Release History

4.6  (March 2015)
4.5.2  (February 2015)
4.5.1  (December 2014)
4.5  (October 2014)
4.4  (April 2014)
4.3.1  (November 2013)
4.3  (October 2013)
4.2  (March 2013)
4.1  (September 2012)
4.0.2  (July 2012)
4.0.1  (July 2012)
4.0  (March 2012)
3.9  (September 2011)
3.8  (April 2011)
3.7  (October 2010)
3.6.1  (June 2010)
3.6  (March 2010)
3.5.1  (December 2009)
3.5  (October 2009)
3.4  (January 2009)
3.3.1 (August 2007)
3.3 (May 2007)
3.2.1 (July 2006)
3.2 (May 2006)
3.1 (December 2004)
3.0.1 (February 2004)
3.0 (October 2003)
2.4 (May 2002)
2.3 (August 2001)
2.2 (October 2000)
2.1 (January 2000)
2.0 (June 1999)
1.2 (January 1999)
1.1 (July 1998)
1.0 (April 1998)
0.9 (June 1997)
Number of lines of code of CGAL
(using David A. Wheeler's 'SLOCCount', restricted to the include/CGAL/ and src/ directories).
Releases size graph

Release 4.6

Release date: March 2015

2D Generalized Barycentric Coordinates (new package)

  • This package offers an efficient and robust implementation of two-dimensional closed-form generalized barycentric coordinates defined for simple two-dimensional polygons.

Scale-Space Surface Reconstruction (new package)

  • This new package provides a class gathering a dedicated smoothing algorithm and some convenience functions to help the creation of a surface out of a point set using the 3D Alpha Shapes package. The particularity of this reconstruction pipeline is that the input point are in the output and no new points are created. Note that in the current version, the output is a triangle soup that is not necessarily a valid (manifold) polyhedral surface.

Surface Mesh (new package)

  • The surface mesh class provided by this package is a data structure that can be used as halfedge data structure or polyhedral surface. It is an alternative to the packages CGAL::Polyhedron_3 and CGAL::HalfedgeDS.

Triangulation (new package)

  • This new package provides classes for manipulating triangulations in Euclidean spaces whose dimension can be specified at compile-time or at run-time.

dD Geometry Kernel

  • It has been reported that the recently introduced Epick_d kernel may not work with Intel C++ Compiler prior to version 15. Documentation has been updated.

3D Convex Hulls

  • Add functions halfspace_intersection_3 and halfspace_intersection_with_constructions_3 to compute the intersection of halfspaces defining a closed polyhedron.
  • Fix a bug introduced in CGAL 4.5 that can appear while computing the convex hull of coplanar points.
  • Fix a robustness issue in Convex_hull_traits_3. This traits is used by default with the kernel Exact_predicates_inexact_constructions_kernel.

Combinatorial Maps and Linear Cell Complex

  • Added correct_invalid_attributes, set_automatic_attributes_management and are_attributes_automatically_managed methods in CombinatorialMap concept. This allows high level operations to not update non void attributes during massive calls of these operations, but only after the end of their executions.

2D Triangulations

  • The class Constrained_triangulation_plus_2 now can handle polylines as constraints.
  • As a consequence a Constraint_id has been introduced which replaces pair<Vertex_handle,Vertex_handle> as identifier of a constraint.

3D Mesh Generation

  • Add member functions output_boundary_to_off and output_facets_in_complex_to_off in the class CGAL::Mesh_complex_3_in_triangulation_3 to export the boundary of a domain or a subdomain.

3D Fast Intersection and Distance Computation

  • Add new constructors to AABB_halfedge_graph_segment_primitive and AABB_face_graph_triangle_primitive in order to be able to build primitives one by one.

Spatial Searching

  • Fixed a bug in CGAL::Splitters.h sliding mitdpoint rule, where degenerated point sets (e.g.,points on segment) caused the kd-tree to get linear.
  • Improved performance of Orthogonal_k_neighbor_search. Note that VC 2013 does not compile boost::container::deque of Boost 1_55 and does hence have a workaround which does not have the improvement.
  • Breaking change: The concept OrthogonalDistance has new function overloads for min_distance_to_rectangle and max_distance_to_rectangle with an additional reference parameter std::vector.
  • Breaking change: The order of the points in the iterator range [tree.begin(),tree.end()] is not the order of insertion of the points into the tree. This was not guaranteed before but might have beeen observed and exploited by users.
  • Derived kd_tree_leaf_node and kd_tree_internal_node from kd_tree_node to save memory.

Geometric Object Generators

  • Add a new function random_convex_hull_in_disc_2 that efficiently generates a random polygon as the convex hull of uniform random points chosen in a disc.

Release 4.5.2

Release date: February 2015


  • Fix a bug that prevented the compilation with recent versions of Boost (>=1.56) when explicit conversions operators (from C++11) are supported. That prevented the compilation with Microsoft Visual Studio 2013.

3D Convex Hulls

  • Fix a non-robust predicate bug that was showing up when input points where lexicographically sorted.

3D Mesh Generation

  • Fix a bug in the sliver perturbation optimization method. It could create some holes on the surface of the mesh.

Release 4.5.1

Release date: December 2014

3D Mesh Generation

  • Fix a bug in the sliver exudation preservation of boundaries.

Release 4.5

Release date: October 2014


  • Changes in the set of supported platforms:
    • The Microsoft Windows Visual C++ compiler 2008 (VC9) is no longer supported since CGAL-4.5.
  • Since CGAL version 4.0, Eigen was the recommended third-party library to use with Planar Parameterization of Triangulated Surface Meshes, Surface Reconstruction from Point Sets, Approximation of Ridges and Umbilics on Triangulated Surface Meshes, and Estimation of Local Differential Properties of Point-Sampled Surfaces packages. From CGAL version 4.5, Taucs, Blas and Lapack are no longer supported.
  • CGAL is now compatible with the new CMake version 3.0.

Triangulated Surface Mesh Deformation (new package)

  • This package allows to deform a triangulated surface mesh under positional constraints of some of its vertices without requiring any additional structure other than the surface mesh itself. The methods provided implements an as-rigid-as-possible deformation. Note that the main class name has changed between the 4.5-beta1 and the 4.5 releases to better match the CGAL naming conventions (from CGAL::Deform_mesh to CGAL::Surface_mesh_deformation).

CGAL and the Boost Graph Library (major changes)

  • Cleanup of the HalfedgeGraph concept. In particular:
    • Introduction of the notion of halfedge_descriptor in the specialization of the class boost::graph_traits.
    • Deprecation of halfedge_graph_traits.
    • A model of HalfedgeGraph is considered as an undirected graph. Thus any call to edges() should be replaced by halfedges() and num_edges() now returns the number of (undirected) edges.
    • Breaking change: is_border_edge and is_border_halfedge properties are removed. The free functions is_border() and is_border_edge() should be used instead.
    • Renaming of HalfedgeGraph specific free functions.
  • Introduction of the FaceGraph concept.
  • Adaptation of the package Triangulated Surface Mesh Simplification and of the class AABB_halfedge_graph_segment_primitive from the package 3D Fast Intersection and Distance Computation to the API change.
  • Update of the package Triangulated Surface Mesh Segmentation and of the class AABB_face_graph_triangle_primitive from the package 3D Fast Intersection and Distance Computation to accept model of the newly introduced concepts.
  • Offer Euler operations as free functions for models of the graph concepts provided by CGAL.
  • Specialization of boost::graph_traits for OpenMesh::PolyMesh_ArrayKernelT as proof of concept. A OpenMesh::PolyMesh_ArrayKernelT becomes a model of the aforementioned concepts when including CGAL/boost/graph/graph_traits_PolyMesh_ArrayKernelT.h.

dD Geometry Kernel

  • A new model Epick_d of the Kernel_d concept is introduced. It provides better performance through arithmetic filtering and specializations for fixed dimensions. It may not work with compilers as old as gcc-4.2, but was tested with gcc-4.4.

3D Convex Hulls

  • Clean up the documentation of the concepts

2D Arrangements

  • Fixed a bug in removing an unbounded curve (e.g., a ray) from an arrangement induced by unbounded curves.

2D Snap Rounding

  • Replaced use of private kd_tree with CGAL's official Kd_tree from Spatial_searching package; results in a small performance gain. Removed the private kd_tree package.

3D Triangulations

  • Add an experimental parallel version of the Delaunay triangulation and the regular triangulation algorithms, which allows parallel insertion and removal of point ranges.

3D Mesh Generation

  • Add a new constructor for the class Labeled_mesh_domain_3 which takes an Iso_cuboid_3.
  • Add a new labeling function wrapper for meshing multi-domain.
  • The meshing functionality in the Qt demos in demo/Polyhedron/ and demo/Mesh_3/ can now use the handling of 1d-features, that exists in CGAL since version 3.8.
  • Add an experimental parallel version of the 3D mesh refinement and mesh optimization methods.
  • Add caching of circumcenters to Regular_triangulation_cell_base_3. The cache value is computed when cell->circumcenter() or rt.dual(cell) functions are called.

Point Set Processing and Surface Reconstruction from Point Sets

  • The former demo has been removed and is fully merge in the Polyhedron demo.

Point Set Processing

  • Workaround a bug in dijsktra shortest path of boost 1.54 by shipping and using the boost header from the 1.55 release. This header will be used only if you are using the version 1.54 of boost.

Triangulated Surface Mesh Simplification

  • Breaking change: Due to the cleanup of the concepts of the package CGAL and the Boost Graph Library, the named parameter edge_is_border_map has been removed, and the named parameter edge_is_constrained_map now expects a property map with an edge descriptor as key type (vs. halfedge descriptor before).
  • Add some optimization in the code making the implementation faster (depending on the cost and the placement chosen). However, for an edge which collapse is not topologically valid, the vector of vertices of the link provided by its profile might contains duplicates, thus also breaking the orientation guarantee in the vector. This must not be a problem for users as the edge is not collapsible anyway but if it is a absolute requirement for user defined cost/placement, defining the macro CGAL_SMS_EDGE_PROFILE_ALWAYS_NEED_UNIQUE_VERTEX_IN_LINK will restore the former behavior.

dD Spatial Searching

  • Added methods reserve(size_t size) and size_t capacity() to class Kd_tree to allocate memory to store size points and to report that number (STL compliance).

STL Extensions for CGAL

  • Add Compact_container::operator[], allowing a direct access to the ith element of a compact container.
  • Add Concurrent_compact_container, a compact container which allows concurrent insertion and removal.

Release 4.4

Release date: April 2014


  • Additional supported platforms:
    • The Apple Clang compiler version 5.0 is now supported on OS X Mavericks.
    • The Microsoft Windows Visual C++ compiler 2013 (VC12) is now supported.

Triangulated Surface Mesh Segmentation (new package)

  • This package implements the segmentation of triangulated surface meshes based on the Shape Diameter Function (SDF). In addition, it also provides functions to generate segmentations based on a user defined alternative to the SDF.

Number Types

  • A new class CGAL::Mpzf is introduced on some platforms for exact ring operations. It is used to improve the speed of the evaluation of predicates in degenerate situations.

2D and 3D Geometry Kernel

  • Fix a bug introduced in CGAL 4.3 when computing the intersection of two 3D triangles.

2D Polygon Partitioning

  • Bug fix to make the partition algorithms working with a Lazy kernel such as Exact_predicates_exact_constructions_kernel.

2D Regularized Boolean Set-Operations

  • Fix two memory leaks in CGAL::General_polygon_set_2.

Combinatorial Maps and Linear Cell Complex

  • null_dart_handle is no longer a static data member in the CombinatorialMap concept. This implies to move the following methods of Dart concept into CombinatorialMap concept: is_free, highest_nonfree_dimension, opposite and other_extremity. We also transform the static methods vertex_attribute and point of Linear_cell_complex class into non static methods. You can define the CGAL_CMAP_DEPRECATED macro to keep the old behavior.

2D Arrangements

  • Revise the API of polylines. In particular, construction is now done using functors and iteration is possible only on the segments of a polyline.
  • Fix a bug in the Landmark point-location strategy.

2D Snap Rounding

  • Fix a memory leak

2D Triangulations

  • Add different overloads of the function insert_constraints that inserts a range of points and segments, or a range of segments. These functions uses the spatial sorting in order to speed up the time needed for the insertion.

3D Periodic Triangulations

  • Add a method to locate point with inexact predicates.

3D Alpha Shapes

  • Add member functions in CGAL::Alpha_shape_3 to give access to the alpha status of edges and facets (get_alpha_status()).
  • Add another filtration method (filtration_with_alpha_values()) that reports the alpha value at which each face appears in the filtration.

3D Mesh Generation

  • Fix the access to functions number_of_facets and number_of_cells in Mesh_complex_3_in_triangulation_3.
  • Change the internal API of the sliver perturber, to make possible for developers to optimize another criterion than the (default) minimal dihedral angle. Developers can also define a new perturbation vector (for angles we had gradient of squared circumradius, gradient of volume, gradient of minimal dihedral angle, and random) which is better suitable to optimize their criterion.
  • Improve the use of cache values in Mesh_cell_base_3 to (re)compute circumcenters and sliver criterion values only when needed.

Triangulated Surface Mesh Simplification

  • Fix a bug in the way edges can be marked as non-removable by adding a named-parameter edge_is_constrained_map to the function edge_collapse

dD Spatial Searching

  • Fix a documentation bug: The property map passed as template parameter to the classes Search_traits_adapter and Distance_adapter must be a lvalue property map. To avoid incorrect usage, a static assertion has been added in the CGAL code to prevent the user from instantiating these classes with an incorrect property map type.

CGAL ipelets

  • Better description of the demo ipelets in the user manual
  • New ipelet for pencils of circles
  • New ipelet for hyperbolic geometry in Poincaré model
  • The generator ipelet now generates point in a selected zone
  • Hilbert sort ipelet implements two policies

Release 4.3

Release date: October 2013

The CGAL Manual

  • The documentation of CGAL is now generated with Doxygen.

