songsenand
/
cgal
mirror of https://github.com/CGAL/cgal
1
0
Fork 0
Code Issues Packages Projects Releases Wiki Activity

Doc: some fixes according to Mariette's review

This commit is contained in:
Clement Jamin 2014-03-19 18:00:48 +01:00
parent 35fdca409a
commit 5e351fe56e
2 changed files with 19 additions and 25 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

40
Triangulation/doc/Triangulation/Concepts/TriangulationDataStructure.h
View File

@ -3,19 +3,16 @@
\ingroup PkgTriangulationsConcepts
\cgalConcept
The `TriangulationDataStructure` concept describes objects responsible for storing and
maintaining the combinatorial part of a
\f$ d\f$-dimensional pure simplicial complex (all simplices that are not
sub-faces of another have the same dimension \f$ d\f$).
Its topology is the topology
of the sphere \f$ \mathcal S^d\f$ with \f$ d\in[-2,D]\f$.
In a pure (or homogeneous) simplicial \f$ d\f$-complex, all
faces are sub-faces of some \f$ d\f$-simplex. (A
simplex is also a face of itself.) In particular, it does not
contain any \f$ d+1\f$-face, and any \f$ d-1\f$-face belongs to exactly
two \f$ d\f$-dimensional full cells.
The `TriangulationDataStructure` concept describes objects responsible for
storing and maintaining the combinatorial part of a
\f$ d\f$-dimensional pure simplicial complex that has the topology
of the \f$ d\f$-dimensional sphere \f$ \mathcal S^d\f$ with \f$ d\in[-2,D]\f$.
Since the simplicial \f$ d\f$-complex is pure, all
faces are sub-faces of some \f$ d\f$-simplex. And since it has the
topology of the sphere \f$ \mathcal S^d\f$, it is manifold, thus
any \f$ d-1\f$-face belongs to exactly two \f$ d\f$-dimensional full cells.
Values of \f$ d\f$ (the <I>current dimension</I> of the complex) include
Possible values for the current dimension \f$ d\f$ include
<DL>
<DT><B>-2</B><DD> This corresponds to the non-existence of any object in
@ -43,7 +40,7 @@ is a proper face of \f$ \sigma\f$.
We call a \f$ 0\f$-simplex a <I>vertex</I>, a \f$ (d-1)\f$-simplex a <I>facet</I> and a
\f$ d\f$-simplex a <I>full cell</I>. A <I>face</I> can have any dimension.
Two full cells are <I>adjacent</I> if they share a facet. Two faces are
Two full cells are <I>neighbors</I> if they share a facet. Two faces are
<I>incident</I> if one is included in the other.
Input/Output
@ -86,14 +83,14 @@ public:
/*!
Vertex type.
The vertex type. A model of the concept `TriangulationDSVertex`.
*/
typedef Hidden_type Vertex;
/*!
Full cell type.
The full cell type. A model of the concept `TriangulationDSFullCell`.
*/
typedef Hidden_type Full_cell;
@ -101,7 +98,7 @@ typedef Hidden_type Full_cell;
/*!
The concept `TriangulationDataStructure` also defines a type for
describing facets of the triangulation with codimension 1.
describing faces of the triangulation with codimension 1.
The constructor `Facet(c,i)` constructs a `Facet` representing the facet of
full cell `c` opposite to its `i`-th vertex. Its dimension is
@ -140,24 +137,21 @@ typedef Hidden_type Full_cell_handle;
/// @}
/// \name Rebind
/// Requirements for `Vertex` and `Full_cell` are described in
/// concepts `TriangulationDataStructure::Vertex` and
/// `TriangulationDataStructure::FullCell` .
/// @{
/*!
This nested template class allows to get the type of a triangulation
data structure that only changes the vertex type. It has to define a type
`Other` which is a <I>rebound</I> triangulation data structure, that is, the
one whose `TriangulationDSVertexBase` will be `Vb2`.
`Other` which is a <I>rebound</I> triangulation data structure with `Vb2`
as vertex type.
*/
typedef Hidden_type template <typename Vb2> struct Rebind_vertex;
/*!
This nested template class allows to get the type of a triangulation
data structure that only changes the full cell type. It has to define a type
`Other` which is a <I>rebound</I> triangulation data structure, that is, the
one whose `TriangulationDSFullCellBase` will be `Fcb2`.
`Other` which is a <I>rebound</I> triangulation data structure with `Fcb2`
as full cell type.
*/
typedef Hidden_type template <typename Fcb2> struct Rebind_full_cell;

4
Triangulation/doc/Triangulation/Triangulation.txt
View File

@ -56,8 +56,8 @@ entry</A> for more about simplicial complexes.
## What's in this package? ##
This \cgal package deals with pure finite simplicial complexes
without boundary, which
This \cgal package deals with pure simplicial complexes which are connected
and have no singularities, which
we will simply call in the sequel <I>triangulations</I>. It provides three main classes
for creating and manipulating triangulations.