diff --git a/Combinatorial_map/doc_tex/Combinatorial_map/Combinatorial_map.tex b/Combinatorial_map/doc_tex/Combinatorial_map/Combinatorial_map.tex index 5eed6ac9243..94f8fff0f4d 100644 --- a/Combinatorial_map/doc_tex/Combinatorial_map/Combinatorial_map.tex +++ b/Combinatorial_map/doc_tex/Combinatorial_map/Combinatorial_map.tex @@ -5,16 +5,16 @@ \newcommand{\nulldart}{\texttt{null\_dart\_handle}} \section{Introduction} -A $d$D combinatorial map is a data structure representing an -orientable subdivided $d$D % \emph{quasi-manifold}, \emph{i.e.} a $d$D -object obtained by taking $d$D cells, and allowing to glue $d$D cells -along $(d-1)$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 -halfedge data structure to higher dimension.\footnote{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.} +A $d$-dimensional combinatorial map is a data structure representing +an orientable subdivided $d$-dimensional object obtained by taking +$d$D cells, and allowing to glue $d$D cells along $(d-1)$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 halfedge data +structure to higher dimension.\footnote{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.} We denote $i$-cell for an $i$-dimensional cell (for example in 3D, 0-cells are \emph{vertices}, 1-cells are \emph{edges}, 2-cells are