2D Periodic Triangulations (new package)

  • This package allows to build and handle triangulations of point sets in the two dimensional flat torus. Triangulations are built incrementally and can be modified by insertion or removal of vertices. They offer point location facilities. The package provides Delaunay triangulations and offers nearest neighbor queries and primitives to build the dual Voronoi diagrams.

API Changes

2D and 3D Geometry Kernel

  • The intersection functions and functors used to return a CGAL::Object in order to deal with the different possible return types. However, depending on the arguments it is possible to reduce the possible return types to a small set. For this reason and to take advantage of the type safety, we decided to use boost::variant instead of CGAL::Object. The result_of protocol is now even more useful to determine the return type of the intersection functions and functors. The change should be relatively transparent to the user thanks to the implicit constructor added to CGAL::Object. However, it is recommended to upgrade your code. The previous behavior can be restored by defining the macro CGAL_INTERSECTION_VERSION to 1.

2D Arrangements

  • The type of the result of point location queries changed to boost::variant (from CGAL::Object). For convenience, the previous behavior can be restored by defining the macro CGAL_ARR_POINT_LOCATION_VERSION to 1.
  • Introduced an optimization for operations on large and dense arrangements.

3D Fast Intersection and Distance Computation

  • Following the intersection API change, Object_and_primitive_id has been replaced by a template class Intersection_and_primitive_id<Query> to determine the type depending on the query object type.

CGAL and Boost Property Maps

  • The key_type of the property maps provided by CGAL used to be an iterator. In order to be more easily re-used, the key_type has been changed to be the value_type of the iterator. The packages that have been updated to match these changes are Point Set Processing and Surface Reconstruction from Point Sets. However, for most users this change should be transparent if the default property maps were used. For convenience, the former behavior can be enabled by defining the macro CGAL_USE_PROPERTY_MAPS_API_V1.

Algebraic Foundations

  • For convenience, add an overload of make_rational() taking a pair of numbers.

2D and 3D Geometry Kernel

  • A Iso_rectangle_2 can now be constructed from a Bbox_2 and an Iso_cuboid_3 from a Bbox_3.
  • The implementation of CGAL::Object has been updated and now uses boost::shared_ptr and boost::any. This implementation is faster.
  • Add to Bbox_2 and Bbox_3 a += operator as well as free functions to get the bounding box of a range of geometric objects.

Combinatorial Maps

  • Two bug fixes: do not use the 2 least significant bits for cell attribute without dart support; share the mark when copying a CMap_cell_iterator.
  • Add a constructor taking a given combinatorial map as argument, possibly with different dimension and/or different attributes. This allows to transform a combinatorial map.
  • Add operator= and swap method.
  • Add dynamic onmerge/onsplit functions that can be associated dynamically to i-attributes and which are automatically called when i-cells are split/merged.
  • Add a function allowing to reverse the orientation of a combinatorial map, and another one to reverse one connected component of a combinatorial map.

3D Boolean Operations on Nef Polyhedra

  • Bug-fix in IO when using Lazy_exact_nt as number type or Exact_predicates_exact_constructions_kernel as kernel.

2D Triangulations

  • Extend the concept TriangulationDataStructure_2 to require a more general copy_tds function that allows a copy between TDS of different types. The CGAL model has been updated.
  • Add a way to efficiently insert a range of points with information into the 2D constrained Delaunay triangulations.

3D Triangulations

  • Extend the concept TriangulationDataStructure_3 to require a more general copy_tds function that allows a copy between TDS of different types. The CGAL model has been updated.
  • Add an advanced function to set the infinite vertex of the triangulation for low level operations
  • Fix a bug in the function inserting a range of points with info when the Fast_location tag is used

2D Segment Delaunay Graph

  • Add functions insert_points and insert_segments to insert a range of points and segments. These functions uses the spatial sorting in order to speed up the time needed for the insertion. The function insert(Input_iterator first, Input_iterator beyond, Tag_true) has been updated to dispatch the input when possible to these functions.

2D Apollonius Graphs

  • Modified insertion algorithm so that the code can handle pseudo-circles as well.
  • Updated implementation of the vertex conflict predicate by a faster version.

3D Mesh Generation

  • Speed-up Mesh_3 and in particular the global optimizers (Lloyd and ODT) by introducing a parameter do_freeze to prevent from moving vertices which would move of very small displacements.
  • Introduce new data structures and options for speed-up and compacity. Note that Compact_mesh_cell_base_3 and Mesh_vertex_base_3 are now our favoured implementations of the concepts MeshCellBase_3 and MeshVertexBase_3.
  • Introduce a new constructor for Polyhedral_mesh_domain_3 that takes a bounding polyhedron to be meshed along with a polyhedral surface entirely included in it. This allows the user to mesh a polyhedral domain with internal surface(s) which can be non-watertight and even non-manifold.
  • Several documentation bug fixes.
  • Provide the ability to plug in custom cell_base/vertex_base classes into the Mesh_triangulation_3 class.

Triangulated Surface Mesh Simplification

  • Fix a segmentation fault that was happening when some edges of length 0 were in the input mesh.

3D Fast Intersection and Distance Computation

  • Following the intersection API change, Object_and_primitive_id has been replaced by a template class Intersection_and_primitive_id<Query> to determine the type depending on the query object type.
  • Introduce the class AABB_halfedge_graph_segment_primitive, which replaces the class AABB_polyhedron_segment_primitive (which is now deprecated). The new class is more general and can be used with any model of HalfedgeGraph.
  • Introduce the class AABB_face_graph_triangle_primitive which replaces the class AABB_polyhedron_triangle_primitive (which is now deprecated).
  • Document the classes AABB_segment_primitive and AABB_triangle_primitive that were already used in some examples.
  • Add a generic primitive class AABB_primitive that allows to define a primitive type by defining only two property maps.
  • Introduce a new concept of primitive AABBPrimitiveWithSharedData. It allows to have some data shared between the primitives stored in a AABB_tree. With this you can, for example have a primitive wrapping an integer which refers to the position of a geometric object in a std::vector. Only one reference to this vector will be stored in the traits of the tree. The concept AABBTraits, its model AABB_traits and the class AABB_tree have been updated accordingly. However, everything is backward compatible.
  • Fix a memory leak in the destructor of the class AABB-tree

STL Extensions for CGAL

  • Add to Dispatch_output_iterator and Dispatch_or_drop_output_iterator an operator to accept and dispatch a tuple of values.

Concurrency in CGAL

  • Add a FindTBB CMake module so that one can easily link with TBB to write shared-memory parallel code.
  • Introduce two new tags: Sequential_tag and Parallel_tag

Release 4.2

Release date: March 2013


  • Additional supported platforms:
    • The Microsoft Windows Visual C++ compiler 2012 (VC11) is now supported.
  • With Microsoft Visual C++ (all supported versions), the compiler flags /bigobj and /wd4503 are added by CGAL CMake scripts.
  • This is the last release whose "UseCGAL.cmake" file (if using CGAL in a CMake build environment) contains the line
    as this is a deprecated CMake command. The correct way to link with CGAL's libraries (as for required 3rd party libraries) is to use 'target_link_libraries' which specifies for each build target which libraries should be linked. The following serves as example:
      add_executable(myexe main.cpp)
      target_link_libraries(myexe ${CGAL_LIBRARIES}
    We also expect further changes in CGAL's CMake setup (change of variable names, consistency of filename and output, removing essential libraries, building executables, removal of '${CGAL_3RD_PARTY_LIBRARIES}').

2D Arrangements

  • Enhanced the 2D-arrangements demonstration program and ported it to Qt4. The new demonstration program makes use of the CGAL Graphics View framework, in which the 2D primitives are individually represented as objects in a scene. (The implementations of several demos in CGAL already make use of this framework.) This project was carried out as part of the 2012 Google Summer of Code program.
  • Fixed a bug in the Walk-Along-A-Line point location strategy for arrangements induced by unbounded curves.

2D Circular Geometry Kernel

  • Fix the intersection type computed when intersecting two identical circles.
  • Forward correctly the result type of the linear kernel functors

2D Triangulations

  • Add mechanism to avoid call stack overflow in Delaunay_triangulation_2 and Constrained_Delaunay_triangulation_2.
  • Add a constructor for Regular_triangulation_2 and Delaunay_triangulation_2 from a range of points or a range of points with info.

2D Voronoi Diagram Adaptor

  • Bug-fix: Add ccb() method in face type as documented.

3D Minkowski Sum of Polyhedra

  • Fix a memory leak.

3D Fast Intersection and Distance Computation

  • Update requirements of the concepts AABBTraits and AABBGeomTraits to match the implementation of the package.


  • Addition of the Combination_enumerator

STL Extensions

  • Introduction of CGAL::cpp11::result_of as an alias to the tr1 implementation from boost of the result_of mechanism. When all compilers supported by CGAL will have a Standard compliant implemention of the C++11 decltype feature, it will become an alias to std::result_of.

Surface Reconstruction from Point Sets

  • Performance improvements and addition of an option to better reconstruct undersampled zones. The poisson reconstruction plugin of the Polyhedron demo has an option to switch it on.

Release 4.1

Release date: October 2012


  • Additional supported platforms:
    • The Apple Clang compiler versions 3.1 and 3.2 are now supported on Mac OS X.
  • Improved configuration for essential and optional external third party software
  • Added more general script to create CMakeLists.txt files: cgal_create_CMakeLists
  • Availability tests for C++11 features are now performed with the help of Boost.Config. A Boost version of 1.40.0 or higher is needed to use C++11 features.

2D Arrangement

  • Improved the implementation of the incremental randomized trapezoidal decomposition point-location strategy. The new implementation enables point location in unbounded arrangements. It constructs a search structure of guaranteed linear size with guaranteed logarithmic query time.

2D Convex Hulls and Extreme Points

  • Speed up the preprocessing stage of the Akl-Toussaint implementation (used by the free function convex_hull_2 when forward iterators are provided as input).

Combinatorial Maps

  • Minor bugfix; replace some functors by methods.

Linear Cell Complex

  • Improve the demo: add a widget showing all the volumes and an operation to create a Menger sponge.


  • All Kernel functors now support the result_of protocol.

STL_Extensions for CGAL

  • The namespace cpp0x has been renamed cpp11. The old name is still available for backward compatibility.

Release 4.0.2

Release date: Jul 2012

This is a bug fix release. It fixes a bug in the CMakeLists.txt for CGAL-4.0.1, that prevented even building the libraries.

Release 4.0.1

Release date: Jul 2012

This is a bug fix release. Apart various minor fixes in the documentation, the following has been changed since CGAL-4.0:

2D Voronoi Diagram Adaptor (re-added)

  • The package 2D Voronoi Diagram Adaptor was temporarily removed from the CGAL distribution because of license issues. That package is now back into CGAL.

2D and 3D Geometry Kernel

  • Fix a bug in the Segment_3-Triangle_3 intersection function in the case the segment is collinear with a triangle edge.
  • Fix a bug in the Projection_traits_.._3 class in the case a segment was parallel to the x-axis.

Algebraic Kernel

  • Avoid the linking error "duplicate symbols" when two compilation units using the algebraic kernel are linked.

3D Boolean Operations on Nef Polygons Embedded on the Sphere

  • Fix a memory leak due to the usage of an internal mechanism that has been replaced by boost::any. This also influences the packages 2D Boolean Operations on Nef Polygons, 3D Boolean Operations on Nef Polyhedra, Convex Decomposition of Polyhedra, and 3D Minkowski Sum of Polyhedra.

2D Arrangement

  • Fix several memory leaks.

2D Mesh Generation

  • Fix a compilation error in the header <CGAL/Mesh_2/Do_not_refine_edges.h> when g++ version 4.7 is used.

Surface Mesh Generation and 3D Mesh Generation

  • Fix an important bug in the CGAL_ImageIO library, that could lead to wrong result when meshing from a 3D image.
  • Fix the compilation of the demo in demo/Surface_mesher, when Boost version 1.48 or 1.49 is used.

Surface Mesh Parameterization

  • Fix a memory leak.
  • Fix a compatibility issue with Eigen-3.1 of Eigen_solver_traits. This fix also affects the usage of that class in the package Surface Reconstruction from Point Sets.

Release 4.0

Release date: March 2012

CGAL 4.0 offers the following improvements and new functionality :

License Changes

The whole CGAL-3.x series was released under a combination of LGPLv2 (for the foundations of CGAL), and QPL (for the high-level packages). QPL was the former license of the graphical toolkit Qt, but that license is not supported by any major free software project. Furthermore, the terms of the LGPLv2 license are ambiguous for a library of C++ templates, like CGAL.

The CGAL project, driven by the CGAL Editorial Board, has decided to change the license scheme of CGAL. We increased the major number of the CGAL version to '4' in order to reflect this license change. The CGAL-4.x series is released under:

  • LGPLv3+ (that is LGPL "either version 3 of the License, or (at your option) any later version"), for the foundations of CGAL, instead of LGPLv2,
  • GPLv3+ for the high-level packages, instead of QPL.


  • On Windows, CGAL libraries are now built by default as shared libraries (also called DLL). To run applications that use .dll files of CGAL, you must either copy the .dll files into the directory of the application, or add the path of the directory that contains those .dll files into the PATH environment variable.
  • On Windows, the CMake scripts of CGAL now search for shared version of the Boost libraries. You must ensure that the .dll files of Boost are found by the dynamic linker. You can, for example, add the path to the Boost .dll files to the PATH environment variable.
  • On Windows, CMake version 2.8.6 or higher is now required.
  • Eigen version 3.1 or later is now the recommended third party library to use in Planar Parameterization of Triangulated Surface Meshes, Surface Reconstruction from Point Sets, Approximation of Ridges and Umbilics on Triangulated Surface Meshes, and Estimation of Local Differential Properties of Point-Sampled Surfaces packages. If you use Eigen you no longer need Taucs, Lapack or Blas to use those packages (and any other in CGAL).

