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[Small Feature] Remove TensorFlow support
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@sloriot @maxGimeno @MaelRL @lrineau @sgiraudot @efifogel @afabri @gdamiand @janetournois @LiangliangNan @kkatrio @danston
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Release History

Release 5.3

Release date: June 2021


  • Point set, polygon soup, and polygon mesh file I/O functions have been harmonized and documented:

A comprehensive list of the supported file formats is available in the Stream_support package here; inversely, the following page can be used to find out which CGAL data structures can be used given a specific file format.

Polygon Mesh Processing

  • Added the class CGAL::Polyhedral_envelope providing a way to quickly check if a primitive (point, segment, or triangle) is within a polyhedral envelope around a set of triangles. It is based on the work of Bolun Wang, Teseo Schneider, Yixin Hu, Marco Attene, and Daniele Panozzo. "Exact and efficient polyhedral envelope containment check." (ACM Trans. Graph., 39-4, July 2020).
  • Added more functions in the visitor of the corefinement based methods to track all edge creations.

Surface Mesh Simplification

  • Added a filtering mechanism so that costly tests get only applied to the next candidate for the edge collapse.
  • Added the class Polyhedral_envelope_filter that enables to perform mesh simplification inside a polyhedral envelope of the input mesh.

Surface Mesh Topology

  • Added the function CGAL::Surface_mesh_topology::Curves_on_surface_topology::is_homotopic_to_simple_cycle(), which can be used to determine whehter a closed path on a surface mesh can be continously transformed to a cycle without self intersection.

2D Regularized Boolean Set Operations

  • Added documentation for the free functions oriented_side(const Point_2& p, ....) that accept a point and a polygon, and improved the documentation of all other functions

2D Polyline Simplification

  • When polylines have common subsequences of vertices these subsequences may be simplifified simultaneously.

2D and 3D Alpha Shapes

  • The following deprecated classes have been removed: Alpha_shape_euclidean_traits_2, Weighted_alpha_shape_euclidean_traits_2, Alpha_shape_euclidean_traits_3, and Weighted_alpha_shape_euclidean_traits_3. All CGAL kernel can be used directly as models of the concepts of the 2D and 3D Alpha Shape packages.

dD Triangulations

  • Added the function insert_if_in_star() to the class CGAL::Regular_triangulation, which enables users to insert a point p in a regular triangulation on the condition that p appears post-insertion in the star of a user-specified, existing vertex.


  • Breaking change: the support for TensorFlow was dropped, the classifier CGAL::TensorFlow::Neural_network_classifier was removed.

Release 5.2

Release date: December 2020

dD Geometry Kernel

CGAL and the Boost Graph Library (BGL)

3D Fast Intersection and Distance Computation (AABB Tree)

  • Added the move constructor and the assignment operator to the AABB Tree class.

2D Arrangements

  • Replaced the use of legacy CGAL::Object to modern boost::variant.
  • Changed make-x-monotone return type from legacy CGAL::Object to boost::variant in all traits concepts and models. As there exists an implicit conversion from boost::variant to CGAL::Object, the new code is backward compatible. However, it is recommended that all calls to the make-x-monotone functions are fixed to use the new return type.
  • Changed decompose() interface to use boost::variant instead of legacy CGAL::Object As explained above, the code is backward compatible. However, it is recommended that all calls to decompose() are fixed to use the new interface.

Surface Mesh

Polygon Mesh Processing

Surface Mesh Parameterization

  • Added a new parameterization method, Iterative Authalic Parameterization. It is based on the work of Jain, Hardik, Manuel Wollhaf, and Olaf Hellwich, "Learning to Reconstruct Symmetric Shapes using Planar Parameterization of 3D Surface." (IEEE International Conference on Computer Vision Workshops, 2019).


Point Set Processing

3D Convex Hulls

3D Triangulations

Release 5.1

Release date: September 2020

Tetrahedral Remeshing (new package)

  • This package implements a tetrahedral isotropic remeshing algorithm, that improves the quality of tetrahedra in terms of dihedral angles, while targeting a given edge length.

    See also the associated blog entry.

Surface Mesh Topology (new package)

  • This package enables the computation of some topological invariants of surfaces, such as:

    • test if two (closed) curves on a combinatorial surface are homotopic. Users can choose between free homotopy and homotopy with fixed endpoints;
    • test is a curve is contractible;
    • compute shortest non-contractible cycles on a surface, with or without weights on edges.

    See also the associated blog entry.

Optimal Bounding Box (new package)

  • This package implements an optimization algorithm that aims to construct a close approximation of the optimal bounding box of a mesh or a point set, which is defined as the smallest (in terms of volume) bounding box that contains a given mesh or point set.

    See also the associated blog entry.


  • The CGAL_Core library no longer requires Boost.Thread, even if the g++ compiler is used.
  • The minimal supported version of Boost is now 1.66.0.


2D and 3D Linear Geometry Kernel

dD Geometry Kernel

Surface Mesh

CGAL and the Boost Graph Library (BGL)

3D Fast Intersection and Distance Computation (AABB Tree)

2D Arrangements

  • Changed intersection return type from legacy CGAL::Object to modern boost::variant in all traits concepts and models. As there exists an implicit conversion from boost::variant to CGAL::Object, the new code is backward compatible. However, it is recommended that all calls to the intersection functions are fixed to use the new return type.

2D Regularized Boolean Set-Operations

2D Minkowski Sums

  • Changed intersection return type from legacy CGAL::Object to modern boost::variant in the (internally used) model Arr_labeled_traits_2.

dD Spatial Searching

  • The kd-tree can now be built in parallel: CGAL::Kd_tree::build() is given an optional template parameter ConcurrencyTag (default value remains CGAL::Sequential_tag for backward compatibility).
  • Improved the performance of the kd-tree in some cases:
    • Not storing the points coordinates inside the tree usually generates a lot of cache misses, leading to non-optimal performance. This is the case for example when indices are stored inside the tree, or to a lesser extent when the points coordinates are stored in a dynamically allocated array (e.g., Epick_d with dynamic dimension) — we says "to a lesser extent" because the points are re-created by the kd-tree in a cache-friendly order after its construction, so the coordinates are more likely to be stored in a near-optimal order on the heap. In these cases, the new EnablePointsCache template parameter of the CGAL::Kd_tree class can be set to CGAL::Tag_true. The points coordinates will then be cached in an optimal way. This will increase memory consumption but provides better search performance. See the updated GeneralDistance and FuzzyQueryItem concepts for additional requirements when using such a cache.
    • In most cases (e.g., Euclidean distance), the distance computation algorithm knows before its end that the distance will be greater than or equal to some given value. This is used in the (orthogonal) k-NN search to interrupt some distance computations before its end, saving precious milliseconds, in particular in medium-to-high dimension.

Intersecting Sequences of dD Iso-oriented Boxes

Spatial Sorting

  • Added parallel versions of the functions CGAL::hilbert_sort() and CGAL::spatial_sort() in 2D and 3D when the median policy is used. The parallel versions use up to four threads in 2D, and up to eight threads in 3D.

3D Convex Hulls

Polygon Mesh Processing

Point Set Processing

  • Breaking change: CGAL::remove_outliers() has been parallelized and thus has a new template parameter ConcurrencyTag. To update your code simply add as first template parameter CGAL::Sequential_tag or CGAL::Parallel_tag when calling this function.
  • Add a function CGAL::cluster_point_set() that segments a point cloud into connected components based on a distance threshold.
  • Added wrapper functions for registration:

2D Triangulations

  • To fix an inconsistency between code and documentation and to clarify which types of intersections are truly allowed in constrained Delaunay triangulations, the tag CGAL::No_intersection_tag has been deprecated in favor of two new tags: CGAL::No_constraint_intersection_tag and CGAL::No_constraint_intersection_requiring_constructions_tag. The latter is equivalent to the now-deprecated CGAL::No_intersection_tag, and allows constraints to intersect as long as no new point has to be created to represent that intersection (for example, the intersection of two constraint segments in a 'T'-like junction is an existing point and as such does not require any new construction). The former tag, CGAL::No_constraint_intersection_tag, does not allow any intersection, except for the configuration of two constraints having a single common endpoints, for convience.
  • Added the function CGAL::split_subconstraint_graph_into_constraints() to Constrained_triangulation_plus_2 to initialize the constraints from a soup of disconnected segments that should first be split into polylines.

3D Triangulations

3D Triangulation Data Structure

Surface Mesh Simplification

  • Added a new simplification method based on the quadric error defined by Garland and Heckbert.
  • The concept EdgeProfile has been removed. This concept was not actually in use as the CGAL-provided model CGAL::Edge_profile was imposed to the user. Other concepts have been clarified to reflect the fact that the API uses this particular class.

