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Replace $d$D by $d$-dimensional (remark of Andreas).

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Guillaume Damiand 2011-06-26 12:18:04 +00:00
parent 058d43a0fb
commit 38428ec768
1 changed files with 10 additions and 10 deletions
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Combinatorial_map/doc_tex/Combinatorial_map/Combinatorial_map.tex
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@ -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