Linear Cell Complex (new package)

  • This package implements linear cell complexes, objects in d-dimension with linear geometry. The combinatorial part of objects is described by a combinatorial map, representing all the cells of the object plus the incidence and adjacency relations between cells. Geometry is added to combinatorial maps simply by associating a point to each vertex of the map. This data structure can be seen as the generalization in dD of the Polyhedron_3.

2D Voronoi Diagram Adaptor (temporarily removed)

  • As the copyright holder of this package has not granted the right to switch from QPL to GPL, this package is removed from the distribution. Note that it is "only" an adapter, that is the functionality of point/segment/disk Voronoi diagram is offered through the Delaunay triangulation, segment Delaunay graph, and Apollonius graph.


  • Document constness of member functions of the AABB_tree class.
  • The class AABB_tree is now guaranteed to be read-only thread-safe. As usual in CGAL, this small overhead introduced for thread-safety can be deactivated by defining CGAL_HAS_NO_THREADS.

2D Alpha Shapes

  • Add an extra template parameter to the class Alpha_shape_2 that allows a certified construction using a traits class with exact predicates and inexact constructions.
  • An object of type Alpha_shape_2 can now be constructed from a triangulation.

3D Alpha Shapes

  • Add an extra template parameter to the class Alpha_shape_3 that allows a certified construction using a traits class with exact predicates and inexact constructions.

Geometric Object Generators

  • Random_points_in_iso_box_d (deprecated since 3.8) has been removed. Use Random_points_in_cube_d instead.

Linear and Quadratic Programming Solver

  • Minor bugfix.

Spatial Searching

  • The const-correctness of this package have been worked out. The transition for users should be smooth in general, however adding few const in user code might be needed in some cases.
  • The class Kd_tree is now guaranteed to be read-only thread-safe. As usual in CGAL, this small overhead introduced for thread-safety can be deactivated by defining CGAL_HAS_NO_THREADS.
  • Bug-fix in Orthogonal_incremental_neighbor_search and Incremental_neighbor_search classes. Several calls to begin() now allow to make several nearest neighbor search queries independently.

STL Extension

  • CGAL::copy_n is now deprecated for CGAL::cpp0x::copy_n which uses std::copy_n, if available on the platform.
  • CGAL::successor and CGAL::predecessor are now deprecated for CGAL::cpp0x::next and CGAL::cpp0x::prev. These functions use the standard versions if available on the platform. Otherwise, boost::next and boost::prior are used.


  • Fix a thread-safety issue in Delaunay_triangulation_2 remove functions. As usual in CGAL, the small overhead introduced for thread-safety can be deactivated by defining CGAL_HAS_NO_THREADS.
  • Add extraction operator for the class Constrained_triangulation_2 (and thus to all inheriting classes).

Release 3.9

Release date: September 2011

CGAL 3.9 offers the following improvements and new functionality :


  • The class Root_of_2 is now deprecated. It is recommended to use the class Sqrt_extension instead.
  • The class Sqrt_extension is now used everywhere in CGAL where an algebraic number of degree 2 is needed. This change has been done in the Root_of_traits mechanism (indirectly packages 2D Circular kernel and 3D Spherical kernel) and the packages 2D Segment Delaunay Graphs and 2D Arrangements.
  • Various fixes in the manual.

Combinatorial Maps (new package)

  • This package provides a new combinatorial data structure allowing to describe any orientable subdivided object whatever its dimension. It describes all cells of the subdivision and all the incidence and adjacency relations between these cells. For example it allows to describe a 3D object subdivided in vertices, edges, faces and volumes. This data structure can be seen as the generalization in dD of the halfedge data structure.

3D Convex Hull (major performance improvement)

  • The quickhull implementation of CGAL (CGAL::convex_hull_3) has been worked out to provide very better performances.
  • The function CGAL::convex_hull_3 no longer computes the plane equations of the facets of the output polyhedron. However an example is provided to show how to compute them easily.
  • A global function convex_hull_3_to_polyhedron_3 is now provided to extract the convex hull of a 3D points set from a triangulation of these points.

dD Spatial Searching (major new feature added)

  • A traits-class and distance adapter that together with a point property map, allow to make nearest neighbor queries on keys instead of points have been added.
  • Few bug fixes in the documentation have revealed some inconsistencies that have been corrected. Two traits class concept are now documented (RangeSearchTraits and SearchTraits). Most other changes concerns only classes documented as advanced. One issue that user can encounter is due to an additional requirement on the nested class Construct_cartesian_const_iterator_d defined in the concept SearchTraits that must provide a nested type result_type.

Spatial Sorting (major new feature added)

  • General dimension is now supported.
  • Hilbert sorting admits now two policies: splitting at median or at middle (see user manual).
  • Using a property map, sorting on keys instead of points is now easier

dD Kernel

  • The d-dimensional kernel concept and models have been modified to additionally provide two new functors Less_coordinate_d and Point_dimension_d.

2D Arrangements

  • A new geometry-traits class that handles rational arcs, namely Arr_rational_function_traits_2, has been introduced. It replaced an old traits class, which handled the same family of curves, but it was less efficient. The new traits exploits CGAL algebraic kernels and polynomials, which were not available at the time the old traits class was developed.
  • A new geometry traits concept called ArrangementOpenBoundaryTraits_2 has been introduced. A model of this concept supports curves that approach the open boundary of an iso-rectangular area called parameter space, which can be unbounded or bounded. The general code of the package, however, supports only the unbounded parameter space. We intend to enhance the general code to support also bounded parameter spaces in a future release.
  • The deprecated member function is_at_infinity() of Arrangement_2::Vertex has been removed. It has been previously replaced new function is_at_open_boundary().
  • The tags in the geometry traits that indicate the type of boundary of the embedding surface were replaced by the following new tags:
    It is still possible not to indicate the tags at all. Default values are assumed. This however will produce warning messages, and should be avoided.

Release 3.8

Release date: April 2011

CGAL 3.8 offers the following improvements and new functionality :


  • Boost version 1.39 at least is now required.
  • Initial support for the LLVM Clang compiler (prereleases of version 2.9).
  • Full support for the options -strict-ansi of the Intel Compiler 11, and -ansi of the GNU g++ compiler.
  • Adding a concept of ranges. In the following releases, it will be the way to provide a set of objects (vs. a couple of iterators).
  • Fix a memory leak in CORE polynomials.
  • Various fixes in the manual.

3D Mesh Generation (major new feature added)

  • Adding the possibility to handle sharp features: the 3D Mesh generation package now offers the possibility to get in the final mesh an accurate representation of 1-dimensional sharp features present in the description of the input domain.

2D Triangulations (major new feature added)

  • Add a way to efficiently insert a range of points with information into a 2D Delaunay and regular triangulation.
  • Add member function mirror_edge taking an edge as parameter.
  • Fix an infinite loop in constrained triangulation.

3D Triangulations (major new feature added)

  • Add a way to efficiently insert a range of points with information into a 3D Delaunay and regular triangulation.
  • Add a member function to remove a cluster of points from a Delaunay or regular triangulation.
  • function vertices_in_conflict is renamed vertices_on_conflict_zone_boundary for Delaunay and regular triangulation. Function vertices_inside_conflict_zone is added to regular triangulation.
  • Structural filtering is now internally used in locate function of Delaunay and regular triangulation. It improves average construction time by 20%.
  • Added demo.

3D Alpha Shapes (major new feature added)

  • The new class Fixed_alpha_shape_3 provides a robust and faster way to compute one alpha shape (with a fixed value of alpha).

AABB tree

  • Adding the possibility to iteratively add primitives to an existing tree and to build it only when no further insertion is needed.

2D and 3D Kernel

  • Better handling of 2D points with elevation (3D points projected onto trivial planes). More general traits classes (Projection_traits_xy_3, Projection_traits_yz_3,Projection_traits_yz_3) are provided to work with triangulations, algorithms on polygons, alpha-shapes, convex hull algorithm... Usage of former equivalent traits classes in different packages is now deprecated.
  • Exact_predicates_exact_constructions_kernel now better use the static filters which leads to performance improvements.
  • Add an overload for the global function angle, taking three 3D points.
  • In the 2D and 3D kernel concept, the constant Boolean Has_filtered_predicates is now deprecated. It is now required to use Has_filtered_predicates_tag (being either Tag_true or Tag_false).
  • Compare_distance_2 and Compare_distance_3 provide additional operators for 3 and 4 elements.
  • Add intersection test and intersection computation capabilities between an object of type Ray_3 and either an object of type Line_3, Segment_3 or Ray_3.
  • Improve intersection test performance between an object of type Bbox_3 and an object of type Plane_3 or Triangle_3 by avoiding arithmetic filter failures.

2D Envelope

  • Env_default_diagram_1 is deprecated, Envelope_diagram_1 should be used instead.

3D Envelope

  • A new demo program called L1_Voronoi_diagram_2 has been introduced. It demonstrates how 2D Voronoi diagrams of points under the L1 metric are constructed using lower envelopes.

dD Kernel

  • Add functor Compute_coordinate_d to Kernel_d concept.

Geometric Object Generators

  • CGAL::Random uses boost::rand48 instead of std::rand.
  • Adding to CGAL::Random a way to generate random integers.
  • Adding generators for dD points.

Algebraic Foundations

  • Algebraic_structure_traits now provides an Inverse functor for Fields. There is also a new global function inverse.

Bounding Volumes

  • dD Min sphere of spheres has a new traits class for the min sphere of points.

Triangulated Surface Mesh Simplification

  • The priority queue internally used to prioritize edge simplifications is no longer a relaxed heap but a binomial heap. This fix guarantees that all edges satisfying a simplification criteria are removed (if possible).

3D Boolean Operations on Nef Polyhedra

  • Allow construction of a 3D nef polyhedron from a 3D polyhedron with normals.

2D Arrangements

  • Fix a bug in the method insert_at_vertices of the Arrangement_2 class.
  • Fix several bugs in the traits class Arr_Bezier_curve_traits_2 for arrangement of Bezier curves.

2D Minkowski Sums

  • A bug in the convolution method was fixed.

Release 3.7

Release date: October 2010

CGAL 3.7 offers the following improvements and new functionality :


  • The configuration of CGAL libraries now requires CMake>=2.6.
  • Changes in the set of supported platforms:
    • GNU g++ 4.5 supported (with or without the compilation option -std=c++0x).
    • Initial support for the option -strict-ansi of the Intel Compiler 11. The CGAL libraries compile with that option, and most CGAL headers have been fixed. The packages "3D Boolean Operations on Nef Polyhedra" (Nef_3), "Convex Decomposition of Polyhedra" (Convex_decomposition_3), and "3D Minkowski Sum of Polyhedra" (Minkowski_sum_3) are known to still fail to compile with that compiler flag.
    • The Microsoft Windows Visual C++ compiler 2010 (VC10), that was experimentally supported by CGAL-3.6.1, is now fully supported. Note that CMake>=2.8.2 is required for that support.
    • The Microsoft Windows Visual C++ compiler 2005 (VC8) is no longer supported by the CGAL project since CGAL-3.7.
    • With Microsoft Windows Visual C++ (VC9 and VC10), the optional dependencies Gmp, Mpfr, Blas, Lapack, Taucs no longer use Boost-style name mangling. Only one variant is now provided by the CGAL Windows installer (release, with dynamic runtime).
  • Some demos now require a version of Qt4 >= 4.3.
  • CGAL_PDB is no longer provided with CGAL. An alternative solution for people interested in reading PDB files is to use ESBTL (
  • Fix issues of the CGAL wrappers around the CORE library, on 64 bits platforms.

Arithmetic and Algebra

  • New models Algebraic_kernel_d_1 and Algebraic_kernel_d_2 for the corresponding concepts. They provide generic support for various coefficient types


  • A new model Arr_algebraic_segment_traits_2 of ArrangementTraits_2 that supports algebraic curves of arbitrary degree in the plane

2D Triangulations

  • The Delaunay and regular 2D triangulations now use a symbolic perturbation to choose a particular triangulation in co-circular cases.
  • The return type of the template member function insert(It beg, It end), taking an iterator range of points, has been changed from int to std::ptrdiff_t.
  • Classes Triangulation_euclidean_traits_xy_3, Triangulation_euclidean_traits_yz_3 and Triangulation_euclidean_traits_xz_3 are now model of the concept ConstrainedTriangulationTraits_2. They can be used with and without intersection of constraints.
  • 2D Delaunay and basic triangulations now provide vertex relocation by the mean of these two new methods: move and move_if_no_collision. The methods are also available for the hierarchy (Triangulation_hierarchy_2).

3D Triangulations

  • The return type of the template member function insert(It beg, It end), taking an iterator range of points, has been changed from int to std::ptrdiff_t.
  • 3D Delaunay triangulations now provide vertex relocation by the mean of these two new methods: move and move_if_no_collision. This works in both Compact_policy and Fast_policy.

2D and 3D Alpha Shapes

  • The type int in the API has been changed to std::size_t so that CGAL can deal with large data sets (64 bit addresses).

2D Mesh Generation

  • The execution of the 2D mesh generator is now deterministic (same at each run).

3D Mesh Generation

  • The efficiency of the 3D mesh generator has been improved (the number of calls to the oracle per inserted vertex has globally decrease). This is achieved through a slight change of the mesh generator strategy which implies that a surface component that is not detected at the surface mesher level will never be discovered by chance, owing to the refinement of some tetrahedra, as it could happen before. Please note that defining the macro CGAL_MESH_3_USE_OLD_SURFACE_RESTRICTED_DELAUNAY_UPDATE switches back to the old behavior.
  • A demo program is now available.