STL Extensions for CGAL

Release 5.0

Release date: November 2019

General changes

  • CGAL 5.0 is the first release of CGAL that requires a C++ compiler with the support of C++14 or later. The new list of supported compilers is:
    • Visual C++ 14.0 (from Visual Studio 2015 Update 3) or later,
    • Gnu g++ 6.3 or later (on Linux or MacOS),
    • LLVM Clang version 8.0 or later (on Linux or MacOS), and
    • Apple Clang compiler versions 7.0.2 and 10.0.1 (on MacOS).
  • Since CGAL 4.9, CGAL can be used as a header-only library, with dependencies. Since CGAL 5.0, that is now the default, unless specified differently in the (optional) CMake configuration.
  • The section "Getting Started with CGAL" of the documentation has been updated and reorganized.
  • The minimal version of Boost is now 1.57.0.

Polygonal Surface Reconstruction (new package)

  • This package provides a method for piecewise planar object reconstruction from point clouds. The method takes as input an unordered point set sampled from a piecewise planar object and outputs a compact and watertight surface mesh interpolating the input point set. The method assumes that all necessary major planes are provided (or can be extracted from the input point set using the shape detection method described in Point Set Shape Detection, or any other alternative methods).The method can handle arbitrary piecewise planar objects and is capable of recovering sharp features and is robust to noise and outliers. See also the associated blog entry.

Shape Detection (major changes)

  • Breaking change: The concept ShapeDetectionTraits has been renamed to EfficientRANSACTraits.
  • Breaking change: The Shape_detection_3 namespace has been renamed to Shape_detection.
  • Added a new, generic implementation of region growing. This enables for example applying region growing to inputs such as 2D and 3D point sets, or models of the FaceGraph concept. Learn more about this new algorithm with this blog entry.

dD Geometry Kernel

  • A new exact kernel, Epeck_d, is now available.

2D and 3D Linear Geometry Kernel

  • Added a new concept, ComputeApproximateAngle_3, to the 3D Kernel concepts to compute the approximate angle between two 3D vectors. Corresponding functors in the model (Compute_approximate_angle_3) and free function (approximate_angle) have also been added.
  • The following objects are now hashable and thus trivially usable with std::unordered_set and std::unordered_map: CGAL::Aff_transformation_2, CGAL::Aff_transformation_3, CGAL::Bbox_2, CGAL::Bbox_3, CGAL::Circle_2, CGAL::Iso_cuboid_3, CGAL::Iso_rectangle_2, CGAL::Point_2, CGAL::Point_3, CGAL::Segment_2, CGAL::Segment_3, CGAL::Sphere_3, CGAL::Vector_2, CGAL::Vector_3, CGAL::Weighted_point_2 and CGAL::Weighted_point_3.

Polygon Mesh Processing

3D Point Set

  • The PLY IO functions now take an additional optional parameter to read/write comments from/in the PLY header.

Point Set Processing

2D Triangulations

  • Breaking change: Removed the deprecated functions CGAL::Constrained_triangulation_plus_2:: vertices_in_constraint_{begin/end}(Vertex_handle va, Vertex_handle vb) const;, and CGAL::Constrained_triangulation_plus_2::remove_constraint(Vertex_handle va, Vertex_handle vb), that is a pair of vertex handles is no longer a key for a polyline constraint. Users must use a version prior to 5.0 if they need this functionality.
  • Breaking change: Removed the deprecated classes CGAL::Regular_triangulation_euclidean_traits_2, CGAL::Regular_triangulation_filtered_traits_2. Users must use a version prior to 5.0 if they need these classes.
  • Breaking change: The graph traits enabling CGAL's 2D triangulations to be used as a parameter for any graph-based algorithm of CGAL (or boost) have been improved to fully model the FaceGraph concept. In addition, only the finite simplicies (those not incident to the infinite vertex) of the 2D triangulations are now visibile through this scope. The complete triangulation can still be accessed as a graph, by using the graph traits of the underlying triangulation data structure (usually, CGAL::Triangulation_data_structure_2).
  • Breaking change: The insert() function of CGAL::Triangulation_2 which takes a range of points as argument is now guaranteed to insert the points following the order of InputIterator. Note that this change only affects the base class Triangulation_2 and not any derived class, such as Delaunay_triangulation_2.
  • Added a new constructor and insert() function to CGAL::Triangulation_2 that takes a range of points with info.
  • Introduced a new face base class, Triangulation_face_base_with_id_2 which enables storing user-defined integer IDs in the face of any 2D triangulation, a precondition to use some BGL algorithms.
  • Added range types and functions that return ranges, for example for all vertices, enabling the use of C++11 for-loops. See this new example for a usage demonstration.

3D Triangulations

  • Breaking change: The constructor and the insert() function of CGAL::Triangulation_3 which take a range of points as argument are now guaranteed to insert the points following the order of InputIterator. Note that this change only affects the base class Triangulation_3 and not any derived class, such as Delaunay_triangulation_3.
  • Added constructor and insert() function to CGAL::Triangulation_3 that takes a range of points with info.
  • Added range types and functions that return ranges, for example for all vertices, which enables to use C++11 for-loops. See this new example for a usage demonstration.

Surface Mesh

  • Introduced new functions to read and write using the PLY format, CGAL::read_ply() and CGAL::write_ply(), enabling users to save and load additional property maps of the surface mesh.

CGAL and Solvers

  • Added concepts and models for solving Mixed Integer Programming (MIP) problems with or without constraints.

3D Boolean Operations on Nef Polyhedra

IO Streams

Release 4.14

Release date: March 2019

2D Periodic Hyperbolic Triangulations (new package)

  • This package allows the computation of Delaunay triangulations of the Bolza surface. The Bolza surface is the most symmetric hyperbolic surface of genus 2. Its fundamental domain is the regular hyperbolic octagon with angles π/4 centered at the origin of the Poincaré disk. Triangulations of the Bolza surface can be seen as triangulations of the hyperbolic plane that are periodic in the four directions defined by the sides of this regular octagon.

2D Hyperbolic Triangulations (new package)

  • This package allows the computation of Delaunay Triangulations of sets of points in the Poincaré disk, which is one of the conformal models for the hyperbolic plane.

The Heat Method (new package)

  • This package provides an algorithm that solves the single- or multiple-source shortest path problem by returning an approximation of the geodesic distance for all vertices of a triangle mesh to the closest vertex in a given set of source vertices.

Triangulated Surface Mesh Approximation (new package)

  • This package implements the Variational Shape Approximation method to approximate an input surface triangle mesh by a simpler surface triangle mesh.

Polygon Mesh Processing package

  • Added the following new functions to detect and repair issues in polygon soups:

    • CGAL::Polygon_mesh_processing::remove_isolated_points_in_polygon_soup(), which detects and removes points that are not used in any polygon of the soup.
    • CGAL::Polygon_mesh_processing::merge_duplicate_points_in_polygon_soup(), which detects and merges points that share the same geometric position.
    • CGAL::Polygon_mesh_processing::merge_duplicate_polygons_in_polygon_soup(), which detects and merges polygons that are identical.
    • CGAL::Polygon_mesh_processing::repair_polygon_soup(), which applies a number of repairing steps (a subset of which are the functions above) to clean and repair a polygon soup.
  • Added the following new functions to detect and repair degeneracies in polygon meshes:

    • CGAL::Polygon_mesh_processing::degenerate_edges()
    • CGAL::Polygon_mesh_processing::degenerate_faces()
    • CGAL::Polygon_mesh_processing::is_non_manifold_vertex()
    • CGAL::Polygon_mesh_processing::is_degenerate_triangle_face()
    • CGAL::Polygon_mesh_processing::is_degenerate_edge()
    • CGAL::Polygon_mesh_processing::is_needle_triangle_face()
    • CGAL::Polygon_mesh_processing::is_cap_triangle_face()
    • CGAL::Polygon_mesh_processing::duplicate_non_manifold_vertices()
    • CGAL::Polygon_mesh_processing::extract_boundary_cycles()
    • CGAL::Polygon_mesh_processing::merge_duplicated_vertices_in_boundary_cycle()
    • CGAL::Polygon_mesh_processing::merge_duplicated_vertices_in_boundary_cycles()
  • Added the class CGAL::Rigid_triangle_mesh_collision_detection to detect intersections between meshes and volumes undergoing affine transformations.

Regularized Boolean Set Operations in 2D package

  • Fixed the validation of orientation of relative simple polygons.

