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
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\newcommand{\nulldart}{\texttt{null\_dart\_handle}} \newcommand{\nulldart}{\texttt{null\_dart\_handle}}
\section{Introduction} \section{Introduction}
A $d$D combinatorial map is a data structure representing an A $d$-dimensional combinatorial map is a data structure representing
orientable subdivided $d$D % \emph{quasi-manifold}, \emph{i.e.} a $d$D an orientable subdivided $d$-dimensional object obtained by taking
object obtained by taking $d$D cells, and allowing to glue $d$D cells $d$D cells, and allowing to glue $d$D cells along $(d-1)$D cells. It
along $(d-1)$D cells. It provides a description of all the cells of provides a description of all the cells of the subdivision (for
the subdivision (for example vertices and edges), together with incidence example vertices and edges), together with incidence and adjacency
and adjacency relationships. This package is a generalization of the relationships. This package is a generalization of the halfedge data
halfedge data structure to higher dimension.\footnote{A 2D structure to higher dimension.\footnote{A 2D combinatorial map is
combinatorial map is equivalent to a halfedge data structure: there equivalent to a halfedge data structure: there is a one-to-one
is a one-to-one mapping between elements of both data structures, mapping between elements of both data structures, halfedges
halfedges corresponding to darts.} corresponding to darts.}
We denote $i$-cell for an $i$-dimensional cell (for example in 3D, 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 0-cells are \emph{vertices}, 1-cells are \emph{edges}, 2-cells are