The Computational Geometry Algorithms Library (CGAL) is an open source software

library A library is a collection of materials, books or media that are accessible for use and not just for display purposes. A library provides physical (hard copies) or digital access (soft copies) materials, and may be a physical location or a vir ...

computational geometry Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems ar ...

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...

s. While primarily written in

C++ C++ (pronounced "C plus plus") is a high-level general-purpose programming language created by Danish computer scientist Bjarne Stroustrup as an extension of the C programming language, or "C with Classes". The language has expanded significan ...

Scilab Scilab is a free and open-source, cross-platform numerical computational package and a high-level, numerically oriented programming language. It can be used for signal processing, statistical analysis, image enhancement, fluid dynamics simulat ...

bindings and bindings generated with SWIG (supporting

Python Python may refer to: Snakes * Pythonidae, a family of nonvenomous snakes found in Africa, Asia, and Australia ** ''Python'' (genus), a genus of Pythonidae found in Africa and Asia * Python (mythology), a mythical serpent Computing * Python (pro ...

and

Java Java (; id, Jawa, ; jv, ꦗꦮ; su, ) is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea to the north. With a population of 151.6 million people, Java is the world's List ...

for now) are also available. The software is available under dual licensing scheme. When used for other open source software, it is available under

open source license An open-source license is a type of license for computer software and other products that allows the source code, blueprint or design to be used, modified and/or shared under defined terms and conditions. This allows end users and commercial compa ...

s (

LGPL The GNU Lesser General Public License (LGPL) is a free-software license published by the Free Software Foundation (FSF). The license allows developers and companies to use and integrate a software component released under the LGPL into their own ...

GPL The GNU General Public License (GNU GPL or simply GPL) is a series of widely used free software licenses that guarantee end users the four freedoms to run, study, share, and modify the software. The license was the first copyleft for general u ...

depending on the component). In other cases commercial license may be purchased, under different options for academic/research and industrial customers.

History

The CGAL project was founded in 1996, as a consortium of eight research institutions in Europe and Israel:

Utrecht University Utrecht University (UU; nl, Universiteit Utrecht, formerly ''Rijksuniversiteit Utrecht'') is a public research university in Utrecht, Netherlands. Established , it is one of the oldest universities in the Netherlands. In 2018, it had an enrollme ...

ETH Zurich (colloquially) , former_name = eidgenössische polytechnische Schule , image = ETHZ.JPG , image_size = , established = , type = Public , budget = CHF 1.896 billion (2021) , rector = Günther Dissertori , president = Joël Mesot , ac ...

Free University of Berlin The Free University of Berlin (, often abbreviated as FU Berlin or simply FU) is a public research university in Berlin, Germany. It is consistently ranked among Germany's best universities, with particular strengths in political science and t ...

INRIA The National Institute for Research in Digital Science and Technology (Inria) () is a French national research institution focusing on computer science and applied mathematics. It was created under the name ''Institut de recherche en informatiq ...

Sophia Antipolis (wisdom), gr, (Ἀντίπολις, antipolis) ("opposite city" from its position on the opposite side of the Var estuary from Nice, also former name of Antibes, part of the technology park) , postal_code = 06220 (Vallauris), 06250 (Mo ...

Martin-Luther-University Halle-Wittenberg Martin Luther University of Halle-Wittenberg (german: Martin-Luther-Universität Halle-Wittenberg), also referred to as MLU, is a public, research-oriented university in the cities of Halle and Wittenberg and the largest and oldest university i ...

Max Planck Institute for Informatics The Max Planck Institute for Informatics (German: ''Max-Planck-Institut für Informatik'', abbreviated ''MPI-INF'' or ''MPII'') is a research institute in computer science with a focus on algorithms and their applications in a broad sense. It hosts ...

Saarbrücken Saarbrücken (; french: link=no, Sarrebruck ; Rhine Franconian: ''Saarbrigge'' ; lb, Saarbrécken ; lat, Saravipons, lit=The Bridge(s) across the Saar river) is the capital and largest city of the state of Saarland, Germany. Saarbrücken is S ...

Johannes Kepler University Linz The Johannes Kepler University Linz (German: ''Johannes Kepler Universität Linz'', short: ''JKU'') is a public institution of higher education in Austria. It is located in Linz, the capital of Upper Austria. It offers bachelor's, master's, d ...

, and

Tel-Aviv University Tel Aviv University (TAU) ( he, אוּנִיבֶרְסִיטַת תֵּל אָבִיב, ''Universitat Tel Aviv'') is a public research university in Tel Aviv, Israel. With over 30,000 students, it is the largest university in the country. Loc ...

. The original funding for the project came from the ESPRIT project of the

European Union The European Union (EU) is a supranational political and economic union of member states that are located primarily in Europe. The union has a total area of and an estimated total population of about 447million. The EU has often been des ...