Point Set Processing

  • CGAL::mst_orient_normals() can now be called with a set of user-selected seed points that are known to be already oriented. A new optional named parameter point_is_constrained_map is added for this purpose. The original behavior (using one unique and automatically selected seed) is kept if this parameter is not used.


  • Added a new experimental classifier TensorFlow::Neural_network_classifier.

  • For uniformity, ETHZ_random_forest_classifier is renamed ETHZ::Random_forest_classifier and OpenCV_random_forest_classifier is renamed OpenCV::Random_forest_classifier.

  • The training algorithm of ETHZ::Random_forest_classifier was parallelized.

  • Added a constructor to copy a ETHZ::Random_forest_classifier using a different data set as input.

  • Added 3 new geometric features, Height_above, Height_below and Vertical_range.

3D Fast Intersection and Distance Computation

  • The primitives AABB_face_graph_triangle_primitive and AABB_halfedge_graph_segment_primitive now use as Id a pair of descriptor and graph pointer in the case they are configured to deal with a possible different graph per primitive (configuration set using a template tag).

2D Arrangements

  • Fixed a bug in the surface-sweep framework (Surface_sweep_2) that ensures that an event is never left without (left or right) curves.

  • Fixed a constructor of Arr_counting_traits.h. (In particular, added missing const of a parameter).

  • Fixed zone computation of a curve in cases where the lexicographic smallest end of the curve lies on the parameter space.

  • Implemented missing function object Compare_x_near_boundary of Arr_polyline_traits_2, Arr_polycurve_traits_2, and Arr_polycurve_basic_traits_2.

2D and 3D Mesh Generation

  • Added two functions for writing in XML VTK formats:
    • CGAL::write_vtu(), that writes a 2D mesh in a .vtu file,
    • CGAL::output_to_vtu(), that writes a 3D mesh in a .vtu file.

2D Minkowski Sums

  • Fixed a bug in the function that computed the Minkowski sum using the reduced-convolution method. In particular, correctly handled the case where one of the summands does not have an outer boundary.

3D Point Set

  • Added a method copy_properties() that allows to copy the properties from a point set to another one (without copying the content);

  • Added a method insert(const Point_set&, const Index&) to copy a point along with all its associated properties from another point set;

  • remove() methods now only invalidate the end() iterator instead of invalidating all iterators;

  • Added a method is_removed() that takes an index as argument;

  • Added a method cancel_removals() to restore removed points (if no point was inserted since then an garbage was not collected);

  • Breaking change: unified API of method add_normal_map() with add_property_map(): it now returns a pair of property map + bool (that tells if the property was added) instead of just the property map;

  • Added a method properties_and_types() in addition to properties(): this new one returns pairs of std::string + std::type_info in order to also know the type of each property.

CGAL and the Boost Graph Library (BGL)

  • Added function write_wrl() for writing into VRML 2.0 format.
  • Added functions CGAL::write_vtp() for writing a triangulated face graph in a .vtp file (XML VTK format).

Release 4.13

Release date: October 2018

3D Periodic Mesh Generation (new package)

  • This package generates 3-dimensional periodic meshes. It computes isotropic simplicial meshes for domains described through implicit functional boundaries over the flat torus (which can also seen in the Euclidean space as a periodic cube). The output is a periodic 3D mesh of the domain volume and conformal surface meshes for all the boundary and subdividing surfaces. The package is closely related to the 3D Mesh Generation package, with similar concepts, classes, and API.


  • The library CGAL_Qt5 now contains a fork of the version 2.7.0 of libQGLViewer. The corresponding code is in the package GraphicsView. The dependency for the external library libQGLViewer is therefore dropped for all demos.


  • A new function CGAL::draw() is added in the packages Polyhedral Surface, Surface Mesh, Linear Cell Complex, 2D Triangulations, and 3D Triangulations, enabling to draw the corresponding data structures.

2D and 3D Linear Geometry Kernel

  • An operator() that takes a Ray_3 has been added to the concept ConstructProjectedPoint_3.

Convex hull 3

  • Added the function extreme_points_3() computing the points on the convex hull without underlying connectivity.

  • Added a traits adapter called Extreme_points_traits_adapter_3 that enables the use of the function extreme_points_3() on a range of keys, each key being associated to 3D point using a property map. This can be used to get the vertices of a mesh that are on it convex hull, or the indices of points in a range that are on it convex hull.

  • Fix a bug in the computation of the 3D convex hull that was leaving extra points within subset of coplanar points that do not belong to the minimal convex hull.

2D and 3D Triangulations

  • Added a new type of intersection to handle the insertion of intersecting constraints in a Constrained_triangulation_2.

  • Breaking change: The long-deprecated class Triangulation_cell_base_with_circumcenter_3 and its associated concept have been removed. Users should use the classes Delaunay_cell_base_with_circumcenter_3 or Regular_cell_base_with_circumcenter_3, depending on which type of triangulation they are using.

  • Breaking change: The deprecated functions mirror_index and mirror_vertex of the class Triangulation_face_base_2 have been removed. Users should use the equivalent functions from the class Triangulation_2.

3D Mesh Generation

  • Breaking change: The template parameters of the class template Labeled_mesh_domain_3 have been simplified. The three constructors of that class template have been replaced by a new unique constructor using Boost named parameters. Three new static template member functions that act as named constructors have been added:

    • create_gray_image_mesh_domain(), to create a domain from a 3D gray image,
    • create_labeled_image_mesh_domain(), to create a domain from a 3D labeled image, and
    • create_implicit_mesh_domain(), to create a domain from an implicit function.
  • The class templates Implicit_mesh_domain_3, Gray_image_mesh_domain_3, and Labeled_image_mesh_domain_3 are now deprecated.

  • Breaking change: The headers <CGAL/Mesh_3/Implicit_to_labeled_function_wrapper.h> and <CGAL/Mesh_3/Labeled_mesh_domain_3.h>, that were deprecated since CGAL 4.5, have been removed.

  • Breaking change: the concepts MeshCellCriteria_3 and MeshFacetCriteria_3 now require the triangulation to be passed in their operator(). Models of these concepts that are provided by CGAL have been modified accordingly.

  • Breaking change: It is no longer possible to use the deprecated, pre-CGAL 3.8 specifications in MeshCellCriteria_3 and MeshFacetCriteria_3 (that is, using Facet_badness and Cell_badness instead of Is_facet_bad and Is_cell_bad).

  • The concept MeshFacetCriteria_3 no longer requires the function operator()(Cell_handle c, int i).

  • The concept MeshEdgeCriteria_3 no longer requires the function operator()(const Edge& e).

  • The concept MeshComplexWithFeatures_3InTriangulation_3 no longer requires the functions number_of_edges(Curve_index index) and number_of_corners(Corner_index index).

  • Introduced the concept MeshTriangulationTraits_3, which covers the needs of the traits class used in Mesh_3 (and Periodic_3_mesh_3). The traits class used as template parameter of Mesh_triangulation_3 and Periodic_3_mesh_triangulation_3 must be a model of this concept.

  • Added the function Mesh_domain_with_polyline_features_3::add_corner(), which allows users to add a single corner (that is not incident to any polyline) to the mesh complex.

  • Breaking change: CGAL::lloyd_optimize_mesh_3 now depends on the Eigen library.

Polygon Mesh Processing

  • Added a named parameter in stitching functions that allows to choose whether the operation should be performed per connected component or globally.

  • Added a function, CGAL::Polygon_mesh_processing::transform(), to apply a transformation to a mesh.

  • Added a named parameter visitor in corefinement-related functions that makes it possible to pass a visitor to the function in order to track the creation of new faces.

  • Added a named parameter throw_on_self_intersection in all corefinement-related functions, which enables to check for self-intersecting faces involved in the intersection before trying to corefine the input meshes. This new parameter replaces the bool parameter in corefine().

  • Added the function corefine_and_compute_boolean_operations(), which can be used to compute the result of several Boolean operations between two volumes at the same time.

  • Added the function clip(), which can be used to clip a triangulated surface mesh by a plane or a clipping volume.

  • Constrained vertices are now guaranteed to be kept in the mesh after calling isotropic_remeshing() (and not only the points associated to constrained vertices, as it was before).

  • Added a function, CGAL::Polygon_mesh_processing::extrude_mesh(), to perform an extrusion of an open polygon mesh.

Estimation of Local Differential Properties of Point-Sampled Surfaces Reference

  • Breaking change: CGAL::Monge_via_jet_fitting now depends on the Eigen library.