Surface Reconstruction from Point Sets

  • Improved performance and minor bug fix.

2D Range and Neighbor Search

  • The type int in the API has been changed to std::size_t so that CGAL can deal with large data sets (64 bit addresses).

Release 3.6.1

Release date: June 2010

This is a bug fix release. The following has been changed since CGAL-3.6:


  • Fix compilation errors with recent Boost versions (since 1.40).
  • Initial support for the Microsoft Visual C++ compiler 10.0 (MSVC 2010). For that support, CMake>=2.8.2 is required. Note also that the compiler option "/bigobj" is necessary to compile some CGAL programs with MSVC 2010.


  • Fix compilation errors with the Microsoft Visual C++ compiler and the Intel C++ compiler.


  • Fix a compilation errors in demo/Polyhedron/:
  • issue with the location of qglobal.h of Qt4 on MacOS X,
  • missing texture.cpp, if TAUCS is used,
  • Fix the location of built plugins of demo/Polyhedron/, when CGAL is configured with WITH_demos=ON

3D Periodic Triangulations

  • Fixed bug in the triangulation hierarchy for periodic triangulations.

2D Mesh Generation

  • Fix a bug that lead to precondition violation.
  • Improve the user manual about the member function is_in_domain() of the Face type.
  • The 2D meshing process is now deterministic (sorting of bad faces no longer relies on pointers comparisons).

3D Mesh Generation

  • Fix a linking errors (duplicate symbols) when <CGAL/refine_mesh_3.h> is included in different compilation units.

Spatial Searching

  • Fix a bug in <CGAL/Orthogonal_k_neighbor_search.h> when several nearest neighbors are at the same distance from the query point.

IO Streams

  • Fix a bug in <CGAL/IO/VRML_2_ostream.h> that generated VRML 2 files with an invalid syntax for IndexedFaceSet nodes.


  • Add missing Compare_distance_2 functor in trait classes Triangulation_euclidean_traits_xy_3 Triangulation_euclidean_traits_yz_3 and Triangulation_euclidean_traits_xz_3. This was preventing calling member function nearest_vertex of Delaunay_triangulation_2 instantiated with one of these traits.

Release 3.6

Release date: March 2010

CGAL 3.6 offers the following improvements and new functionality :


  • Boost version 1.34.1 at least is now required.

Arithmetic and Algebra

Algebraic Kernel (new package)

  • This new package is targeted to provide black-box implementations of state-of-the-art algorithms to determine, compare and approximate real roots of univariate polynomials and bivariate polynomial systems. It includes models of the univariate algebraic kernel concept, based on the library RS.

Number Types

  • Two new arbitrary fixed-precision floating-point number types have been added: the scalar type Gmpfr and the interval type Gmpfi, based on the MPFR and MPFI libraries respectively.

Geometry Kernels

2D and 3D Geometry Kernel

  • Add new do_intersect() and intersection() overloads:
    • do_intersect(Bbox_3, Bbox_3/Line_3/Ray_3/Segment_3)
    • intersection(Triangle_3, Line_3/Ray_3/Segment_3)


2D Regularized Boolean Set-Operations

  • Fixed General_polygon_set_2::arrangement() to return the proper type of object.


2D Arrangements

  • Fixed passing a (const) traits object to the constructor of Arrangement_2.
  • Introduced Arrangement_2::fictitious_face(), which returns the fictitious face in case of an unbounded arrangement.
  • Fixed a bug in Bezier-curve handling.
  • Added (back) iterator, number_of_holes(), holes_begin(), and holes_end() to the default DCEL for backward compatibility.
  • Added (simple) versions of the free overlay() function. It employs the default overlay-traits, which practically does nothing.


  • Fix a compilation errors in demo/Polyhedron/:
    • issue with the location of qglobal.h of Qt4 on MacOS X,
    • missing texture.cpp, if TAUCS is used,
  • Fix the location of built plugins of demo/Polyhedron/, when CGAL is configured with WITH_demos=ON
  • Fix a bug in test_facet function of the incremental builder: the function did not test if while a new facet makes a vertex manifold, no other facet incident to that vertex breaks the manifold property.

Triangulations and Delaunay Triangulations

2D/3D Regular Triangulations

  • Weighted_point now has a constructor from Cartesian coordinates.

3D Triangulations

  • Regular_triangulation_3 : semi-static floating-point filters are now used in its predicates, which can speed up its construction by a factor of about 3 when Exact_predicates_inexact_constructions_kernel is used.
  • The class Regular_triangulation_filtered_traits_3 is deprecated, the class Regular_triangulation_euclidean_traits_3 must be used instead. The predicates of that traits will be filtered if the kernel given as template parameter of that traits is itself a filtered kernel.
  • Triangulation_hierarchy_3 is now deprecated, and replaced by a simpler CGAL::Fast_location policy template parameter of Delaunay_triangulation_3.
  • The old version of remove() (enabled with CGAL_DELAUNAY_3_OLD_REMOVE) has been deleted.

3D Periodic Triangulations

  • New demo: 3D periodic Lloyd algorithm.
  • New functionality for Voronoi diagrams: dual of an edge and of a vertex, volume and centroid of the dual of a vertex.
  • The package can now be used with the 3D Alpha Shapes package to compute periodic alpha shapes.

3D Alpha shapes

  • The class Weighted_alpha_shape_euclidean_traits_3 is deprecated, the class Regular_triangulation_euclidean_traits_3 must be used instead.
  • The package can now be used together with the 3D Periodic Triangulation package to compute periodic alpha shapes.

2D/3D Triangulations, 2D Segment Delaunay Graph, 2D Apollonius Graph, and 3D Periodic Triangulations

  • The constructor and insert function taking ranges now produce structures whose iterator orders is now deterministic (same at each run).

Mesh Generation

2D Mesh Generation

  • The 2D mesh generator can now be used with a constrained Delaunay triangulation with constraints hierarchy (Constrained_triangulation_plus_2).
  • In some cases (refinement of a constrained edge that is on the convex hull), the 2D mesh generator from CGAL-3.4 and CGAL-3.5 could create invalid triangulations. This bug is now fixed.

3D Mesh Generation

  • The mesh generator has been enriched with an optimization phase to provide 3D meshes with well shaped tetrahedra (and in particular no slivers). The optimization phase involves four different optimization processes: two global optimization processes (ODT and Lloyd), a perturber and an exuder. Each of these processes can be activated or not, and tuned to the users needs and to available computer resources.

Support library

CGAL ipelets

  • Add support for version 7 of Ipe.

Release 3.5.1

Release date: December 2009

This is a bug fix release.


  • Fixes in the documentation (the online documentation of CGAL-3.5 is now based on CGAL-3.5.1).
  • Fixes to the bibliographic references.

Windows installer

  • The Windows installer of CGAL-3.5.1 fixes an issue with downloading of precompiled binaries of the external library TAUCS.

Bug fixes in the following CGAL packages

AABB tree

  • Fix a linker issue in do_intersect(Bbox_3,Bbox_3).
  • Fix compilation issue in do_intersect(Bbox_3,Ray_3) when using the parameters in this order.

3D Mesh Generation

  • Fix a bug in initial points construction of a polyhedral surface.

Release 3.5

Release date: October 2009

CGAL releases will now be published about every six months. As a transition release, CGAL-3.5 has been developed during 9 months from the release CGAL-3.4.

Version 3.5 differs from version 3.4 in the platforms that are supported and in functionality. There have also been a number of bug fixes for this release.


  • Additional supported platforms:
    • GNU g++ 4.4 supported.
    • Intel Compiler 11 supported on Linux
  • Fixed ABI incompatibilities when mixing CGAL and Boost Program Options on Windows/Visual C++ (the compilation flag -D_SECURE_SCL=0 is not longer use in Debug mode).

Geometry Kernels

3D Spherical Geometry Kernel

  • Add functionalities to manipulate circles, circular arcs and points that belong to the same sphere.


2D Regularized Boolean Set-Operations

  • The polygon validation operations were enhanced and their interface was improved. They are now offered as free functions and applied properly.

2D Straight Skeleton and Polygon Offsetting

  • Updated the manual to document the new partial skeletons feature (already in the code since 3.4)


2D Arrangements

  • The member function is_at_infinity() of Arrangement_2::Vertex was replaced by the new function is_at_open_boundary(). The former is deprecated. While still supported in version 3.5, It will not be supported in future releases. The member functions boundary_type_in_x() and boundary_type_in_y() were permanently replaced by the functions parameter_space_in_x() and parameter_space_in_y(), respectively. The 2 new functions return an enumeration of a new type, namely Arr_parameter_space.
  • The tags in the geometry traits that indicate the type of boundary of the embedding surface were replaced by the following new tags: Arr_left_side_tag Arr_bottom_side_tag Arr_top_side_tag Arr_right_side_tag In addition, the code was change, and now it is possible not to indicate the tags at all. Default values are assumed. This however will produce warning messages, and should be avoided.
  • All operations of the geometry traits-class were made 'const'. This change was reflected in the code of this package and all other packages that are based on it. Traits classes that maintain state, should declare the data members that store the state as mutable.

Envelopes of Surfaces in 3D

  • A few bugs in the code that computes envelopes were fixed, in particular in the code that computes the envelopes of planes.

Triangulations and Delaunay Triangulations

3D Periodic Triangulations (new package)

  • This package allows to build and handle triangulations of point sets in the three dimensional flat torus. Triangulations are built incrementally and can be modified by insertion or removal of vertices. They offer point location facilities.

Mesh Generation

Surface Reconstruction from Point Sets (new package)

  • This CGAL package implements an implicit surface reconstruction method: Poisson Surface Reconstruction. The input is an unorganized point set with oriented normals.

3D Mesh Generation (new package)

  • This package generates 3 dimensional meshes. It computes isotropic simplicial meshes for domains or multidomains provided that a domain descriptor, able to answer queries from a few different types on the domain, is given. In the current version, Mesh_3 generate meshes for domain described through implicit functional, 3D images or polyhedral boundaries. The output is a 3D mesh of the domain volume and conformal surface meshes for all the boundary and subdividing surfaces.

Geometry Processing

Triangulated Surface Mesh Simplification

  • BREAKING API change in the passing of the visitor object.
  • Fixed a bug in the link_condition test
  • Added a geometric test to avoid folding of facets
  • Fixed a bug in the handling of overflow in the LindstromTurk computations
  • Updated the manual to account for the new visitor interface

Point Set Processing (new package)

  • This packages implements a set of algorithms for analysis, processing, and normal estimation and orientation of point sets.

Spatial Searching and Sorting

AABB tree (new package)

  • This package implements a hierarchy of axis-aligned bounding boxes (a AABB tree) for efficient intersection and distance computations between 3D queries and sets of input 3D geometric objects.

Support Library

CGAL_ipelets (new package):

  • Object that eases the writing of Ipe's plugins that use CGAL. Plugins for CGAL main 2D algorithm are provided as demo.

Release 3.4

Release date: January 2009

Version 3.4 differs from version 3.3.1 in the platforms that are supported and in functionality. There have also been a number of bug fixes for this release.


  • GNU g++ 4.3 supported. Support for g++ 3.3 is dropped.
  • Visual 9 supported. Support for Visual 7 is dropped.
  • Boost version 1.33 at least is now required.
  • CGAL now depends on Boost.Threads, which implies to link against a compiled part of Boost.
  • The new macro CGAL_NO_DEPRECATED_CODE can be defined to disable deprecated code, helping users discover if they rely on code that may be removed in subsequent releases.
  • Assertion behaviour: It is not possible anymore to set the CONTINUE mode for assertion failures. Functions that allow to change the assertion behaviour are now declared in <CGAL/assertions_behaviour.h>.
  • Qt3 based demos are still there but the documentation has been removed as the CGAL::Qt_Widget will be deprecated.
  • Qt4 based demos use the Qt GraphicsView framework and the libQGLViewer.


  • install_cgal has been replaced by CMake.

Polynomial (new package)

  • This package introduces a concept Polynomial_d, a concept for multivariate polynomials in d variables.

Modular Arithmetic (new package)

  • This package provides arithmetic over finite fields.

Number Types

  • the counter Interval_nt::number_of_failures() has been removed, replaced by a profiling counter enabled with CGAL_PROFILE.
  • Fix of a bug in CORE/Expr.h; as a consequence, the arrangement demo works properly when handling arrangements of conics, for example, when defining an arc with 5 points.

3D Spherical Geometry Kernel (new package)

  • This package is an extension of the linear CGAL Kernel. It offers functionalities on spheres, circles, circular arcs and line segments in the 3D space.

Linear Kernel

  • We recommend that you use the object_cast() function instead of assign() to extract an object from a CGAL::Object, for efficiency reasons.
  • The Kernel archetypes provided by the 2D/3D linear kernel have been removed.
  • The deprecated linear kernel functors Construct_supporting_line_2 and Construct_supporting_line_3 have been removed.
  • Ambiant_dimension and Feature_dimenison have been added to retrieve the potentially compile-time dimension of a space or of an object.
  • barycenter() functions have been added.
  • The geometric object Circle_3 as well as predicates and constructions have been added to the kernel
  • The missing intersection/do_intersect between Line_3 and Line_3 has been added as well.

