Package Overview

If you want to download and run any of the precompiled demos, here you can find the dlls that are shared by all of them.

The resulting solution is certified: along with the claims that the problem under consideration has an optimal solution, is infeasible, or is unbounded, the algorithms also deliver proofs for these facts. These proofs can easily (and independently from the algorithms) be checked for correctness.

The solution algorithms are based on a generalization of the simplex method to quadratic objective functions.

This package provides a 2D polygon class and operations on sequences of points, like bounding box, extremal points, signed area, simplicity and convexity test, orientation, and point location.

The demo includes operations on polygons, such as computing a convex partition, and the straight skeleton.

In 2D, a combinatorial map is equivalent to an halfedge data structure.

The package provides basic creations, modification operations, and several iterators allowing to run through some specific part of the object.

Taking a 2D combinatorial map, and using 3D points, gives a linear cell complex equivalent to a Polyhedron_3.

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.

The package provides plain triangulation (whose faces depend on the insertion order of the vertices) and Delaunay triangulations. Regular triangulations are also provided for sets of weighted points. Delaunay and regular triangulations offer nearest neighbor queries and primitives to build the dual Voronoi and power diagrams.

Finally, constrained and Delaunay constrained triangulations allows to force some constrained segments to appear as edges of the triangulation. Several versions of constrained and Delaunay constrained triangulations are provided: some of them handle intersections between input constraints segment while others do not.

The package provides plain triangulation (whose faces depends on the insertion order of the vertices) and Delaunay triangulations. Regular triangulations are also provided for sets of weighted points. Delaunay and regular triangulations offer nearest neighbor queries and primitives to build the dual Voronoi and power diagrams.

The package provides Delaunay triangulations and offers nearest neighbor queries and primitives to build the dual Voronoi diagrams.

Conforming Delaunay triangulations are obtained from constrained Delaunay triangulations by refining constrained edges until they are Delaunay edges. Conforming Gabriel triangulations are obtained by further refining constrained edges until they become Gabriel edges.

The package provides also a 2D mesh generator that refines triangles and constrained edges until user defined size and shape criteria on triangles are satisfied. The package can handle intersecting input constraints and set no restriction on the angle formed by two constraints sharing an endpoint.

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.

The construction of a triangular mesh of a smooth skin surface is often necessary for further analysis and for fast visualization. This package provides functions to construct a triangular mesh approximating the skin surface from a set of balls and a shrink factor. It also contains code to subdivide the mesh efficiently.

This package implements an interface to Geomview, an interactive 3D viewing program, originally developed at the Geometry Center in Minneapolis.