Point Set Processing

  • Added a callback mechanism to the following functions: CGAL::bilateral_smooth_point_set(), CGAL::compute_average_spacing(), CGAL::grid_simplify_point_set(), CGAL::hierarchy_simplify_point_set(), CGAL::jet_estimate_normals(), CGAL::jet_smooth_point_set(), CGAL::pca_estimate_normals(), CGAL::remove_outliers() and CGAL::wlop_simplify_and_regularize_point_set().


  • Added data structures to handle classification of Surface Meshes and of Clusters.

  • Added public API to compute features in parallel.

  • Breaking change: features based on products/divisions of eigenvalues are replaced by simple eigenvalue features. Features based on statistics on the HSV color channels are replaced by simple HSV color channel features.

  • Breaking change: the API of CGAL::Classification::Point_set_feature_generator has been simplified.

Bounding Volumes

  • Breaking change: CGAL::Approximate_min_ellipsoid_d now depends on the Eigen library.


  • The output of the natural and regular neighbor functions (resp. the gradient fitting functions) is no longer restricted to a Point/Coordinate pair (resp. Point/Vector pair). Instead, users can provide their own functor to format the output as they desire.

  • The interpolation functions can now operate on any combination of Type/Coordinate, provided that the values and gradients functors can also be evaluated using 'Type'.

    The combination of these two changes allow, for example, to operate with Vertex/Coordinate pairs, which enables a more efficient access to values and gradients by storing information directly in the vertex.

  • The concepts InterpolationTraits and GradientFittingTraits have been updated to reflect the real needs of the code (some types and operators were used in the code but did not appear in the concepts).

CGAL and the Boost Graph Library (BGL)

  • Added a helper function, CGAL::is_valid_polygon_mesh, that checks the validity of a polygon mesh using BGL functions.

  • Improved the function CGAL::Euler::collapse_edge such that the target vertex of the collapsed edge is now always kept after the collapse.

  • The function copy_face_graph() now uses named parameters, some allowing it to use property maps instead of output iterators.

  • Addition of the following named parameters :

    • vertex_to_vertex_output_iterator
    • halfedge_to_halfedge_output_iterator
    • face_to_face_output_iterator
    • vertex_to_vertex_map
    • halfedge_to_halfedge_map
    • face_to_face_map

CGAL and Solvers

  • Breaking change: CGAL::Diagonalize_traits is now deprecated and should not be used. The class CGAL::Eigen_diagonalize_traits (along with the Eigen library) should be used instead.

CGAL and Boost Property Maps

  • Added a read-write property map to convert on-the-fly geometric objects from Cartesian kernels.

2D Arrangements

  • Refracted and fixed the graph_traits for the dual of an arrangement of the following types: Arrangement_on_surface_2, Arrangement_2, Arrangement_on_surface_with_history_2, and Arrangement_with_history_2.

  • Breaking change: The old <CGAL/graph_traits_Dual_Arrangement_2.h> header file has been replaced by the four header files below; each defines the graph_traits for dual of the corresponding arrangement type. <CGAL/graph_traits_dual_arrangement_on_surface_2.h>, <CGAL/graph_traits_dual_arrangement_2.h>, <CGAL/graph_traits_dual_arrangement_on_surface_with_history_2.h>, and <CGAL/graph_traits_dual_arrangement_with_history_2.h.

Release 4.12

Release date: April 2018

Important Notice

  • The CMake scripts used by CGAL have been changed to use modern patterns introduced by CMake 2.8.12 and CMake 3.0: instead of setting CMake variables, the script now defines imported targets and uses link interfaces.

    That is mostly backward-compatible with existing usages of CGAL CMake scripts. The only non-compatible effect is that the CMAKE_BUILD_TYPE and compilation flags are no longer copied from the CGAL_DIR to the project using it. Note also that the CMAKE_BUILD_TYPE is no longer set to Release by default. For a developer using the Visual Studio IDE or the Xcode IDE, the change should be transparent. Developers using makefiles or the Ninja build-system should set the CMAKE_BUILD_TYPE to Release manually, to avoid using CGAL libraries without any compile-time optimization.

Header-only Mode

  • Since CGAL-4.9, it has been possible to use CGAL by configuring it using CMake, but without compiling the CGAL libraries. With CGAL-4.12, it is now possible to use CGAL header-only, without even configuring it. CMake is then used only to configure programs using CGAL.

Compiler Support

  • The Microsoft Visual C++ 2017 version 15.3 has introduced support for C++17, with the compilation flag /std:c++17. CGAL 4.12 has an initial support for that flag: the code will compile, but a lot of deprecation warnings will remain. Note that Boost version 1.67 is the first version of Boost supporting /std:c++17.

  • The compilation flag /permissive- of Visual C++ is now supported.

2D Movable Separability of Sets (new package)

  • A new package called "2D Movable Separability of Sets" has been introduced. It handles a class of problems that deal with moving sets of objects in the plane; the challenge is to avoid collisions between the objects while considering different kinds of motions and various definitions of separation.

    At this point this package consists of the implementations of various predicates and constructions related to castings of polygonal objects. In particular, it can be used to determine whether a feasible mold for a polygonal object does exist. If a mold exists, the package can also be used to compute all possible orientations of the feasible molds and the corresponding motions needed to remove the casted object from the mold.

Classification (new package)

  • This package offers an algorithm that classifies a data set into a user-defined set of labels (such as ground, vegetation, buildings, etc.). A flexible API is provided so that users can classify any type of data, compute their own local features on the input data set, and define their own labels.

Kinetic Data Structures (removed package)

  • This package has been removed from CGAL-4.12. Users of the package will have to keep using the source code available in CGAL-4.11 or earlier.

3D Convex Hull

  • Breaking change: The header <CGAL/convex_hull_3.h> no longer includes <CGAL/Polyhedron_3.h>, as the convex hull function works with any model of the concept MutableFaceGraph.

2D Arrangements

  • When removing an edge from an arrangement and the user has requested to remove the end-vertices in case they become redundant (either isolated or approach infinity), defer the removal of the such end-vertices to occur after the observer is notified that the edge has been removed. This is symmetric (opposite) to the order of notification when an edge is inserted.

    The user can restore old (non-symmetric) behaviour by defining the macro:


2D Periodic Triangulations

  • Breaking change: The class Periodic_2_triangulation_hierarchy_vertex_base_2 (and its corresponding header) have been removed. Users should directly use the class Triangulation_hierarchy_vertex_base_2, which is identical.
  • Breaking change: The functions circumcenter(), side_of_oriented_circle(), and is_extensible_in_1_sheet_h[12]() are related to Delaunay triangulations and have been moved from Periodic_2_triangulation_2 to Periodic_2_Delaunay_triangulation_2.

2D Alpha Shapes

  • It is now possible to use CGAL::Periodic_2_triangulation_2 as underlying triangulation for Alpha_shape_2.

3D Surface Mesh Generation

  • Add the function facets_in_complex_2_to_triangle_mesh() that exports Surface_mesh_complex_2_in_triangulation_3 facets into a MutableFaceGraph.

3D Mesh Generation

  • Add the function facets_in_complex_3_to_triangle_mesh() that exports Mesh_complex_3_in_triangulation_3 facets into a MutableFaceGraph.
  • Breaking change: The concept MeshDomainWithFeatures_3 has been modified, to improve the performance and the reliability of the sampling of 1D curves of the domain.
  • Add the ability to ensure that the output mesh surface describes a manifold, when the input surface is a manifold. New named parameters manifold(), manifold_with_boundary(), and non_manifold() are added.

Optimal Transportation Curve Reconstruction

  • New method run_under_wasserstein_tolerance() which allows the user to perform curve reconstruction by relying on a threshold on the Wasserstein distance. This is useful when the number of edges in the expected output reconstruction is not known.

Polygon Mesh Processing

  • Added two functions for orienting connected components :

    • CGAL::Polygon_mesh_processing::orient()
    • CGAL::Polygon_mesh_processing::orient_to_bound_a_volume()
  • Added a new function for intersection tests between triangle meshes and/or polylines or range of polylines, and another one to report all the pairs of meshes intersecting from a range of meshes:

    • CGAL::Polygon_mesh_processing::do_intersect()
    • CGAL::Polygon_mesh_processing::intersecting_meshes()
  • Added new functions for feature detection and feature-guided segmentation:

    • CGAL::Polygon_mesh_processing::detect_sharp_edges()
    • CGAL::Polygon_mesh_processing::detect_vertex_incident_patches()
    • CGAL::Polygon_mesh_processing::sharp_edges_segmentation()

Point Set Shape Detection

  • Breaking change: CGAL::Shape_detection_3::Efficient_RANSAC_traits is now called CGAL::Shape_detection_3::Shape_detection_traits.
  • New algorithm: CGAL::Region_growing. This is a deterministic alternative to RANSAC for plane detection.
  • Breaking change: the API of CGAL::regularize_planes() is generalized to accept other types of input than the RANSAC output.
  • Add a callback mechanism for both CGAL::Efficient_RANSAC and CGAL::Region_growing.

