CGAL 3.1

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CGAL 3.1

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 traits 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.