3D Triangulations

  • Removed the deprecated functions Cell:mirror_index() and Cell::mirror_vertex().
  • Derecursification of two functions that in some cases lead to stack overflows

3D Nef Polyhedron

  • n-ary union/intersection
  • intersection with halfspace under standard kernel
  • constructor for polylines

CGAL and the Qt4 GraphicsView (new package)

  • 2D CGAL Kernel objects and many data structures have can be rendered in a QGraphicsView

STL Extensions:

  • The functor adaptors for argument binding and composition (bind_*, compose, compose_shared, swap_*, negate, along with the helper functions set_arity_* and Arity class and Arity_tag typedefs) which were provided by <CGAL/functional.h> have been removed. Please use the better boost::bind mecanism instead. The concept AdaptableFunctor has been changed accordingly such that only a nested result_type is required.
  • The accessory classes Twotuple, Threetuple, Fourtuple and Sixtuple are also deprecated (use CGAL::array instead).
  • CGAL::Triple and CGAL::Quadruple are in the process of being replaced by boost::tuple. As a first step, we strongly recommend that you replace the direct access to the data members (.first, .second, .third, .fourth), by the get<i>() member function; and replace the make_triple and make_quadruple maker functions by make_tuple.
    This way, in a further release, we will be able to switch to boost::tuple more easily.
  • The class CGAL::Uncertain<> has been documented. It is typically used to report uncertain results for predicates using interval arithmetic, and other filtering techniques.

2D Arrangements

  • Changed the name of the arrangement package from Arrangement_2 to Arrangement_on_surface_2 to reflect the potential capabilities of the package to construct and maintain arrangements induced by curves embedded on two dimensional surfaces in three space. Most of these capabilities will become available only in future releases though.
  • Enhanced the geometry traits concept to handle arrangements embedded on surfaces. Each geometry-traits class must now define the 'Boundary_category' tag.
  • Fixed a bug in Arr_polyline_traits_2.h, where the operator that compares two curves failed to evaluate the correct result (true) when the curves are different, but their graphs are identical.
  • Permanently removed IO/Arr_postscript_file_stream.h and IO/Polyline_2_postscript_file_stream.h, as they depend on obsolete features and LEDA.
  • Fixed several bugs in the arrangement demo and enhanced it. e.g., fixed background color change, allowed vertex coloring , enabled "smart" color selection, etc.
  • Enhanced the arrangement demo with new features, such as allowing the abortion of the merge function (de-select), updated the how-to description, etc.
  • Replace the functions CGAL::insert_curve(), CGAL::insert_curves(), CGAL::insert_x_monotone_curve(), and CGAL::insert_x_monotone_curves() with a single overloaded function CGAL::insert(). The former 4 functions are now deprecated, and may no longer be supported in future releases.

Envelopes of Surfaces in 3D

  • Fixed a bug in the computation of the envelope of unbounded planes caused by multiple removals of vertices at infinity.

2D Regularized Boolean Set-Operations

  • Fixed a bug in connect_holes() that caused failures when connecting holes touching the outer boundary.
  • Fixed the concept GeneralPolygonSetTraits_2. Introduced two new concepts GpsTraitsGeneralPolygon_2 and GpsTraitsGeneralPolygonWithHoles_2. Fixed the definition of the two nested required types Polygon_2 and Polygon_with_holes_2 of the GeneralPolygonSetTraits_2 concept. They must model now the two new concepts above.
  • Added a default template parameter to 'General_polygon_set_2' to allow users to pass their specialized DCEL used to instantiate the underlying arrangement.
  • Enhanced the BOP demo to use multiple windows.

2D Minkowski Sums

  • Fixed a few bugs in the approximate offset function, making it robust to highly degenerate inputs.
  • Fixed a bug in the exact Minkowski sum computation when processing degenerate inputs that induce overlapping of contiguous segments in the convolution cycles.
  • Optimized the approximate offset function (reduced time consumption up to a factor of 2 in some cases).
  • Added functionality to compute the offset (or to approximate the offset) of a Polygon_with_holes_2 (and not just of a Polygon_2).
  • Added the functionality to compute (or to approximate) the inner offset of a polygon.

Release 3.3.1

Release date: August 2007

This is a bug fix release.


  • Intel C++ 9 was wrongly recognized as unsupported by install_cgal.
  • Added autolink (for Visual C++) for the CGALImageIO and CGALPDB libraries.
  • Fixed bug in Memory_sizer when using more than 4GB of memory (64bit).

Number Types

  • Fixed bug in FPU rounding mode macros (affected only the alpha architecture).
  • Fixed bug in MP_Float constructor from double for some particular values.
  • Fixed bug in to_double(Lazy_exact_nt) sometimes returning NaN.


  • Fixed forgotten derivation in Circular_kernel_2::Has_on_2
  • Added some missing functions in Bbox_3 compared to Bbox_2.

Skin Surface Meshing

  • The new Skin Surface Meshing package had been forgotten in the list of changes and the release announcement of CGAL 3.3: This package allows to build a triangular mesh of a skin surface. Skin surfaces are used for modeling large molecules in biological computing.


  • Fixed a bug in the Arrangement_2 package in dual arrangement representation for Boost graphs when reporting all halfedges of a face.
  • Fixed a bug in the Arrangement sweep-line when using a specific polyline configuration.
  • Fixed bug in Arrangement_2 in walk along a line point location for unbounded curves.
  • Fixed bug in aggregated insertion to Arrangement_2.
  • Fixed bug in Arrangment_2 class when inserting an unbounded curve from an existing vertex.
  • Fixed bug when dealing with a degenerate conic arc in Arr_conic_traits_2 of the Arrangment package, meaning a line segment which is part of a degenerate parabola/hyperbola.
  • Fixed bug in the Bezier traits-class: properly handle line segments. properly handle comparison near a vertical tangency.

2D Polygon

  • Fixed bug in degenerate case of Polygon_2::is_convex() for equal points.

2D Triangulations

  • Fixed bug in Regular_triangulation_2.

3D Triangulations

  • Added a circumcenter() function in the default Cell type parameter Triangulation_ds_cell_base_3, so that the .dual() member function of Delaunay still work as before, without requiring the explicit use of Triangulation_cell_base.
  • Added missing operator->() to Facet_circulator.


  • Fixed bug in Interpolation 3D about the normalization coefficient initialization.

3D Boolean Operations on Nef Polyhedra

  • Fixed bug in construction of Nef_polyhedron_3 from off-file. Now, always the inner volume is selected.
  • Fixed bug in conversion from Nef_polyhedron_3 to Polyhedron_3. Polyhedron_3 was not cleared at the beginning.
  • Fixed bug in Nef_polyhedron_3 in update of indexes for construction of external structure.

Third Party Libraries Shipped with CGAL

  • TAUCS supports now 64 bits platforms.
  • CAUTION: Since version 3.3.1, CGAL is no longer compatible with the official release of TAUCS (currently 2.2). Make sure to use the version modified by the CGAL project and available from the download section of

Release 3.3

Release date: May 2007

Version 3.3 differs from version 3.2.1 in the platforms that are supported and in functionality. There have also been a number of bug fixes for this release.

Additional supported platforms

  • GNU g++ 4.1 and 4.2
  • Intel C++ compiler 9
  • Microsoft Visual C++ compiler 8.0

The following platforms are no longer supported:

  • Intel 8

CGAL now supports Visual C++ "Checked iterators" as well as the debug mode of GNU g++'s STL (-D_GLIBCXX_DEBUG).

CGAL now works around the preprocessor macros 'min' and 'max' defined in <windows.h> which were clashing with min/max functions.


  • On Windows the libraries built in Developer Studio now have names which encode the compiler version, the runtime and whether it was built in release or debug mode. The libraries to link against are chosen with linker pragmas in header files.
  • On all platforms but Windows shared and static versions of the libraries are generated


  • The Package Overview page now also hosts the precompiled demos.

Algebraic Foundations

  • Algebraic Foundations (new package)
    This package defines what algebra means for CGAL, in terms of concepts, classes and functions. The main features are: (i) explicit concepts for interoperability of types (ii) separation between algebraic types (not necessarily embeddable into the reals), and number types (embeddable into the reals).

  • Number Types
    Fixed_precision_nt and Filtered_exact number types have been removed.


  • 2D Circular Kernel
    Efficiency improved through geometric filtering of predicates, introduced with the filtered kernel Filtered_bbox_circular_kernel_2<.>, and also chosen for the predefined kernel Exact_circular_kernel_2.
  • Linear Kernel
    Exact_predicates_exact_constructions_kernel memory and run-time improvements through usage of lazy geometric constructions instead of lazy arithmetic.

Data Structures and Algorithms

  • Surface Mesh Simplification (new package)
    This package provides a mesh simplification framework using edge collapse operations, and provides the Turk/Lindstrom simplification algorithm.

  • Skin Surface Meshing (new package)
    This package allows to build a triangular mesh of a skin surface. Skin surfaces are used for modeling large molecules in biological computing. The surface is defined by a set of balls, representing the atoms of the molecule, and a shrink factor that determines the size of the smooth patches gluing the balls together.

  • Estimation of Local Differential Properties (new package)
    This package allows to compute local differential quantities of a surface from a point sample

  • Approximation of Ridges and Umbilics on Triangulated Surface Meshes (new package)
    This package enables the approximation of differential features on triangulated surface meshes. Such curvature related features are lines: ridges or crests, and points: umbilics.

  • Envelopes of Curves in 2D (new package)
    This package contains two sets of functions that construct the lower and upper envelope diagram for a given range of bounded or unbounded curves.

  • Envelopes of Surfaces in 3D (new package)
    This package contains two sets of functions that construct the lower and upper envelope diagram for a given range of bounded or unbounded surfaces. The envelope diagram is realized as a 2D arrangement.

  • Minkowski Sums in 2D (new package)
    This package contains functions for computing planar Minkowski sums of two closed polygons, and for a polygon and a disc (an operation also known as offsetting or dilating a polygon). The package also contains an efficient approximation algorithm for the offset computation, which provides a guaranteed approximation bound while significantly expediting the running times w.r.t. the exact computation procedure.

  • Surface Mesh Parametrization
    Added Jacobi and SSOR preconditioners to OpenNL solver, which makes it much faster and more stable.

  • 2D Arrangements
    • Added support for unbounded curves.
    • Added a traits class that supports bounded and unbounded linear objects, namely lines, rays and line segments.
    • Added traits classes that handle circular arcs based on the circular kernel.
    • Added a traits class that supports Bezier curves.
    • Enhanced the traits class that supports rational functions to handle unbounded (as well as bounded) arcs
    • Added a free function called decompose() that produces the symbolic vertical decomposition of a given arrangement, performing a batched vertical ray-shooting query from all arrangement vertices.
    • Fixed a memory leak in the sweep-line code.
    • Fixed a bug in computing the minor axis of non-degenerate hyperbolas.
  • Boolean Set Operations
    • Added the DCEL as a default template parameter to the General_polygon_set_2 and Polygon_set_2 classes. This allows users to extend the DCEL of the underlying arrangement.
    • Added a function template called connect_holes() that connects the holes in a given polygon with holes, turning it into a sequence of points, where the holes are connceted to the outer boundary using zero-width passages.
    • Added a non-const function member to General_polygon_set_2 that obtains the underlying arrangement.

  • 2D and 3D Triangulations
    • The constructors and insert member functions which take an iterator range perform spatial sorting in order to speed up the insertion.

  • Optimal Distances
    • Polytope_distance_d: has support for homogeneous points; bugfix in fast exact version.

  • Bounding Volumes
    • Min_annulus_d has support for homogeneous points; bugfix in fast exact version.

Support Library

  • CGAL and the Boost Graph Library (BGL) (new package)
    This package provides the glue layer for several CGAL data structures such that they become models of the BGL graph concept.

  • Spatial Sorting (new package)
    This package allows to sort points and other objects along a Hilbert curve which can improve the performance of algorithms like triangulations. It is used by the constructors of the triangulation package which have an iterator range of points as argument.

  • Linear and Quadratic Programming Solver (new package)
    This package contains algorithms for minimizing linear and convex quadratic functions over polyhedral domains, described by linear equations and inequalities.

Release 3.2.1

Release date: July 2006

This is a bug fix release

Number Types

  • Fix MP_Float constructor which crashed for some values.


  • Rename Bool to avoid a clash with a macro in X11 headers.


  • Derived the Arr_segment_traits_2 Arrangement_2 traits class from the parameterized Kernel. This allows the use of this traits class in an extended range of applications that require kernel objects and operations on these objects beyond the ones required by the Arrangement_2 class itself.
  • Fixed a compilation bug in the code that handles overlay of arrangements instantiated with different DCEL classes.
  • Fixed a couple of bugs in the implementation of the Trapezoidal RIC point-location strategy

Triangulation, Alpha Shapes

  • Qualify calls to filter_iterator with "CGAL::" to avoid overload ambiguities with Boost's filter_iterator.

Surface Mesher

  • Fixed a bug in iterators of the class template Surface_mesh_complex_2_in_triangulation_3

Surface Mesh Parametrisation

  • Updated the precompiled taucs lib

Kinetic Data Structures

  • Fixed problems caused by old versions of gcc being confused by operator! and operator int()
  • Added point removal support to the Active_objects_vector

Release 3.2

Release date: May 2006

Version 3.2 differs from version 3.1 in the platforms that are supported and in functionality. There have also been a number of bug fixes for this release.

The following platforms are no longer supported:

  • SunPro CC versions 5.4 and 5.5 on Solaris
  • SGI Mips Pro

For Visual C++ the installation scripts choose the multi-threaded dynamically linked runtime (/MD). Before it was the single-threaded static runtime (/ML).


  • The install tool tries to find third party libraries at "standard" locations.
  • Installers for Apple, Windows, and rpms.


  • User and Reference manual pages of a package are in the same chapter


  • 2D Circular Kernel (new package)
    This package is an extension of the linear CGAL Kernel. It offers functionalities on circles, circular arcs and line segments in the plane.

Data Structures and Algorithms

  • 2D Regularized Boolean Set-Operations (new package)
    This package consists of the implementation of Boolean set-operations on point sets bounded by weakly x-monotone curves in 2-dimensional Euclidean space. In particular, it contains the implementation of regularized Boolean set-operations, intersection predicates, and point containment predicates.

  • 2D Straight Skeleton and Polygon Offsetting (new package)
    This package implements an algorithm to construct a halfedge data structure representing the straight skeleton in the interior of 2D polygons with holes and an algorithm to construct inward offset polygons at any offset distance given a straight skeleton.