Point Set Processing

  • Breaking change: the API of CGAL::structure_point_set() is generalized to accept other types of input than the RANSAC output.
  • Breaking change: the API of all functions of Point Set Processing is modified to use ranges (instead of iterators) and Named Parameters (similarly to the API of Polygon Mesh Processing). The old API is kept as deprecated.

CGAL and the Boost Graph Library (BGL)

  • Add helper function CGAL::expand_face_selection_for_removal that expands a face selection to avoid creating a non manifold mesh when removing the selected faces.

  • Added support for dynamic property maps.

  • Added an interface to the METIS library, which allows to partition any mesh that is a model of FaceListGraph. Wrappers to the METIS functions METIS_PartMeshNodal and METIS_PartMeshDual are offered.

Release 4.11

Release date: September 2017

3D Periodic Regular Triangulations (new feature)

  • Added the class Periodic_3_regular_triangulation_3, which provides functionality for 3D periodic weighted Delaunay triangulations. The construction is fully dynamic: it provides both point insertion and vertex removal.

dD Regular Triangulations (new feature)

  • Added the class Regular_triangulation, which provides functionality for dD weighted Delaunay triangulations. Note that the removal of points is not yet supported.

2D and 3D Linear Geometry Kernel (breaking change)

  • Breaking change: The dangerous implicit conversions between weighted points and points in the concept Kernel have been disabled. Constructors offering to build a weighted point from a point (and reversely) are still requested by the concept Kernel but must now be marked with the explicit specifier.
  • Breaking change: The removal of implicit conversions between points and weighted points in the concept Kernel has incidentally created various minor breaking changes in the following packages: 2D Alpha Shapes, 2D and 3D Triangulations, and 3D Mesh Generation. See the full changelog for details.

Surface Mesh

  • Breaking change: operator >>(std::istream&, Surface_mesh&) no longer clears the surface mesh.

Triangulated Surface Mesh Parameterization (breaking change)

  • Breaking change: The package has been rewritten and can operate on any model of the MutableFaceGraph concept. All previous parameterization methods are still offered, although with a different, simpler API. The documentation has been updated and offers a gentle introduction to the new API. Users who wish to use the former API must use a version prior to 4.11.
  • Breaking change: The adapter to add virtual seams is now the class CGAL::Seam_mesh in the package CGAL and the BGL.
  • Breaking change: The package has been restructured and most headers have been moved. In a general manner, users should replace <CGAL/XXX.h> with <CGAL/Surface_mesh_parameterization/XXX.h>
  • Add the As Rigid As Possible Parameterization method. This parameterization allows the user to prioritize angle preservation, shape preservation, or a balance of both.
  • Add the Orbifold Tutte Embedding method. This parameterization method allows to parameterize meshes that are topological spheres.

3D Surface Subdivision Methods (breaking changes)

  • The subdivision algorithms now work on any model of a MutableFaceGraph. A new API to the subdivision methods is offered, which uses optional named parameters to pass the number of iterations and a vertex property map.
  • Breaking change: Removed the headers <CGAL/Subdivision_method_3.h> and <CGAL/Subdivision_mask_3.h>. The headers <CGAL/Subdivision_method_3/subdivision_methods_3.h> and <CGAL/Subdivision_method_3/subdivision_masks_3.h> should respectively be used instead.
  • Sqrt3 subdivision can now handle input surfaces with a border.

Scale-Space Surface Reconstruction (breaking change)

  • Breaking change: the API was rewritten to separate the smoothing and meshing algorithm and making it possible for the user to use different ones. The default algorithms used are the same as before this API change, but methods are moved to the classes Weighted_PCA_smoother and Alpha_shape_mesher.
  • Alternative smoothing and meshing methods are provided: Jet_smoother and Advancing_front_mesher.

2D Alpha Shapes

  • Breaking change: Mirrored the concepts of the 2D alpha shape package with those of the 3D Alpha Shapes package. Consequently, a new concept, WeightedAlphaShapeTraits_2, is introduced to provide requirements on the traits class for 2D weighted alpha shapes. All models of the concept Kernel are models of this new concept.
  • The concept AlphaShapeTraits_2 now provides requirements on the traits class for 2D basic alpha shapes, and refines DelaunayTriangulationTraits_2.


  • Breaking change: The concept GradientFittingTraits now additionally requests a weighted point type Weighted_point_d and a functor Construct_point_d. The model CGAL::Interpolation_gradient_fitting_traits_2 has been appropriately modified to still be a model of the concept GradientFittingTraits.

2D and 3D Triangulations

  • Breaking change: Added a new functor requirement, Construct_point_2, to the concepts TriangulationTraits_2 and RegularTriangulationTraits_2 and a new functor requirement, Construct_point_3, to the concepts TriangulationTraits_3 and RegularTriangulationTraits_3. All models of the concept Kernel already provide these functors.
  • Breaking change: Introduced the concepts RegularTriangulationVertexBase_2 and RegularTriangulationVertexBase_3. These concepts describe the requirements on classes meant to represent a vertex of a regular triangulation. Concepts that previously refined TriangulationVertexBase_2 or TriangulationVertexBase_3 but described in fact a vertex class used in a regular triangulation, such as the concept MeshVertexBase_3 in the 3D mesh generation package, now refine the corresponding new regular vertex concept.
  • Breaking change: Uniformized the point type across all vertex and cell concepts. The triangulation point type name is now always Point. Note that this does not change the requirements but only the name: Point is still expected to be equal to Traits::Point_[23] for basic and Delaunay triangulations or to Traits::Weighted_point_[23] for regular triangulations. Consequently:
    • The concept RegularTriangulationVertexBase_2 now requests a Point type (equal to Traits::Weighted_point_2)
    • The concept RegularTriangulationCellBase_3 now requests a Point type instead of a Weighted_point type (but still equal to Traits::Weighted_point_3)
    • The concept DelaunayTriangulationCellBase_3 now requests a Point type instead of a Point_3 type (but still equal to Traits::Point_3).
  • Introduced a new concept, RegularTriangulationCellBaseWithWeightedCircumcenter_3, which describes the requirements on a cell of a regular triangulation that caches its circumcenter. The existing class Regular_triangulation_cell_base_with_weighted_circumcenter_3 is the default model of this concept.
  • Added a new 3D traits class, Robust_weighted_circumcenter_filtered_traits_3 which provides robust versions of the kernel functors Construct_weighted_circumcenter_3, Compute_squared_radius_3, and Compute_squared_radius_smallest_orthogonal_sphere_3. This class can be used as traits class in the Mesh_3 package to efficiently yet robustly generate 3D meshes.
  • Add a new type of polyhedral domain with features, Polyhedral_complex_mesh_domain_3. The domain is defined by a collection of triangulated surfaces, forming a complex.

3D Periodic Triangulations

  • Added new locate and geometric access functions for 3D periodic triangulations.
  • The class Periodic_3_Delaunay_triangulation_traits_3 now inherits Periodic_3_triangulation_traits_3.
  • Breaking change: Some geometric access functions in Periodic_3_triangulation_3 were renamed. The introduction of Periodic_3_regular_triangulation_3 required to distinguish between functions such as segment() returning a segment of weightless points, or a segment of weighted points. As a general rule, previous geometrical access functions will return objects with point type that of the triangulation (thus, weighted objects when using weighted triangulations) and functions containing construct in the name will always return weightless geometrical objects.
  • Breaking change: The concept Periodic_3TriangulationTraits_3 now requests a domain getter: get_domain().
  • Introduced a new concept, RegularTriangulationCellBaseWithWeightedCircumcenter_3, which describes the requirements on a cell of a regular triangulation that caches its circumcenter. The existing class Regular_triangulation_cell_base_with_weighted_circumcenter_3 is the default model of this concept.

3D Mesh Generation

  • Breaking change: The type of the surface center in the concept MeshCellBase_3 has been changed from Triangulation::Point to TriangulationTraits::Point_3 to reflect that it is a weightless point.
  • Breaking change: The function invalidate_circumcenter() of the concept MeshCellBase_3 is renamed to invalidate_weighted_circumcenter_cache() and moved to the new concept RegularTriangulationCellBaseWithWeightedCircumcenter_3, which the concept MeshCellBase_3 now refines.

