CGAL

CGAL
Name	CGAL
Developer	CGAL Project
Released	1996
Programming language	C++
Operating system	Cross-platform
License	LGPL with exceptions / dual licensing

CGAL CGAL is a software project providing a C++ library for computational geometry algorithms. It serves researchers and engineers working with Eurographics Association, ACM SIGGRAPH, INRIA, ETH Zürich, and École Polytechnique Fédérale de Lausanne by offering robust implementations used in Microsoft Research, Google, NASA, Siemens, and Zaha Hadid Architects-related projects. The library integrates with toolchains from GNU Project, LLVM, Intel, and NVIDIA and is cited alongside works from David Mount, Hanan Samet, Herbert Edelsbrunner, Jack Snoeyink, and Leonidas Guibas.

Overview

CGAL provides algorithms for computational geometry with an emphasis on correctness, performance, and interoperability with C++ standards from ISO/IEC JTC 1/SC 22, Boost (C++ libraries), and STL. Its scope includes routines for triangulation, mesh generation, polygon operations, geometric optimization, and surface reconstruction used in contexts such as Blender Foundation, Autodesk, Dassault Systèmes, Bentley Systems, and Esri. CGAL is used in academic courses at Massachusetts Institute of Technology, University of Cambridge, Stanford University, University of Tokyo, and University of Oxford.

History and Development

The project originated in the 1990s with contributors from INRIA, CNRS, ETH Zürich, and TU Berlin, inspired by foundational research by Kurt Mehlhorn, Erickson, Mark de Berg, and Otfried Cheong. Early milestones were associated with workshops at SoCG and publications in Computational Geometry: Theory and Applications and proceedings of ACM STOC. Development received support from European programs including ESPRIT and collaborations with industrial partners such as Thales Group, Airbus, and Philips. Major version releases tracked C++ evolution—including C++98, C++11, and C++17—and integrated contributions from researchers connected to ETH Zurich's Geometry Center and labs at Max Planck Society.

Core Components and Algorithms

CGAL implements classical and modern algorithms: Delaunay triangulation and Voronoi diagrams tied to work by Boris Delaunay and Georges Voronoi; convex hull algorithms influenced by Preparata and Shamos; Boolean operations on polygons using approaches comparable to those by F. Martínez and E. Welzl; and arrangements built upon arrangements research from Boissonnat and Yvinec. It includes robust predicates via exact arithmetic libraries like GMP, MPFR, and integration patterns similar to Shewchuk's robust predicates. Other algorithmic modules reflect topics from Computational Topology conferences and authors such as Jean-Daniel Boissonnat, Herbert Edelsbrunner, and Ulrich Reif.

Libraries and Data Structures

CGAL exposes template-based components consistent with patterns from Boost (C++ libraries) and STL. Core data structures include triangulation classes echoing design in Bowyer–Watson algorithms and mesh data structures comparable to those used in TetGen and Gmsh. It provides polyhedral surface representations influenced by Half-edge data structure work and integrates with kernel models similar to Exact Geometric Computation paradigms championed by Robust Geometric Computation researchers. Additional modules interoperate with Eigen (library), OpenMesh, VTK, and CGAL::Surface_mesh-style containers enabling use in toolchains deployed by ParaView and Kitware.

Applications and Use Cases

CGAL is applied in domains ranging from CAD pipelines in Dassault Systèmes and Siemens PLM Software to medical imaging workflows in GE Healthcare and Siemens Healthineers. It supports archaeology and heritage projects allied with Smithsonian Institution and British Museum for surface reconstruction, and is used in robotics path planning research aligned with Carnegie Mellon University and ETH Zurich labs. In computational science, it is used alongside solvers such as PETSc and Trilinos and meshing tools like TetGen, Gmsh, and MeshLab for finite element analysis in projects at Argonne National Laboratory and Lawrence Berkeley National Laboratory.

Licensing and Governance

CGAL is governed by a steering committee with representatives from academic institutions including INRIA, ETH Zürich, TU Darmstadt, and companies that license commercial support from vendors such as CGAL SAS and organizations offering enterprise services akin to Red Hat support models. Licensing uses a dual scheme combining GNU Lesser General Public License variants with commercial licensing options similar to proprietary offerings from Oracle or Microsoft for enterprise integration. The project roadmap and releases are coordinated through community-driven processes resembling governance in Apache Software Foundation-style projects, with contributions from researchers affiliated with Universität des Saarlandes, University of British Columbia, and TU Wien.

Category:Computational geometry software