Subject: CGAL 3.2 Released, Computational Geometry Algorithms Library
The CGAL Open Source Project is pleased to announce the release 3.2 of
CGAL, the Computational Geometry Algorithms Library.
Besides improvements of existing packages this release offers
the following new algorithms and data structures.
o 2D Regularized Boolean Set-Operations
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.
o 2D Straight Skeleton and Polygon Offsetting
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.
o 2D Voronoi Diagram
The 2D Voronoi diagram 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.
o 3D Surface Mesher
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.
o 3D Surface Subdivision Methods
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.
o Planar Parameterization of Triangulated Surface Meshes
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.
o Principal Component Analysis
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.
o 2D Placement of Streamlines
Visualizing vector fields is important for many application domains.
A good way to do it is to generate streamlines that describe the
flow behavior. This package implements the "Farthest Point Seeding"
algorithm for placing streamlines in 2D vector fields. It generates
a list of streamlines corresponding to an input flow using a
specified separating distance. The algorithm uses a Delaunay
triangulation to model objects and adress different queries, and
relies on choosing the centers of the biggest empty circles to start
the integration of the streamlines.
o Kinetic Data Structures
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.
o Kinetic Framework
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.
o Smallest Enclosing Ellipsoid
An approximative algorithm for constructing the smallest enclosing
ellipsoid in d-dimensional Euclidean space.
See http://www.cgal.org/releases_frame.html for a complete list of
The CGAL project is a collaborative effort to develop a robust,
easy-to-use, and efficient C++ software library of geometric data
structures and algorithms, like
- triangulations (2D constrained triangulations and Delaunay
triangulations in 2D and 3D),
- Voronoi diagrams (for 2D and 3D points, 2D additively weighted
Voronoi diagrams, and segment Voronoi diagrams),
- Boolean operations on polygons and polyhedra,
- arrangements of curves,
- mesh algorithms (2D Delaunay mesh generation and 3D surface mesh
generation, surface mesh subdivision and parameterization),
- alpha shapes,
- convex hull algorithms (in 2D, 3D and dD),
- operations on polygons (straight skeleton and offset polygon),
- search structures (kd trees for nearest neighbor search, and
range and segment trees),
- interpolation (natural neighbor interpolation and placement of
- optimisation algorithms (smallest enclosing sphere of points or
spheres, smallest enclosing ellipsoid of points, principal
- kinetic data structures.
Some modules are distributed under the terms of the LGPL Open Source
license(GNU Lesser General Public License v2.1).
Most modules are distributed under the terms of the QPL Open Source
license (Q Public License v1.0).
If your intended usage does not meet the criteria of the
aforementioned licenses, a commercial license must be purchased from
For further information and for downloading the library and its
documentation, please visit the CGAL web site: http://www.cgal.org/
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