Poisson Surface Reconstruction

  • A new global function CGAL::poisson_surface_reconstruction_delaunay() is provided in addition to the current class-based API in order to make it easier to use.

Point Set Processing

  • New functions to read from and write to LAS/LAZ files (LIDAR format), with or without taking additional properties into account.
  • Breaking change: The API of the PLY function to read points with properties is modified for unification with LAS (see CGAL::read_ply_points_with_properties()). A new function to write PLY with properties is provided (CGAL::write_ply_points_with_properties()).

Spatial Searching

  • Add function Kd_tree::remove(Point).

3D Fast Intersection and Distance Computation

  • Add a template parameter to AABB_traits for a property map that associates a bounding box to a primitive

CGAL and the Boost Graph Library

  • Add a partial specialization for the class CGAL::Linear_cell_complex_for_combinatorial_map so that it is a model of the graph concepts BidirectionalGraph and EdgeAndVertexListGraph and of the concept MutableFaceGraph. This class can thus now be used in all BGL functions and algorithms.
  • Helper functions to create an icosahedron, a regular prism and a pyramid have been added.
  • Add class CGAL::Face_filtered_graph that wraps an existing graph and hide all simplices that are not in the selected connected components.
  • Added the class CGAL::Seam_mesh. The Seam_mesh is a graph adaptor which allows to create virtual borders when marking edges as seam edges.
  • Add the functions read_off() and write_off().

Release 4.10

Release date: May 2017


  • The minimum required version of CMake is now 3.1. All CMake versions up to 3.7 are supported.
  • The compilation of some demo may require a C++11 compiler. The CGAL library itself still support C++03 compilers.
  • The shell script cgal_create_cmake_script now enables C++14 by default.
  • A new mechanism to check which packages of CGAL are used have been added. It is particularly interesting for commercial users to ensure they have a valid commercial license for the packages they used. This can also be used to make sure only LGPL header files are used.
  • Because of a bug in the g++ compiler about the C++11 keyword thread_local, the CGAL_Core library now always requires Boost.Thread if the g++ compiler is used.

Generalized Maps (new package)

  • This package implements Generalized Maps in d dimensions. A generalized map is a data structure enabling to represent an orientable or non orientable subdivided object by describing all the cells of the subdivision (for example in 3D vertices, edges, faces, volumes) and all the incidence and adjacency relationships between these cells. This data structure is the generalization of the combinatorial maps in order to be able to represent non orientable objects.

3D Point Set (new package)

  • This package provides a flexible data structure CGAL::Point_set_3 that allows the user to easily handle point sets with an arbitrary number of attributes (such as normal vectors, colors, labeling, etc.).

Combinatorial Maps and Linear cell complex

  • Breaking change: the requirements of the item class used to customize a combinatorial map and a linear cell complex changed. Instead of defining the type of darts used, you have to define the information you want to add in each dart. You can define the CGAL_CMAP_DART_DEPRECATED macro to keep the old behavior.

Triangulated Surface Mesh Shortest Paths

  • Breaking change: Rename all functions, types, and enums using barycentric coordinate to barycentric coordinates.

CGAL and the Boost Graph Library (BGL)

  • Breaking change: Addition of a free function reserve() in the concept MutableFaceGraph. Models provided by CGAL have been updated.

2D and 3D Linear Geometry Kernel

  • Breaking change: The function compare_slopes() was renamed compare_slope.
  • Added a 2D and 3D weighted point class and predicates and constructions.
  • Add functions l_infinity_distance() for 2D and 3D.
  • Add a new functor in CGAL Kernel concept to compare the slope of two 3D segments. All models of the Kernel concept now provide the functor Compare_slope_3, and the free function compare_slope() is available.
  • Add an operator in CGAL Kernel concept Angle_3 to qualify the angle between the normal of the triangle given by three points, and a vector.

3D Convex Hull

  • The convex hull function can also produce a Surface_mesh, and generally speaking any model of the concept MutableFaceGraph
  • The function convex_hull_3_to_polyhedron_3() is deprecated and convex_hull_3_to_face_graph.h should be used instead.
  • The class Convex_hull_traits_3 now documents a nested type Polygon_mesh instead of Polyhedron_3. The other nested type is kept for backward compatibility.
  • Remove the function CGAL::convex_hull_incremental_3() deprecated since CGAL 4.6.

3D Boolean Operations on Nef Polyhedra

  • Add a new constructor from a face graph model

Linear cell complex

  • Deprecate class Linear_cell_complex which is now renamed Linear_cell_complex_for_combinatorial_map_dart.

2D Triangulation data structure

  • Add function insert_in_hole.

2D Triangulations

  • Breaking change: Removed the arbitrary dimensional weighted point class. Users must use a version prior to 4.9 if they need this class.
  • Breaking change:The number type of weighted points in regular triangulations is no longer a template parameter but the field type of the geometric traits class. Users who need this feature must use a version prior to 4.9
  • The class Regular_triangulation_filtered_traits_2 deprecated since CGAL 3.6 has been removed.
  • Deprecate the class Regular_triangulation_euclidean_traits_2, as the weighted point and the function objects for weighted points are part of the concept Kernel/
  • The class Regular_triangulation_2 can take a kernel as template argument, that is one no longer has to use Regular_triangulation_euclidea_traits_2, although this still works.

3D Triangulations

  • Breaking change: The number type of weighted points in regular triangulations is no longer a template parameter but the field type of the geometric traits class. Users who need this feature must use a version prior to 4.9.
  • The class Regular_triangulation_filtered_traits_3 deprecated since CGAL 3.6 has been removed.
  • Deprecate the class Regular_triangulation_euclidean_traits_3, as the weighted point and the function objects for weighted points are part of the concept Kernel/
  • The class Regular_triangulation_3 can take a kernel as template argument, that is one no longer has to use Regular_triangulation_euclidean_traits_3, although this still works.
  • Add function link_to_face_graph() to copy the set of faces incident to a vertex into a model of FaceGraph.

3D Mesh Generation

  • The constructor CGAL::Polyhedral_mesh_domain_with_features_3(std::string) is deprecated.

Polygon Mesh Processing

  • Add fast and robust corefinement and Boolean operation functions for triangulated surface meshes:
    • CGAL::Polygon_mesh_processing::corefine_and_compute_union()
    • CGAL::Polygon_mesh_processing::corefine_and_compute_difference()
    • CGAL::Polygon_mesh_processing::corefine_and_compute_intersection()
    • CGAL::Polygon_mesh_processing::corefine()
    • CGAL::Polygon_mesh_processing::does_bound_a_volume()
    • CGAL::Polygon_mesh_processing::surface_intersection()
  • Add functions to compute approximated Hausdorff distances between two meshes, a mesh and a point set, or a point set and a mesh: sample_triangle_mesh(), approximated_Hausdorff_distance(), approximated_symmetric_Hausdorff_distance(), max_distance_to_triangle_mesh(), max_distance_to_point_set().
  • The function CGAL::Polygon_mesh_processing::bbox_3() has been renamed CGAL::Polygon_mesh_processing::bbox().

Point Set Processing

  • Function CGAL::remove_outliers() has an additional parameter based on a distance threshold to make it easier and more intuitive to use.
  • New functions for automatic scale estimations: either a global scale or multiple local scales can be estimated for both 2D and 3D point sets based on the assumption that they sample a curve in 2D or a surface in 3D.

CGAL and the Boost Graph Library (BGL)

  • Add function CGAL::convert_nef_polyhedron_to_polygon_mesh() to convert a Nef_polyhedron_3 to any model of the MutableFaceGraph concept.
  • Add class CGAL::Graph_with_descriptor_with_graph that wraps an existing graph and provides a reference to the said graph to all of its descriptors.

Cone Based Spanners

  • Add a parameter to compute half Tao graph and half Theta graph.
  • Add an ipelet for this package.

Geometric Object Generators

  • Add point random generators
    • in a 3D triangle mesh model of the concept FaceListGraph (CGAL::Random_points_in_triangle_mesh_3),
    • on the boundary of a tetrahedral mesh (CGAL::Random_points_in_tetrahedral_mesh_boundary_3),
    • in a tetrahedral mesh (CGAL::Random_points_in_tetrahedral_mesh_3),
    • in a 2D triangle mesh (CGAL::Random_points_in_triangle_mesh_2),
    • in a range of 2D or 3D triangles (CGAL::Random_points_in_triangles_3 and CGAL::Random_points_in_triangles_2).
    • on a 3D segment (CGAL::Random_points_on_segment_3).