. Originally, its licensing terms allowed its software to be used freely for academic purposes, with commercial licenses available for other uses. CGAL Releases 3.x were distributed under the QPL license. Starting with CGAL 4.0, released in 2012, CGAL is distributed under the GPL version 3. it is managed by a thirteen-member editorial board, with an additional 30 developers and reviewers. The project started in 1996 as the pooling of the previous efforts of several project participants:PlaGeo and SpaGeo from

LEDA Leda may refer to: Mythology * Leda (mythology), queen of Sparta and mother of Helen of Troy in Greek mythology Places * Leda, Western Australia, a suburb of Perth, Western Australia * Leda makeshift settlement, Bangladesh, a refugee camp ...

of the Max-Planck-Institute for Informatics and C++GAL of

. The LEDA library encompasses a broader range of algorithms. A comparison of the two libraries is provided by Kettner and Näher. Three CGAL User workshops held in 2002, 2004, and 2008 highlighted research results related to CGAL, and many additional papers related to CGAL have appeared in other conferences, workshops, and journals.

Scope

The library covers the following topics: * Geometry kernels - basic geometric operations on

geometric primitive In vector computer graphics, CAD systems, and geographic information systems, geometric primitive (or prim) is the simplest (i.e. 'atomic' or irreducible) geometric shape that the system can handle (draw, store). Sometimes the subroutines that ...

s *

Arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...

and

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...

Convex hull In geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space ...

algorithms *

Polygon In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two toge ...

s and

polyhedra In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on t ...

* Polygon and polyhedron operations *

Arrangement In music, an arrangement is a musical adaptation of an existing composition. Differences from the original composition may include reharmonization, melodic paraphrasing, orchestration, or formal development. Arranging differs from orches ...

s *

Point set triangulation A triangulation of a set of points \mathcal in the Euclidean space \mathbb^d is a simplicial complex that covers the convex hull of \mathcal, and whose vertices belong to \mathcal. In the plane (when \mathcal is a set of points in \mathbb^2), tri ...

s *

Delaunay triangulation In mathematics and computational geometry, a Delaunay triangulation (also known as a Delone triangulation) for a given set P of discrete points in a general position is a triangulation DT(P) such that no point in P is inside the circumcircle o ...

s *

Voronoi diagram In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed ...

s *

Mesh generation Mesh generation is the practice of creating a mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells. Often these cells form a simplicial complex. Usually the cells partition the geometric input domain. ...

Geometry processing Geometry processing, or mesh processing, is an area of research that uses concepts from applied mathematics, computer science and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation a ...

* Search structures ( ''k''-d tree) * Shape analysis, fitting, and distances *

Interpolation In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a n ...

* Kinetic data structures

Platforms

The library is supported on a number of platforms:CGAL Supported Platforms
/ref> *

Microsoft Windows Windows is a group of several proprietary graphical operating system families developed and marketed by Microsoft. Each family caters to a certain sector of the computing industry. For example, Windows NT for consumers, Windows Server for serv ...

( GNU G++,

Microsoft Visual C++ Microsoft Visual C++ (MSVC) is a compiler for the C, C++ and C++/CX programming languages by Microsoft. MSVC is proprietary software; it was originally a standalone product but later became a part of Visual Studio and made available in both tri ...

Intel C++ Compiler Intel oneAPI DPC++/C++ Compiler and Intel C++ Compiler Classic are Intel’s C, C++, SYCL, and Data Parallel C++ (DPC++) compilers for Intel processor-based systems, available for Windows, Linux, and macOS operating systems. Overview Intel o ...

) * GNU g++ (

Solaris Solaris may refer to: Arts and entertainment Literature, television and film * ''Solaris'' (novel), a 1961 science fiction novel by Stanisław Lem ** ''Solaris'' (1968 film), directed by Boris Nirenburg ** ''Solaris'' (1972 film), directed by ...

Linux Linux ( or ) is a family of open-source Unix-like operating systems based on the Linux kernel, an operating system kernel first released on September 17, 1991, by Linus Torvalds. Linux is typically packaged as a Linux distribution, which ...

Mac OS Two major famlies of Mac operating systems were developed by Apple Inc. In 1984, Apple debuted the operating system that is now known as the "Classic" Mac OS with its release of the original Macintosh System Software. The system, rebranded "M ...

) *

Clang Clang is a compiler front end for the C, C++, Objective-C, and Objective-C++ programming languages, as well as the OpenMP, OpenCL, RenderScript, CUDA, and HIP frameworks. It acts as a drop-in replacement for the GNU Compiler Collection (GCC), ...

The CGAL library depends on the Boost libraries, and several CGAL packages on the Eigen C++ library.

References

{{Reflist

External links

CGAL Homepage
Geometric algorithms C++ libraries Python (programming language) libraries Free computer libraries Max Planck Institute for Informatics

History

Scope

Platforms

See also

References

External links