Commit eb05f511 authored by Mike Kremer's avatar Mike Kremer

Updated the concepts section of the documentation

git-svn-id: http://www.openvolumemesh.org/svnrepo/OpenVolumeMesh/trunk@138 66977474-1d4b-4f09-8fe9-267525286df2
parent bfc6fb86
......@@ -14,17 +14,20 @@ accomplished by using only these local links to adjacent structures (similar to
This, of course, assumes the surface mesh to be two-manifold.
The main concept of %OpenVolumeMesh is slightly different but shares some of its ideas with
%OpenMesh. In order to represent volumetric meshes (three-manifolds),
%OpenVolumeMesh extends the set of entities by \e cells.
In %OpenVolumeMesh, all entities are stored in arrays (STL vectors) rather than
in adjacency linked lists. This has the major advantage that the data structure allows
for configurations that are not three-manifold (since this is desired in some applications).
%OpenMesh. In order to represent volumetric meshes (three-manifolds) that consist of a
set of polyhedra, %OpenVolumeMesh extends the set of entities by \e cells.
But unlike in the original idea of half-edge data structure,
in %OpenVolumeMesh all entities are stored in arrays (STL vectors) rather than
in adjacency linked lists. This is why %OpenVolumeMesh is index-based which
has the major advantage that the data structure can handle configurations that are
not three-manifold (since this is desired in some applications).
For example, a set of vertices or just a two-manifold surface can be respresented by
%OpenVolumeMesh as well as an entirely three-manifold polyhedral mesh.
In order to offer the possibility to locally navigate on the meshes, we carry over
the idea of splitting edges into half-edges to the faces. This leads to the separation
of the faces into pairs of so-called half-faces. Each of the half-faces has opposite
orientation to its counter-part. The orientation of a half-face is uniquely determined
orientation to its counter-part and can be either incident to a cell or not which
makes the half-face a boundary half-face. The orientation of a half-face is uniquely determined
by its incident half-edges. See Figure 1 for an illustration of this concept.
\image html halfedge_halfface.png "Figure 1. Left: Two half-edges as in OpenMesh. Right: A face split into two half-faces."
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