Release 4.9

Release date: Sept 2016

Header-only mode

  • CGAL can now be used in headers only mode, i.e. without compiling the CGAL libraries and linking with these libraries when compiling examples, tests and demos. Note that running CMake on CGAL is still required in order to generate some configuration files.

Cone Based Spanners (new package)

  • This package provides algorithms for constructing two kinds of cone-based spanners: Yao graph and Theta graph, given a set of vertices on the plane and the directions of cone boundaries.

2D Minkowski Sums

  • Introduce a convex decomposition strategy, namely Polygon_nop_decomposition_2, that merely passed the input polygon to the list of output polygons.
  • Introduce overloads of the function minkowski_sum_2(), which accepts 2 decomposition strategies.
  • Introduce an overloaded function called minkowski_sum_by_decomposition_2(P, Q, decom_no_holes, decomp_with_holes), which computes the 2D Minkowski sum using optimal choices of decomposition strategies.

Combinatorial Maps

  • Deprecate global functions (make_combinatorial_hexahedron(), make_combinatorial_polygon(), make_combinatorial_tetrahedron(), make_edge(), insert_cell_0_in_cell_1(), insert_cell_0_in_cell_2(), insert_cell_1_in_cell_2(), insert_cell_2_in_cell_3(), insert_dangling_cell_1_in_cell_2(), is_insertable_cell_1_in_cell_2(), is_insertable_cell_2_in_cell_3(), is_removable(), remove_cell()) which are now member functions in the CombinatorialMap concept.
  • It is not longer possible to use the old API switched on by defining the macro CGAL_CMAP_DEPRECATED. This API was deprecated since CGAL 4.4.

Point Set Processing

  • New function CGAL::read_ply_custom_points() that allows the user to read any additional point attribute from a PLY input point set.
  • CGAL::structure_point_set(): new algorithm that takes advantage of detected planes to produce a structured point set (with flat regions, sharp edges and vertices).

Point Set Shape Detection

  • New post-processing algorithm: CGAL::regularize_planes(). This allows the user to favor parallelism, orthogonality, coplanarity and/or axial symmetry between detected planes.

Polygon Mesh Processing

  • Add the function CGAL::Polygon_mesh_processing::is_polygon_soup_a_polygon_mesh() to check whether a polygon soup is a polygon mesh.
  • Add some new features to CGAL::isotropic_remeshing():
    • It is now possible to select fixed vertices that survive the remeshing process, and to keep face attributes such as colors valid after remeshing.
    • The user can choose the number of relaxation steps happening at each loop, and to run 1-dimensional relaxation along constrained polylines.
  • The functions CGAL::Polygon_mesh_processing::triangulate_face() and CGAL::Polygon_mesh_processing::triangulate_faces() now indicate whether some faces have not been triangulated.

Surface Mesh Deformation

  • Add a new tag SRE_ARAP to use the Smoothed Rotation Enhanced As-Rigid-As-Possible deformation algorithm.

3D Fast Intersection and Distance Computation

  • Add the functions AABB_tree::first_intersection() and AABB_tree::first_intersected_primitive() that compute the intersection which is closest to the source of a ray

CGAL and the Boost Graph Library (BGL)

  • Add a helper function CGAL::copy_face_graph() to copy a source FaceListGraph into another FaceListGraph of different type.
  • Add a class CGAL::Dual that creates the dual view of a FaceGraph and a creation function CGAL::dual(primal).

CGAL and Boost Property Maps

  • It is not longer possible to use the old API of the property maps provided by CGAL, switched on by defining the macro CGAL_USE_PROPERTY_MAPS_API_V1. This API was deprecated since CGAL 4.3.

Release 4.8

Release date: April 2016


  • The support for Qt3 is dropped and all demos using it got removed.


  • Starting with Visual C++ 2015 we no longer require Boost.Thread as we use the C++11 keyword thread_local and the C+11 class std::mutex .
  • The same holds for g++ 4.8 or later when the C++11 standard is used.

Optimal Transportation Curve Reconstruction (new package)

  • This package implements a method to reconstruct and simplify 2D point sets. The input is a set of 2D points with mass attributes, possibly hampered by noise and outliers. The output is a set of line segments and isolated points which approximate the input points.

2D Regularized Boolean Set-Operations

  • Improve the performance of operations in some settings. Breaking change: This improvement requires changes of the face and halfedge type of the underlying arrangement Dcel. See the concepts GeneralPolygonSetDcelHalfedge and GeneralPolygonSetDcelFace for more details. If you use a different simplex types, inheriting your simplices from CGAL::Gps_face_base and CGAL::Gps_halfedge_base is sufficient to accommodate for the update.

3D Boolean Operations on Nef Polyhedra

  • Add 3 new constructors: from a point range, from a point, and from a segment.

Combinatorial Maps

  • Breaking change: Change the type of Boolean marks, old type is int, new type is size_type. If no more mark is available, get_new_mark throws an exception, instead of returning -1.

2D Arrangements

  • Speed up the edge removal in case the incident faces contains many holes.
  • Set the format of polylines and polycurves. The format of a general polyline or polycurve consists of the sequence of subcurves that comprise the original curve. The format of a polyline of linear segments consists of the sequence of points that define the original curve. (The latter restores the format used before polycurves were introduced in 4.7.) Fix the extraction from istream and insertion into ostream operators of polylines and polycurves accordingly.
  • Fix the traits class that handles Bezier curves. In particular, fix the case where the curve is closed (i.e, the first and last control points coincide).

3D Mesh Generation

  • Add support of 3D gray level images as input for the tetrahedral mesh generation.
  • Breaking change: All models of the concept MeshDomain_3 must now provide a member function bbox().

Advancing Front Surface Reconstruction

  • Optional template functor Filter is replaced by another optional template functor Priority. This allows to change the way facets are prioritized by the algorithm instead of having a simple option to reject some facets. Breaking change: Programs using the old Filter API will not compile anymore as it must be replaced with the Priority API as described in the manual. Codes using the default behavior are not impacted.

Polygon Mesh Processing

  • Add a new triangle-based isotropic remeshing algorithm for triangulated surface meshes, CGAL::Polygon_mesh_processing::isotropic_remeshing() and a helper function for isotropic remeshing : CGAL::Polygon_mesh_processing::split_long_edges()
  • Add the function CGAL::Polygon_mesh_processing::border_halfedges() to collect the border of a given face range
  • Add the function CGAL::Polygon_mesh_processing::remove_isolated_vertices() to be used on any polygon mesh
  • Add the function CGAL::Polygon_mesh_processing::triangulate_face() to triangulate a single face of a polygon mesh
  • Add an overload for CGAL::Polygon_mesh_processing::triangulate_faces() to triangulate a range of faces of a polygon mesh
  • Add function keep_large_connected_components()
  • Add measuring functions for polygon meshes, to compute length, area, and volume of simplices or group of simplices of a polygon mesh.
  • Add function bbox_3() to compute the bounding box of a polygon mesh.

Point Set Processing

  • Breaking change: new template parameter Concurrency_tag for the functions compute_average_spacing(), edge_aware_upsample_point_set(), jet_estimate_normals(), jet_smooth_point_set(), and pca_estimate_normals(). To update your code simply add as first template parameter CGAL::Sequential_tag or CGAL::Parallel_tag when calling one of these functions.
  • CGAL::Parallel_tag can no longer be used in Point Set Processing algorithms if TBB is not available.
  • Add a new simplification algorithm based on hierarchical clustering: CGAL::hierarchy_simplify_point_set(). It allows either to uniformly simplify the point set or to automatically adapt the local density of points to the local variation of the input computed by principal component analysis.
  • New IO functions for PLY format (Polygon File Format): CGAL::read_ply_points(), CGAL::read_ply_points_and_normals(), CGAL::write_ply_points() and CGAL::write_ply_points_and_normals().

Surface Mesh Parameterization

  • LSCM_parameterizer_3 now uses by default Eigen instead of OpenNL as a model of SparseLinearAlgebraTraits_d.

Spatial Searching

  • Add function to find any point in a range query, that is neither all points, nor the closest one.

Principal Component Analysis

  • Add a template parameter DiagonalizeTraits for functions CGAL::linear_least_squares_fitting_2() and CGAL::linear_least_squares_fitting_3(). This allows to either choose the legacy internal diagonalization code from CGAL or the Eigen implementation (or any class that is a model of DiagonalizeTraits). Variants of the function that automatically deduce the kernel also automatically select the diagonalizer, so the API is mostly preserved.

