids
- Fabritiis, V
- 1999
(Show Context)
Citation Context ...me examples for how Cgal data structures get used: 3D regular triangulation for transition mesh generation in geological modelling [2], 3D Delaunay triangulation for coarse grained molecular dynamics =-=[10]-=-, and for surface reconstruction [8], 2D Delaunay triangulations for cell decomposition in air traffic control, polyhedral surfaces for surface extraction from Mris, smallest enclosing spheres for fas... |

1 |
Josuttis The C++ Standard Library, A Tutorial and Reference
- M
- 1999
(Show Context)
Citation Context ... general introduction to C++ template programming. Austern [1] provides a good reference for generic programming and the Stl, and a good reference for the C++ Standard Library is the book of Josuttis =-=[14]-=-. Cgal is not the only library which has adopted this paradigm. It is used by the Matrix Template Library [22], by the Boost Graph Library [23], by the Grid Algorithm Library [3], in the oonumerics [1... |

1 | Template Library programmer’s guide. www.sgi.com/tech/stl - Standard - 1986 |