  • 2D Voronoi Diagram Adaptor (new package)
    This package provides an adaptor that adapts a 2-dimensional triangulated Delaunay graph to the corresponding Voronoi diagram, represented as a doubly connected edge list (DCEL) data structure. The adaptor has the ability to automatically eliminate, in a consistent manner, degenerate features of the Voronoi diagram, that are artifacts of the requirement that Delaunay graphs should be triangulated even in degenerate configurations. Depending on the type of operations that the underlying Delaunay graph supports, the adaptor allows for the incremental or dynamic construction of Voronoi diagrams and can support point location queries.

  • 3D Surface Mesher (new package)
    This package provides functions to generate surface meshes that interpolate smooth surfaces. The meshing algorithm is based on Delaunay refinement and provides some guarantees on the resulting mesh: the user is able to control the size and shape of the mesh elements and the accuracy of the surface approximation. There is no restriction on the topology and number of components of input surfaces. The surface mesher may also be used for non smooth surfaces but without guarantee.

    Currently, implementations are provided for implicit surfaces described as the zero level set of some function and surfaces described as a gray level set in a three-dimensional image.

  • 3D Surface Subdivision Methods (new package)
    Subdivision methods recursively refine a control mesh and generate points approximating the limit surface. This package consists of four popular subdivision methods and their refinement hosts. Supported subdivision methods include Catmull-Clark, Loop, Doo-Sabin and sqrt(3) subdivisions. Their respective refinement hosts are PQQ, PTQ, DQQ and sqrt(3) refinements. Variations of those methods can be easily extended by substituting the geometry computation of the refinement host.

  • Planar Parameterization of Triangulated Surface Meshes (new package)
    Parameterizing a surface amounts to finding a one-to-one mapping from a suitable domain to the surface. In this package, we focus on triangulated surfaces that are homeomorphic to a disk and on piecewise linear mappings into a planar domain. This package implements some of the state-of-the-art surface mesh parameterization methods, such as least squares conformal maps, discrete conformal map, discrete authalic parameterization, Floater mean value coordinates or Tutte barycentric mapping.

  • Principal Component Analysis (new package)
    This package provides functions to compute global informations on the shape of a set of 2D or 3D objects such as points. It provides the computation of axis-aligned bounding boxes, centroids of point sets, barycenters of weighted point sets, as well as linear least squares fitting for point sets in 2D, and point sets as well as triangle sets in 3D.

  • 2D Placement of Streamlines (new package)
    Visualizing vector fields is important for many application domains. A good way to do it is to generate streamlines that describe the flow behaviour. This package implements the "Farthest Point Seeding" algorithm for placing streamlines in 2D vector fields. It generates a list of streamlines corresponding to an input flow using a specified separating distance. The algorithm uses a Delaunay triangulation to model objects and adress different queries, and relies on choosing the centers of the biggest empty circles to start the integration of the streamlines.

  • Kinetic Data Structures (new package)
    Kinetic data structures allow combinatorial structures to be maintained as the primitives move. The package provides implementations of kinetic data structures for Delaunay triangulations in two and three dimensions, sorting of points in one dimension and regular triangulations in three dimensions. The package supports exact or inexact operations on primitives which move along polynomial trajectories.

  • Kinetic Framework (new package)
    Kinetic data structures allow combinatorial geometric structures to be maintained as the primitives move. The package provides a framework to ease implementing and debugging kinetic data structures. The package supports exact or inexact operations on primitives which move along polynomial trajectories.

  • Smallest Enclosing Ellipsoid (new package)
    This algorithm is new in the chapter Geometric Optimisation.

  • 2D Arrangement (major revision)
    This package can be used to construct, maintain, alter, and display arrangements in the plane. Once an arrangement is constructed, the package can be used to obtain results of various queries on the arrangement, such as point location. The package also includes generic implementations of two algorithmic frameworks, that are, computing the zone of an arrangement, and line-sweeping the plane, the arrangements is embedded on.

    Arrangements and arrangement components can also be extended to store additional data. An important extension stores the construction history of the arrangement, such that it is possible to obtain the originating curve of an arrangement subcurve.

  • Geometric Optimisation (major revision)
    The underlying QP solver which is the foundation for several algorithms in the Geometric Optimisation chapter has been completely rewritten.

  • 3D Triangulation (new functionality)
    Regular_triangulation_3 now offers vertex removal.

Release 3.1

Release date: December 2004

Version 3.1 differs from version 3.0 in the platforms that are supported and in functionality. There have also been a number of bug fixes for this release.

Additional supported platforms:

  • MS Visual C++, version 7.3. and 8.0
  • Intel 8.0
  • SunPro CC versions 5.4 and 5.5 on Solaris
  • GNU g++ versions 3.4 on Linux, Solaris, Irix, cygwin, FreeBSD, and MacOS X
  • Darwin (MacOS X) and IA64/Linux support.

The following platforms are no longer supported:

  • MS Visual C++, version 7.0

The following functionality has been added or changed:


  • The CORE 1.7 library for exact real arithmetic.
  • Updated GMP to 4.1.3.
  • Added Mpfr a library for multiple-precision floating-point computations with exact rounding.
  • Added Boost 1.32.0 (only include files).


  • new option --disable-shared to omit building


  • Merged all major manuals in one multi-part manual, which provides now cross-links between the CGAL Kernel, the CGAL Basic Library, and the CGAL Support Library HTML manuals.
  • Improved layout.


  • Improved efficiency of filtered kernels.
  • More predicates and constructions.

Basic Library

  • 2D Segment Voronoi Diagram (new package)
    A data structure for Voronoi diagrams of segments in the plane under the Euclidean metric. The Voronoi edges are arcs of straight lines and parabolas. The algorithm provided in this package is incremental.
  • 2D Conforming Triangulations and Meshes (new package)
    An implementation of Shewchuk's algorithm to construct conforming triangulations and 2D meshes.
  • 3D Boolean Operations on Nef Polyhedra (new package)
    A new class (Nef_polyhedron_3) representing 3D Nef polyhedra, a boundary representation for cell-complexes bounded by halfspaces that supports boolean operations and topological operations in full generality including unbounded cells, mixed dimensional cells (e.g., isolated vertices and antennas). Nef polyhedra distinguish between open and closed sets and can represent non-manifold geometry.
  • 2D and Surface Function Interpolation (new package)
    This package implements different methods for scattered data interpolation: Given measures of a function on a set of discrete data points, the task is to interpolate this function on an arbitrary query point. The package further offers functions for natural neighbor interpolation.
  • Planar Nef polyhedra embedded on the sphere (new package)
    A new class (Nef_polyhedron_S2) designed and supported mainly to represent sphere neighborhoods around vertices of the three- dimensional Nef polyhedra.
  • Box_intersection_d (new package)
    A new efficient algorithm for finding all intersecting pairs for large numbers of iso-oriented boxes, i.e., typically these will be bounding boxes of more complicated geometries. Useful for (self-) intersection tests of surfaces etc.
  • 2D Snap Rounding (new package)
    Snap Rounding is a well known method for converting arbitrary-precision arrangements of segments into a fixed-precision representation. In the study of robust geometric computing, it can be classified as a finite precision approximation technique. Iterated Snap Roundingis a modification of Snap Rounding in which each vertex is at least half-the-width-of-a-pixel away from any non-incident edge. This package supports both methods.
  • 3D Triangulations
    • Triangulation_3: added operator==(),removed push_back() and copy_triangulation().
    • Delaunay_3 : added nearest_vertex(), move_point(), vertices_in_conflict().
    • Regular_3 : added filtered traits class, and nearest_power_vertex().
  • Planar_map and Arrangement_2
    • The interface of the two traits functions that compute the intersection of two given curves changed. The functions nearest_intersection_to_right() and nearest_intersection_to_left() return an object of type CGAL::Object that represents either an empty intersection, a point, or an overlapping subcurve.
    • Requirements to define two binary tags were added to the traits concept of the Planar_map as follows: Has_left_category - indicates whether the functions curves_compare_y_at_x_left() and nearest_intersection_to_left() are implemented in the traits model. Has_reflect_category - indicates whether the functions point_reflect_in_x_and_y() and curve_reflect_in_x_and_y() are implemented in the traits model. They can be used as an alternative to the two function in the previous item.
    • A new constructor of the Segment_cached_2 type that represents a segment in the Arr_segment_cached_traits_2 traits class was introduced. The new constructor accepts the segment endpoints as well as the coefficients of the underlying line.
    • A new version of the conic-arc traits, based on CORE version 1.7 was introduced. This new traits class makes use of CORE's rootOf() operator to compute the intersection points in the arrangement, making its code much simpler and more elegant than the previous version. In addition, new constructors for conic arcs are provided. The new traits class usually performs about 30% faster than the version included in CGAL 3.0
    • The traits class that handles continuous piecewise linear curves, namely Arr_polyline_traits_2, was rewritten. The new class is parametrized with a traits class that handles segments, say Segment_traits. The polyline curve defined within the Arr_polyline_traits_2 class is implemented as a vector of segments of type Segment_traits::Curve_2.
    • A meta traits class, namely Arr_curve_data_traits_2, that extends the curve type of the planar-map with arbitrary additional data was introduced. It should be instantiated with a regular traits-class and a class that contains all extraneous data associated with a curve.
    • The class that represents the trapezoidal-decomposition point location strategy was renamed to Pm_trapezoid_ric_point_location.
    • The Arrangement demo was rewritten. It covers many more features, has a much better graphical user interface, and comes with online documentation.
    • Few bugs in the sweep-line module related to overlapping vertical segments were fixed. This module is used by the aggregate insert method that inserts a collection of curves at once.
  • Triangulation_2
    • added a filtered trait class in the regular triangulation
    • added split and join operations in the triangulation data structure class
  • Alpha_shapes_3
    • major changes in the implementation of the class Alpha_shapes_3.
    • New implementation results in a true GENERAL mode allowing null and negative alpha-values. It also fixed the edges classification bug and introduces a classification of vertices.
  • Min_ellipse_2
    • made access to approximate double representation public
    • fixed bugs in conversion to double representation
    • added is_circle() method
    • minor performance improvements
  • Min_sphere_of_spheres_d:
    • The models Min_sphere_of_spheres_d_traits_2<K,FT,UseSqrt,Algorithm>, Min_sphere_of_spheres_d_traits_3<K,FT,UseSqrt,Algorithm>, and Min_sphere_of_spheres_d_traits_d<K,FT,Dim,UseSqrt,Algorithm> of concept MinSphereOfSpheresTraits now represent a sphere as a std::pair<Point,Radius> (and not any more as a CGAL::Weighted_point<Point,Weight>)
    • Internal code cleanup; in particular, implementation details don't pollute the namespace CGAL anymore
  • Polyhedron_3
    • New Tutorial on CGAL Polyhedron for Subdivision Algorithms with interactive demo viewer in source code available.
    • Added example program for efficient self-intersection test. - Added small helper functions, such as vertex_degree, facet_degree, edge_flip, and is_closed.
  • Apollonius Graph (Voronoi of Circles)
    • Reduced memory requirements by approximately a factor of two.

Release 3.0.1

Release date: February 2004

This is a bug-fix release. No new features have been added in 3.0.1. Here is the list of bug-fixes.

Polyhedral Surface

  • Fixed wrong include files for output support. Added example.


  • Fixed the so called "Walk-along-a-line" point-location strategy to correctly handle a degenerate case.

2D Triangulation

  • added missing figure in html doc
  • in Line_face_circulator_2.h:
    Fixed changes made to support handles with a typedef to iterator. The fix concerns operator== and !=.


  • fixed classify member function for edges.

Number types

  • Lazy_exact_nt:
    • added the possibility to select the relative precision of to_double() (by default 1e-5). This should fix reports that some circumcenters computations have poor coordinates, e.g. nan).
    • when exact computation is triggered, the interval is recomputed, this should speed up some kinds of computations.
  • to_interval(Quotient<MP_Float>): avoid spurious overflows.


  • missing acknowledgment in the manual and minor clarification of intersection() documentation.

Release 3.0

Release date: October 2003

Version 3.0 differs from version 2.4 in the platforms that are supported and in functionality. There have also been a number of bug fixes for this release.

The license has been changed to either the LGPL (GNU Lesser General Public License v2.1) or the QPL (Q Public License v1.0) depending on each package. So CGAL remains free of use for you, if your usage meets the criteria of these licenses, otherwise, a commercial license has to be purchased from GeometryFactory.

Additional supported platforms:

  • MS Visual C++, version 7.1.
  • SunPro CC versions 5.4 and 5.5 on Solaris
  • GNU g++ versions 3.2 and 3.3 on Linux, Solaris, Irix, cygwin, and FreeBSD.
  • MipsPRO CC 7.30 and 7.40 with both the n32 and n64 ABIs.

The following platforms are no longer supported:

  • MS Visual C++, version 6.
  • GNU g++ 2.95.2 (2.95.3 is still supported)
  • Kai C++ and Borland C++, all versions

The following functionality has been added or changed:


  • The CORE library for exact computations is now distributed as part of CGAL as well.


  • 3 typedefs have been added to ease the choice of a robust and fast kernel:
    • Exact_predicates_inexact_constructions_kernel
    • Exact_predicates_exact_constructions_kernel
    • Exact_predicates_exact_constructions_kernel_with_sqrt
  • Progress has been made towards the complete adaptability and extensibility of our kernels.
  • New faster Triangle_3 intersection test routines.
    (see Erratum)
  • Added a Kernel concept archetype to check that generic algorithms don't use more functionality than they should.
  • A few more miscellaneous functions.

