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

Use the macro tred

This commit is contained in:
Guillaume Damiand 2016-08-08 15:25:54 -04:00
parent 5c417c2cf2
commit a7cef53494
1 changed files with 1 additions and 1 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

2
Combinatorial_map/doc/Combinatorial_map/Combinatorial_map.txt
View File

@ -12,7 +12,7 @@ namespace CGAL {
A <I>d</I>-dimensional combinatorial map is a data structure representing an orientable subdivided <I>d</I>-dimensional object obtained by taking <I>d</I>D cells, and allowing to glue <I>d</I>D cells along <I>(d-1)</I>D cells. It provides a description of all the cells of the subdivision (for example vertices and edges), together with incidence and adjacency relationships. This package is a generalization of the \ref chapterHalfedgeDS "halfedge data structure" to higher dimension. Indeed, a 2D combinatorial map is equivalent to a halfedge data structure: there is a one-to-one mapping between elements of both data structures, halfedges corresponding to darts.
\tred{Note that you can use the} \ref ChapterGeneralizedMap "Generalized Map package" \tred{if you need to represent non-orientable objects.}
\tred{Note that you can use the \ref ChapterGeneralizedMap "Generalized Map package" if you need to represent non-orientable objects.}
We denote <I>i</I>-cell for an <I>i</I>-dimensional cell (for example in 3D, 0-cells are <I>vertices</I>, 1-cells are <I>edges</I>, 2-cells are <I>facets</I>, and 3-cells are <I>volumes</I>). A <I>boundary relation</I> is defined on these cells, giving for each <I>i</I>-cell <I>c</I> the set of <I>(i-1)</I>-cells contained in the boundary of <I>c</I>. Two cells <I>c1</I> and <I>c2</I> are <I>incident</I> if there is a path of cells, starting from the cell of biggest dimension to the other cell, such that each cell of the path (except the first one) belongs to the boundary of the previous cell in the path. Two <I>i</I>-cells <I>c3</I> and <I>c4</I> are <I>adjacent</I> if there is an <I>(i-1)</I>-cell incident to both <I>c3</I> and <I>c4</I>. You can see an example of a 2D object and a 3D object in \cgalFigureRef{fig_cmap_example_subdivisions} showing some cells of the subdivision and some adjacency and incidence relations.