CGAL and Solvers

  • This package now includes all CGAL concepts for solvers with models using the third party Eigen library.

CGAL and the Boost Graph Library (BGL)

  • Add function CGAL::split_graph_into_polylines() that allows to extract from a soup of segments given as a graph, polylines with nodes of degree at most 2. In addition a functor can be passed to the function to specify additional polyline endpoints.
  • New functions to manipulate selection of faces, edges and vertices in a halfedge graph are added: CGAL::expand_face_selection(), CGAL::reduce_face_selection(), CGAL::expand_edge_selection(), CGAL::reduce_edge_selection() CGAL::expand_vertex_selection(), CGAL::reduce_vertex_selection() and CGAL::select_incident_faces().
  • Add a helper function CGAL::clear which clears a MutableFaceGraph efficiently and generically.

Release 4.7

Release date: October 2015


  • The minimum required version of CMake is now 2.8.11. CMake versions 3.1, 3.2, and 3.3 are supported.
  • All Qt4 demos have been updated and now require Qt5 to be compiled. Qt5 version 5.3 or higher is required. The support for Qt4 is dropped. To compile libCGAL_Qt5 and demos, you must set the cmake or environment variable Qt5_DIR to point to the path to the directory containing the file Qt5Config.cmake created by your Qt5 installation. If you are using the open source edition it should be /path-to/qt-everywhere-opensource-src-<version>/qtbase/lib/cmake/Qt5.
  • The code of the 3D demos now uses modern OpenGL, with shaders, instead of the fixed pipeline API of OpenGL-1.
  • The Microsoft Windows Visual C++ compiler 2015 (VC14) is now supported. However, since this compiler is not officially supported by Intel TBB 4.4 and Qt 5.5 (the latest versions available at the time of this release), the parallelism features of CGAL and Qt5 demos will not work.

L Infinity Segment Delaunay Graphs (new package)

  • The package provides the geometric traits for constructing the segment Delaunay graph in the max-norm (L Infinity). The traits also contain methods to draw the edges of the dual of the segment Delaunay graph in the max-norm i.e., the segment Voronoi diagram in the max-norm. The algorithm and traits rely on the segment Delaunay graph algorithm and traits under the Euclidean distance. The segment Voronoi diagram in the max-norm has applications in VLSI CAD.

Advancing Front Surface Reconstruction (new package)

  • This package provides a greedy algorithm for surface reconstruction from an unorganized point set. Starting from a seed facet, a piecewise linear surface is grown by adding Delaunay triangles one by one. The most plausible triangles are added first, in a way that avoids the appearance of topological singularities.

Triangulated Surface Mesh Shortest Paths (new package)

  • The package provides methods for computing shortest path on triangulated surface meshes. Given a set of source points on the surface, this package provides a data structure that can efficiently provides the shortest path from any point on the surface to the sources points. There is no restriction on the genus or the number of connected components of the mesh.

Triangulated Surface Mesh Skeletonization (new package)

  • This package provides a (1D) curve skeleton extraction algorithm for a triangulated polygonal mesh without borders based on the mean curvature flow. The particularity of this skeleton is that it captures the topology of the input. For each skeleton vertex one can obtain its location and its corresponding vertices from the input mesh. The code is generic and works with any model of the `FaceListGraph` concept.

3D Point-Set Shape Detection (new package)

  • This package implements the efficient RANSAC method for shape detection, contributed by Schnabel et al. From an unstructured point set with unoriented normals, the algorithm detects a set of shapes. Five types of primitive shapes are provided by this package: plane, sphere, cylinder, cone and torus. Detecting other types of shapes is possible by implementing a class derived from a base shape.

2D Visibility (new package)

  • This package provides several variants to compute the visibility area of a point within polygonal regions in two dimensions.

Polygon Mesh Processing (new package)

  • This package implements a collection of methods and classes for polygon mesh processing, ranging from basic operations on simplices, to complex geometry processing algorithms. The implementation of this package mainly follows algorithms and references given in Botsch et al.'s book on polygon mesh processing.


  • Support for unordered sets and maps of the stdlib and of boost for handle and index classes.

Approximation of Ridges and Umbilics on Triangulated Surface Meshes

  • This package now supports any model of the concept FaceGraph.
  • Breaking change: The package no longer supports models of TriangulatedSurfaceMesh which are not at the same time models of the concept FaceGraph.

dD Geometry Kernel

  • Epick_d gains 3 new functors: Construct_circumcenter_d, Compute_squared_radius_d, Side_of_bounded_sphere_d. Those are essential for the computation of alpha-shapes.

2D Arrangements

  • Introduced a new traits class, called Arr_polycurve_traits_2<SubcurveTraits>, which handles general piece-wise (polycurve) curves. The pieces do not necessarily have to be linear.
  • Introduced two new concepts called ArrangementApproximateTraits_2 and ArrangementConstructXMonotoneCurveTraits_2.
    • The existing ArrangementLandmarkTraits_2 concept, which has two requirements, now refines the two respective concepts above.
    • The template parameter of the existing Arr_polyline_traits_2<SegmentTraits> template must be substituted with a traits class that is a model of the ArrangementConstructXMonotoneTraits_2 concept among the other when Arr_polyline_traits_2 is instantiated.

2D Minkowski Sums

  • Added support for polygons with holes and optimized the construction of Minkowski sums.
    • Introduced an implementation of the "reduced convolution" method, a variant of the method described in "2D Minkowski Sum of Polygons Using Reduced Convolution" by Behar and Lien. The new method supports polygons with holes and in many cases out pergorms the implementation of the exsisting (full) convolution method.
    • Introduced two new classes that decompose polygons into convex pieces (models of the PolygonConvexDecomposition_2 concept) based on vertical decomposition and constrained Delaunay triangulation, respectively. These new models also support the convex decomposition of polygons with holes.

3D Periodic Triangulations

  • Rename Periodic_3_triangulation_traits_3 to Periodic_3_Delaunay_triangulation_traits_3.
  • Rename the concept Periodic_3TriangulationTraits_3 to Periodic_3DelaunayTriangulationTraits_3.
  • Create Periodic_3_triangulation_traits_3 and the concept Periodic_3TriangulationTraits_3.

2D Conforming Triangulations and Meshes

  • Add an optimization method CGAL::lloyd_optimize_mesh_2() that implements the Lloyd (or Centroidal Voronoi Tesselation) optimization algorithm in a Constrained Delaunay Triangulation. For optimization, the triangulation data structure on which the mesher relies needs its VertexBase template parameter to be a model of the new concept DelaunayMeshVertexBase_2.

Point Set Processing and Surface Reconstruction from Point Sets

  • Add the function CGAL::compute_vcm() for computing the Voronoi Covariance Measure (VCM) of a point set. The output of this function can be used with the function CGAL::vcm_is_on_feature_edge() to determine whether a point is on or close to a feature edge. The former function is also internally used by CGAL::vcm_estimate_normals() to estimate the normals of a point set and it is particularly suited to point sets with noise.

Spatial Sorting

  • Add the possibility to sort points on a sphere along a space-filling curve using the functions CGAL::hilbert_sort_on_sphere and CGAL::spatial_sort_on_sphere.

Geometric Object Generators

  • Add new random generator of points in a 2D and 3D triangle and in a tetrahedron (CGAL::Random_points_in_triangle_2, CGAL::Random_points_in_triangle_3, CGAL::Random_points_in_tetrahedron_3).

Release 4.6.2

Release date: August 2015

This release only fixes bugs. See the list of fixed bugs on Github:

Release 4.6.1

Release date: June 2015

This release only fixes bugs. See the list of fixed bugs on Github:

Release 4.6

Release date: April 2015


  • The required version of Boost is now 1.48 or higher.

2D Polyline Simplification (new package)

  • This package enables to simplify polylines with the guarantee that the topology of the polylines does not change. This can be done for a single polyline as well as for a set of polyline constraints in a constrained triangulation. The simplification can be controlled with cost and stop functions.

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 an implementation of the halfedge data structure allowing to represent polyhedral surfaces. It is an alternative to the packages CGAL::Polyhedron_3 and CGAL::HalfedgeDS.

dD 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. It also provides a class that represents Delaunay triangulations.

dD Convex Hulls and Delaunay Triangulations

  • This package is deprecated and the new package Triangulation should be used instead.

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.
  • The function CGAL::convex_hull_incremental_3 is deprecated and the function convex_hull_3 should be used instead.

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 midpoint 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 been 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.
  • 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.

3D Periodic Triangulations

  • Add a method to locate point with inexact predicates.

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.

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 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 address 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.