Basic Library

  • 2D Apollonius Graph (new package)
    Algorithms for computing the Apollonius graph in two dimensions. The Apollonius graph is the dual of the Apollonius diagram, also known as the additively weighted Voronoi diagram. The latter can be thought of as the Voronoi diagram of a set of circles under the Euclidean metric, and it is a generalization of the standard Voronoi diagram for points. The algorithms provided are dynamic.
  • dD Min Sphere of Spheres (new package)
    Algorithms to compute the smallest enclosing sphere of a given set of spheres in Rd. The package provides an algorithm with maximal expected running time O(2O(d) n) and a fast and robust heuristic (for dimension less than 30).
  • Spatial Searching (new package)
    Provides exact and approximate distance browsing in a set of points in d-dimensional space using implementations of algorithms supporting:
    • both nearest and furthest neighbor searching
    • both exact and approximate searching
    • (approximate) range searching
    • (approximate) k-nearest and k-furthest neighbor searching
    • (approximate) incremental nearest and incremental furthest neighbor searching
    • query items representing points and spatial objects.
  • Kd-tree
    this package is deprecated, its documentation is removed. It is replaced by the Spatial Searching package.
  • Largest_empty_rectangle_2
    Given a set of points P in the plane, the class Largest_empty_iso_rectangle_2 is a data structure that maintains an iso-rectangle with the largest area among all iso-rectangles that are inside a given iso-rectangle bounding box, and that do not contain any point of the point set P.
  • 2D Triangulation and 3D Triangulation
    • The classes Triangulation_data_structure_2 (and 3), which implements the data structure for 2D triangulation class, now makes use of CGAL::Compact_container (see Support Library section below).
    • The triangulation classes use a Rebind mecanism to provide the full flexibility on Vertex and Face base classes. This means that it is possible for the user to derive its own Face of Vertex base class, adding a functionality that makes use of types defined by the triangulation data structure like Face_handle or Vertex_handle.
    • New classes Triangulation_vertex_base_with_info_2 (and 3) and Triangulation_face_base_with_info_2 (and 3) to make easier the customisation of base classes in most cases.
  • 2D Triangulation
    • Regular triangulation provides an easy access to hidden points.
    • The Triangulation_hierarchy_2, which provide an efficient location data structure, can now be used with any 2D triangulation class plugged in (including Regular triangulations).
  • 3D Triangulation
    • faster vertex removal function in Delaunay_triangulation_3.
    • Delaunay_triangulation_3 is now independent of the order of insertions of the points (in case of degenerate cosphericity).
    • Regular_triangulation_3 now hides vertices (and updates itself) when inserting a coinciding point with greater weight. This required a new predicate.
    • deprecated functions: copy_triangulation(), push_back(), set_number_of_vertices().
    • Triangulation_3 now gives non-const access to the data structure.
  • Interval Skip List (new package)
    An interval skip list is a data strucure for finding all intervals that contain a point, and for stabbing queries, that is for answering the question whether a given point is contained in an interval or not.
  • Planar Maps and Arrangements
    The changes concern mainly the traits classes.
    1. New traits hierarchy and interface: The set of requirements was made sound and complete. A couple of requirements were eliminated, few others were redefined, and some were renamed. A hierarchy of three traits classes for the Planar_map_2, Planar_map_with_intersections_2, and Arrangement_2 types was established to include only the necessary requirements at each level. It was determined that for the aggregate insertion- operation based on a sweep-line algorithm only a subset of the requirements is needed. Preconditions were added where appropriate to tighten the requirements further.

      The following functions have been renamed:

      • point_is_same() renamed to point_equal()
      • curve_is_same() renamed to curve_equal()
      • curve_is_in_x_range() renamed to point_in_x_range()
      • curve_compare_at_x() renamed to curves_compare_y_at_x() Furthermore, a precondition has been added that the reference point is in the x-range of both curves.
      • curve_compare_at_x_right() renamed to curves_compare_y_at_x_to_right(). Furthermore, a precondition has been added that both curves are equal at the reference point and defined to its right.
      • curve_compare_at_x_left() renamed to curves_compare_y_at_x_to_left(). Furthermore, a precondition has been added that both curves are equal at the reference point and defined to its right.
      • curve_get_point_status() renamed to curve_compare_y_at_x(). Furthermore, a precondition has been added that the point is in the x-range of the curve. Consequently, the function now returns a Comparison_result (instead of a special enum).
      • make_x_monotone() renamed to curve_make_x_monotone() See more details below.
      • curve_flip() renamed to curve_opposite()
      The following functions have been removed:
      • curve_is_between_cw()
      • point_to_left()
      • point_to_right()
      • is_x_monotone()
      • point_reflect_in_x_and_y()
      • curve_reflect_in_x_and_y()
      • do_intersect_to_right()
      • do_intersect_to_left()
      Most functions, are required by the PlanarMapTraits_2 concept, except for the make_x_monotone(), nearest_intersection_to_right(), nearest_intersection_to_left(), curves_overlap() and curve_opposite(). PlanarMapWithIntersectionsTraits_2 requires all these functions, except curve_opposite(), needed only by the ArrangementTraits_2 concept.

      Furthermore, the two functions curve_compare_at_x_left() and nearest_intersection_to_left() can be omitted, if the two functions point_reflect_in_x() and curve_reflect_in_x() are implemented. Reflection can be avoided, if the two _left functions are supplied.

    2. The type X_curve_2 of the PlanarMapWithIntersectionsTraits_2 concept was renamed to X_monotone_curve_2, and the distinction between this type and the Curve_2 type was made firm. The method is_x_monotone() of the PlanarMapWithIntersectionsTraits_2 concept was removed. The related method curve_make_x_monotone() is now called for each input curve of type Curve_2 when curves are inserted into a Planar_map_with_intersections_2 to subdivide the input curve into x-monotone sub-curves (and in case the curve is already x-monotone, this function is responsible for casting it to an x-monotone curve).
    3. New and improved traits classes:
    4. Conic traits - Arr_conic_traits_2 Support finite segments of ellipses, hyperbolas and parabolas, as well as line segments. The traits require an exact real number- type, such as leda_real or CORE::Expr.
    5. Segment cached traits - Arr_segment_cached_traits_2 This class uses an improved representation for segments that helps avoiding cascaded computations, thus achieving faster running times. To work properly, an exact rational number-type should be used.
    6. Polyline traits - Arr_polyline_traits_2 The polyline traits class has been reimplemented to work in a more efficient, generic manner. The new class replaces the obsolete Arr_polyline_traits class. It is parameterized with a segment traits class.
    7. Hyperbola and segment traits - Arr_hyper_segment_traits_2 Supports line segments and segments of canonical hyperbolas. This is the type of curves that arise when projecting segments in three-space rotationally around a line onto a plane containing the line. Such projections are often useful in CAD/CAM problems.
    8. Removed old traits class:
      • The models of the PlanarMapWithIntersectionsTraits_2 concept below became obsolete, as the new conic traits, namely Arr_conic_traits_2, supports the same functionality and is much more efficient.
        • Arr_circles_real_traits
        • Arr_segment_circle_traits
      • The segment traits class and the new polyline traits class were reimplemented using standard CGAL-kernel calls. This essentially eliminated the corresponding leda traits classes, namely:
        • Pm_leda_segment_traits_2
        • Arr_leda_segment_traits_2
        • Arr_leda_polyline_traits
        With the use of the Leda_rat_kernel new external package the same functionality can be achieved with less overhead and more efficiency.
    9. Sweep Line
      • The Sweep_line_2 package was reimplemented. As a consequence it is much more efficient, its traits is tighter (namely neither the two _left nor the reflection functions are required), and its interface has changed a bit.
        1. The following global functions have been removed:
          • sweep_to_produce_subcurves_2()
          • sweep_to_produce_points_2()
          • sweep_to_construct_planar_map_2()
          Instead, the public methods of the Sweep_line_2 class listed below were introduced:
          • get_subcurves() - Given a container of curves, this function returns a list of curves that are created by intersecting the input curves.
          • get_intersection_points() - Given a range of curves, this function returns a list of points that are the intersection points of the curves.
          • get_intersecting_curves() - Given a range of curves, this function returns an iterator to the beginning of a range that contains the list of curves for each intersection point between any two curves in the specified range.
        2. It is possible to construct a planar map with intersections (or an arrangement) by inserting a range of curves into an empty map. This will invoke the sweep-line process to construct the map more efficiently.
      • New interface functions to the Planar_map_with_intersections_2 class. The Planar_map_with_intersections_2 class maintains a planar map of input curves that possibly intersect each other and are not necessarily x-monotone. If an input curve, or a set of input curves, are known to be x-monotone and pairwise disjoint, the new functions below can be used to insert them into the map efficiently.
  • Polyhedral Surface
    • The old design that was deprecated since CGAL 2.3 has been removed.
    • Class Polyhedron_incremental_builder_3:
      • Renamed local enum ABSOLUTE to ABSOLUTE_INDEXING, and RELATIVE to RELATIVE_INDEXING to avoid conflicts with similarly named macros of another library.
      • Changed member functions add_vertex(), begin_facet(), and end_facet() to return useful handles.
      • Added test_facet() to check facets for validity before adding them.
      • Added vertex( size_t i) to return Vertex_handle for index i.
  • Halfedge Data Structure
    • The old design that was deprecated since CGAL 2.3 has been removed.

Support Library

  • New container class Compact_container, which (roughly) provides the flexibility of std::list, with the memory compactness of std::vector.
  • Geomview_stream: added a function gv.draw_triangles(InputIterator begin, InputIterator end) which draws a set of triangles much more quickly than one by one.
  • Number types:
    • number types are now required to provide a function: std::pair<double, double> to_interval(const NT &).
    • number types are now required to provide mixed operators with "int".
    • CLN support removed.
    • faster square() for MP_Float.
    • added Gmp_q.
  • Qt_widget:
    • New classes:
      • Qt_help_window: provides a simple way to show some helpful information about a demo as an HTML page.
      • Qt_widget_history: provides basic functionality to manipulate intervals of Qt_widget class. The current visible area of Qt_widget is mapped to an interval. Each interval could be stored in the Qt_widget_history object. So you can use this object to navigate in history. It is mostly used by Qt_widget_standard_toolbar.
    • Changes:
      • Qt_widget_standard_toolbar: is derived from QToolBar class, so pay attention to modify your code, if you used this class. Some public methods were introduced to control the history object that the toolbar use to navigate.
      • the icons are now part of libCGALQt.
    • Deprecated members of Qt_widget:
      • add_to_history(), clear_history(), back(), forth(): use forward(), back() and clear_history() of the Qt_widget_standard_toolbar instead.
      • custom_redraw(): use redraw_on_back() and redraw_on_front() instead.
    • Optimizations: the output operators of the following classes have been optimized:
      • CGAL::Segment_2 (now tests for intersection with the drawing area)
      • CGAL::Triangle_2 (now tests for intersection with the drawing area)
      • CGAL::Triangulation_2 (is optimized for faster display on zooming)

Erratum in the Kernel manual

  • Intersection test routines

    The documentation of CGAL::do_intersect should mention, for the 3D case:
    Also, in three-dimensional space Type1 can be

    • either Plane_3<Kernel>
    • or Triangle_3<Kernel>
    and Type2 any of
    • Plane_3<Kernel>
    • Line_3<Kernel>
    • Ray_3<Kernel>
    • Segment_3<Kernel>
    • Triangle_3<Kernel>

    In the same way, for Kernel::DoIntersect_3:
    for all pairs Type1 and Type2, where the type Type1 is

    • either Kernel::Plane_3
    • or Kernel::Triangle_3
    and Type2 can be any of the following:
    • Kernel::Plane_3
    • Kernel::Line_3
    • Kernel::Ray_3
    • Kernel::Segment_3
    • Kernel::Triangle_3

    Philippe Guigue (INRIA Sophia-Antipolis) should be mentioned as one of the authors.

Release 2.4

Release date: May 2002

Version 2.4 differs from version 2.3 in the platforms that are supported and in functionality. There have also been a number of bug fixes for this release.

Additional supported platforms:

  • Microsoft Visual C++, version 7.
  • SunPro 5.3 (with patch 111685-05) on Solaris
  • g++ 3.1 on Linux and Solaris

The following functionality has been added or changed:


  • Point_d has been removed from the 2D and 3D kernels. This type is now available from the d-dimensional kernel only.

Basic Library

  • 2D Polygon Partitioning
    Traits requirements for optimal partitioning have been changed slightly.

  • 2D Sweep line
    A new package that implements a sweep-line algorithm to compute arrangements of curves for different families of curves, which are not necessarily line segments (e.g., it also works for circular arcs). The resulting output can be the list of vertex points, the resulting subcurves or a planar map.

  • Planar Maps and Arrangements
    • New quicker insertion functions of Planar_map_2 for cases where more precomputed information is available regarding the position of the inserted curve in the map.
    • New query function for planar maps that determines whether a given point is within a given face of the planar map.
    • New iterator over edges of planar maps in addition to the existing iterator over halfedges.
    • New copy constructor and assignment operator for arrangements.

  • Polyhedral Surface
    • new design introduced with release 2.3 now supported by VC7 compiler
    • Extended functionality of Polyhedron_incremental_builder: absolute indexing allows one to add new surfaces to existing ones.

  • 2D Triangulation
    • There is a new triangulation data structure replacing the two previous ones. This new data structure is coherent with the 3d triangulation data structure and offer the advantages of both previous ones. Backward compatibility is ensured and this change is transparent for the user of triangulation classes.
    • Constrained and Delaunay constrained triangulations are now able to handle intersecting input constraints. The behavior of constrained triangulations with repect to intersection of input constraints can be customized using an intersection tag.
    • A new class Constrained_triangulation_plus offers a constrained hierarchy on top of a constrained triangulations. This additionnal data structure describes the subdivision of the original constraints into edges of the triangulations.

  • 3D Triangulation
    • Running time improved by a better and more compact management of memory allocation
    • Various improvements and small functionalities added:
      • Triangulation_3<GT,Tds>::triangle() returns a triangle oriented towards the outside of the cell c for facet (c,i)
      • New function insert(Point, Locate_type, Cell_handle, int, int) which avoids the location step.
      • New function to get access to cells in conflict in a Delaunay insertion : find_conflicts() and insert_in_hole()
      • New function TDS::delete_cells(begin, end).
      • New functions : degree(v), reorient(), remove_decrease_dimension(), remove_from_simplex().
    • Changes of interface:
      • vertices and cells are the same for the triangulation data structure and the geometric triangulation
      • the triangulation data structure uses Vertex_handle (resp Cell_handle) instead of Vertex* (resp Cell*).
      • incident_cells() and incident_vertices() are templated by output iterators
      • changes in the iterators and circulators interface:
        • Iterators and circulators are convertible to handles automatically, no need to call "->handle()" anymore.
        • Vertex_iterator split into All_vertices_iterator and Finite_vertices_iterator (and similar for cells...).
        • TDS::Edge/Facet iterators now support operator->.

  • 2D Search structures
    Additional range search operations taking a predicate functor have been added

Support Library

  • Qt_widget
    • We have added a new class for visualization of 2D CGAL objects. It is derived from Trolltech's Qt class QWidget and privdes a used to scale and pan.
    • Some demos were developed for the following packages: 2D Alpha shapes, 2D Convex Hull, Largest empty 2D rectangle, Maximum k-gon, Minimum ellipse, Minimum 2D quadrilateral, 2D polygon partitioning 2D regular and constrained triangulation.
    • Tutorials are available to help users get used to Qt_widget

  • Timer
    Fixed Timer class (for user process time) to have no wrap-around anymore on Posix-compliant systems.

The following functionality is no longer supported:

  • Planar maps of infinite curves (the so-called planar map bounding-box).

Bugs in the following packages have been fixed: 3D Convex hull, 2D Polygon partition, simple polygon generator

Also attempts have been made to assure compatability with the upcoming LEDA release that introduces the leda namespace.

Known problems

  • 2D Nef Polyhedra contains a memory leak. Memory problems are also the likely cause of occasional run-time errors on some platforms.
  • The d-dimensional convex hull computation produces run-time errors on some platforms because of memory management bugs.
  • The new Halfedge Data Structure design introduced with release 2.3 does not work on VC6. See the release notes in the manual for more information.
  • The following deficiencies relate to planar maps, planar maps of intersecting curves (pmwx), arrangements and sweep line.
    • On KCC, Borland and SunPro we guarantee neither compilation nor correct execution for all of the packages above.
    • On VC6 and VC7 we guarantee neither compilation nor correct execution of the sweep line package.
    • On CC (on Irix 6.5) the trapezoidal decomposition point location strategy is problematic when used with planar maps, pmwx, or arrangements (mind that this is the default for planar maps).
    • On CC (on Irix 6.5) sweep line with polyline traits does not compile (mind that the so-called leda polyline traits does compile).
    • On g++ (on Irix 6.5) the segment-circle (Arr_segment_circle_traits_2) traits does not compile for either of the above packages.

Release 2.3

Release date: August 2001

Version 2.3 differs from version 2.2 in the platforms that are supported and in functionality.

Additional supported platform:

  • Gnu g++ 3.0 on Solaris and Linux

The following functionality has been added:


  • The 2D and 3D kernels now serve as models of the new kernel concept described in the recent paper, "An Adaptable and Extensible Geometry Kernel" by Susan Hert, Micheal Hoffmann, Lutz Kettner, Sylvain Pion, and Michael Seel to be presented at WAE 2001 (and soon available as a technical report). This new kernel is completely compatible with the previous design but is more flexible in that it allows geometric predicates as well as objects to be easily exchanged and adapted individually to users' needs.
  • A new kernel called Simple_homogeneous is available. It is equivalent to Homogeneous but without reference-counted objects.
  • A new kernel called Filtered_kernel is available that allows one to build kernel traits classes that use exact and efficient predicates.
  • There are two classes, Cartesian_converter and Homogeneous_converter that allows one to convert objects between different Cartesian and homogeneous kernels, respectively.
  • A new d-dimensional kernel, Kernel_d is available. It provides diverse kernel objects, predicates and constructions in d dimensions with two representations based on the kernel families Cartesean_d and Homogeneous_d

Basic Library

Almost all packages in the basic library have been adapted to the new kernel design to realize the flexibility this design makes possible. In several packages, this means that the traits class requirements have changed to conform to the function objects offered in the kernels so the kernels themselves can be used as traits classes in many instances.
  • 2D Convex Hull
    The traits requirements have changed slightly to bring them in line with the CGAL kernels.
  • 3D Convex Hull
    • The function convex_hull_3 now uses a new implementation of the quickhull algorithm and no longer requires LEDA.
    • A new convex_hull_incremental_3 function based on the new d-dimensional convex hull class is available for comparison purposes.

  • Convex_hull_d, Delaunay_d
    Two new application classes offering the calculation of d-dimensional convex hulls and delaunay triangulations

  • Polygons and Polygon Operations
    • The traits class requirements have been changed.
    • The simplicity test has a completely new implementation.
    • Properties like convexity, simplicity and area can now be cached by polygons. You need to set a flag to select this behaviour.

  • Planar Nef Polyhedra
    A new class (Nef_polyhedron_2) representing planar Nef polyhedra = rectilinearly bounded points sets that are the result of binary and topological operations starting from halfplanes.

  • A new package offering functions to partition planar polygons into convex and y-monotone pieces is available.

  • Planar Maps and Arrangements
    • A new class Planar_map_with_intersections_2<Planar_map> for planar maps of possibly intersecting, possibly non-x-monotone, possibly overlapping curves (like Arrangement_2 but without the hierarchy tree).
    • I/O utilities for planar maps and arrangements for textual and graphical streams. (It is possible to save and later reload built planar maps or arrangements.)
    • New arrangement traits class for line segments and circular arcs (Arr_segment_circle_traits<NT>).
    • New faster traits for polylines specialized for using the LEDA rational kernel (Arr_leda_polylines_traits). The LEDA traits for segments was also made faster.
    • A new point location strategy (Pm_simple_point_location<Planar_map>).

  • Halfedge Data Structure

    The halfedge data structure has been completely revised. The new design is more in line with the STL naming scheme and it provides a safe and coherent type system throughout the whole design (no void* pointers anymore), which allows for better extendibility. A user can add new incidences in the mesh easily. The new design also uses standard allocators with a new template parameter that has a suitable default.

    The old design is still available, but its use is deprecated, see the manual of deprecated packages for its documentation. Reported bugs in copying the halfedge data structure (and therefore also polyhedral surfaces) have been fixed in both designs. Copying a list-based representation is now based on hash maps instead of std::map and is therefore considerably faster.

  • Polyhedral Surface

    The polyhedral surface has been rewritten to work with the new halfedge data structure design. The user level interface of the CGAL::Polyhedron_3 class is almost backwards compatible with the previous class. The exceptions are the template parameter list, everything that relies on the flexibility of the underlying halfedge data structure, such as a self-written facet class, and that the distinction between supported normals and supported planes has been removed. Only planes are supported. See the manuals for suggestions how to handle normals instead of planes.

    More example programs are provided with polyhedral surfaces, for example, one about Euler operator and one computing a subdivision surface given a control mesh as input.

    The old design is still available for backwards compatibility and to support older compiler, such as MSVC++6.0. For the polyhedral surface, old and new design cannot be used simultaneously (they have identical include file names and class names). The include files select automatically the old design for MSVC++6.0 and the new design otherwise. This automatism can be overwritten by defining appropriate macros before the include files. The old design is selected with the CGAL_USE_POLYHEDRON_DESIGN_ONE macro. The new design is selected with the CGAL_USE_POLYHEDRON_DESIGN_TWO macro.

  • 2D Triangulation
    • The geometric traits class requirements have been changed to conform to the new CGAL kernels. CGAL kernel classes can be used as traits classes for all 2D triangulations except for regular triangulations.
    • Additionnal functionality:
      • dual method for regular triangulations (to build a power diagram)
      • unified names and signatures for various "find_conflicts()" member functions in Delaunay and constrained Delaunay triangulation.
      • As an alternative to the simple insert() member function, insertion of points in those triangulation can be performed using the combination of find_conflicts() and star_hole() which eventually allows the user to keep track of deleted faces.
    • More demos and examples

  • 3D Triangulation
    • Major improvements
      • A new class Triangulation_hierarchy_3 that allows a faster point location, and thus construction of the Delaunay triangulation
      • A new method for removing a vertex from a Delaunay triangulation that solves all degenerate cases
      • Running time of the usual location and insertion methods improved
    • A bit more functionality, such as
      • New geomview output
      • dual methods in Delaunay triangulations to draw the Voronoi diagram
    • More demos and examples
    • Changes in interface
      • Traits classes requirements have been modified
      • The kernel can be used directly as a traits class (except for regular triangulation)
      • insert methods in Triangulation_data_structure have a new interface

  • A new class (Alpha_shapes_3) that computes Alpha shapes of point sets in 3D is available.

  • The traits requirements for matrix search and minimum quadrilaterals have been changed to bring them in line with the CGAL kernels.

  • Point_set_2
    • now independent of LEDA; based on the CGAL Delaunay triangulation
    • traits class requirements adapted to new kernel concept.
    • function template versions of the provided query operations are available

Support Library

  • Number types:
    • Lazy_exact_nt<NT> is a new number type wrapper to speed up exact number types.
    • MP_Float is a new multiprecision floating point number type. It can do exact additions, subtractions and multiplications over floating point values.
  • In_place_list has a new third template parameter (with a suitable default) for an STL-compliant allocator.
  • Unique_hash_map is a new support class.
  • Union_find is a new support class.
  • Geomview_stream :
    • Geomview version 1.8.1 is now required.
    • no need to have a ~/.geomview file anymore.
    • new output operators for triangulations.
    • new output operators for Ray_2, Line_2, Ray_3, Line_3, Sphere_3.
    • various new manipulators.
  • Window stream In cooperation with Algorithmic Solutions, GmBH (distributors of the LEDA library), we can now offer a visualization package downloadable in binary form that supports visualization on a ported version of the LEDA window lib.

Release 2.2

Release date: October 2000

Version 2.2 differs from version 2.1 in the platforms that are supported and in functionality.

Additional supported platforms:

  • the KAI compiler (4.0) on Solaris 5.8
  • Borland C++ (5.5)

The following functionality has been added:

  • There is a new, non-reference-counted kernel, Simple_cartesian. Because reference counting is not used, and thus coordinates are stored within a class, debugging is easier using this kernel. This kernel can also be faster in some cases than the reference-counted Cartesian kernel.
  • New optimisation algorithms
    • Min_annulus_d - Algorithm for computing the smallest enclosing annulus of points in arbitrary dimension
    • Polytope_distance_d - Algorithm for computing the (squared) distance between two convex polytopes in arbitrary dimension
    • Width_3 - Algorithm for computing the (squared) width of points sets in three dimensions
  • 2D Triangulations
    • There are now two triangulation data structures available in CGAL. The new one uses a list to store the faces and allows one to represent two-dimensional triangulations embedded in three spaces as well as planar triangulations.
    • The triangulation hierarchy which allows fast location query is now available.
  • Inifinite objects can now be included in planar maps.
  • Removal as well as insertions of vertices for 3D Delaunay triangulations is now possible.
  • A generator for ``random'' simple polygons is now available.
  • In directory demo/Robustness, programs that demonstrate typical robustness problems in geometric computing are presented along with the solutions to these problems that CGAL provides.

The following functionality has been removed:

  • The binary operations on polygons (union, intersection ...) have been removed. Those operations were not documented in the previous release (2.1). Arrangements can often be used as a substitute.

Release 2.1

Release date: January 2000

Version 2.1 differs from version 2.0 in the platforms that are supported and in functionality.

Supported platforms:

  • the newest gnu compiler (2.95.2) on Sun, SGI, Linux and Windows.
  • the Microsoft Visual C++ compiler, version 6.
  • the mips CC compiler version 7.3 under Irix.
Support for the old g++ compiler (2.8) and for mips CC 7.2 has been dropped.

The following functionality has been added:
  • Alpha shapes and weighted alpha shapes in 2D. Alpha shapes are a generalization of the convex hull of a point set.
  • Arrangements in 2D. Arrangements are related to and based on planar maps. The major difference between the two is that curves are allowed to intersect in the case of arrangements.
  • Extensions to triangulations in 2D. Constrained triangulations are now dynamic: they support insertions of new constraint as well as removal of existing constraints. There are also constrained Delaunay triangulations.
  • Triangulations in 3D were added, both Delaunay triangulations and regular triangulations.
  • Min_quadrilateral optimisations have been added. These are algorithms to compute the minimum enclosing rectangle/parallelogram (arbitrary orientation) and the minimum enclosing strip of a convex point set.
  • 2d Point_set is a package for 2d range search operations, Delaunay triangulation, nearest neighbor queries. This package works only if LEDA is installed.
  • Support for GeoWin visualization library. This also depends on LEDA.
  • Support for using the CLN number type together with CGAL.

Release 2.0

Release date: June 1999

The main difference from release 1.2 is the introduction of namespaces -- namespace std for code from the standard library and namespace CGAL for the CGAL library.

Release 1.2

Release date: January 1999

Additions to release 1.1 include:

  • topological map
  • planar map overlay
  • regular and constrained triangulations

Release 1.1

Release date: July 1998

Additions to release 1.0 include:

  • 3D intersections
  • kD points
  • 3D convex hull
  • kD smallest enclosing sphere

Release 1.0

Release date: April 1998

Additions to release 0.9 include:

  • Polyhedral surfaces
  • Halfedge Data Structure
  • Planar maps

Release 0.9

Release date: June 1997

Initial (beta) release of the CGAL library.

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