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fixed typos in the doc

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Mariette Yvinec 2001-07-26 11:38:06 +00:00
parent f09dbe57a4
commit f36e293d8a
3 changed files with 47 additions and 38 deletions
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5
Packages/Triangulation_2/changes.txt
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@ -1,8 +1,9 @@
Package triangulation: provides triangulations Delaunay triangulations,
constrained and regular triangulations with tests and examples.
Ver 5.14 (??)
- doc fixes : add an index entry for Voronoi and power diagram
Ver 5.14 (26/7/01)
- fixed typos in the doc
- add an index entries for Voronoi and power diagram
Ver 5.13 (24/7/01)
- added missing data file for examples/Triangulation/voronoi.C

40
Packages/Triangulation_2/doc_tex/Triangulation_2/triangulation_user.tex
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@ -51,7 +51,7 @@ are orientable triangulations
embedded in a plane or in a higher dimensional space.
Strictly speaking, the term {\em face} should be used
to design a face of any dimension
to design a face of any dimension,
and the two-dimensional faces of a triangulation
should be properly called {\em facets}.
However, following a common usage, we hereafter often call {\em
@ -104,14 +104,15 @@ surfaces, see Figure~\ref{I1_Fig_three_levels}. \\
The bottom layer is made of the base classes for vertices and faces.
These base classes store some
geometric informations such as the coordinate of vertices
and any other attribute (such as color, constraint edges etc.)
and any other attribute (such as a color, or boolean marks
for constrained edges etc.)
needed by the application.
The base classes handle
incidence and adjacency relations in term of \ccc{void*} pointers.
The use of \ccc{void*} pointers in the bottom layer
makes easy
the change one of the base
class, to deal with an extra attribute like a color for example.\\
the change of one of the base
classes, to deal with an extra attribute like a color for example.\\
The second layer is the \ccc{triangulation data structure}
which can be can be thought
of as a container for faces and vertices
@ -204,9 +205,8 @@ boundary of the convex hull are simpler to deal with.
In the following, we called {\it infinite} the infinite vertex
and any face or edge
incident to the infinite vertex. Any face or edge non incident
to the infinite vertex as well as any other vertex
is said
to be {\it finite}.
to the infinite vertex as well as any vertex different from
the infinite vertex is said to be {\it finite}.
Although it is convenient to draw a triangulation as in
figure~\ref{I1_Fig_infinite_vertex}, note that
the \ccc{infinite vertex} has no significant
@ -240,7 +240,7 @@ indexed with 0,1,2 in such a way that the neighbor indexed by \ccc{i}
is opposite to the vertex with the same index.
The edges are only implicitly represented
through the adjacency relations betwwen their two incident
through the adjacency relations between their two incident
faces. Each edge has two implicit representations : the edge
of a face \ccc{f} which is opposed to the vertex indexed \ccc{i},
can be represented as well as an edge of the \ccc{neighbor(i)} of
@ -376,7 +376,7 @@ for points located outside the convex hull.
Removal of a vertex is done by removing all adjacent triangles, and
retriangulating the hole. Removal takes a time at most proportionnal to
\ccTexHtml{$d^2$}{d^2} case, where
\ccTexHtml{$d^2$}{d^2}, where
\ccTexHtml{$d$}{d} is the degree of the removed vertex,
which is \ccTexHtml{$O(1)$}{O(1)} for a random vertex.
@ -535,12 +535,16 @@ The \cgal\ kernel classes \ccc{Homogeneous<Nt>} and
\ccc{Cartesian<Nt>}, and the class \ccc{Triangulation_euclidean_traits_2<R>}
are models of the concept \ccc{DelaunayTriangulationTraits_2}
for the euclidean metric.
Three traits classes are provided to deal with
the Delaunay triangulation of two dimensional points which are
the \ccc{xy}, \ccc{yz} or \ccc{zx} projections of three dimensional points:\\
\cgal\ also provides traits classes to deal with terrains,
that are two dimensional triangulated surfaces
embedded in the three dimensional space that have project on
a two dimensional Delaunay triangulation. Namely, the traits classes
\ccc{Triangulation_euclidean_traits_xy_3<R>},\\
\ccc{Triangulation_euclidean_traits_yz_3<R>}, and\\
\ccc{Triangulation_euclidean_traits_zx_3<R>} \\
are to be used to build a a triangulated surface
projecting on the Delaunay triangulation of respectively
the \ccc{xy}, \ccc{yz} or \ccc{zx} projections of its vertices:\\
The requirements for the duality functions and nearest vertex
queries are not yet satisfied by
these last three classes.
@ -612,7 +616,7 @@ in ${ PW}$. In the two-dimensional space,
the dual of this diagram is a triangulation
whose domain covers the convex hull of the set
${ P}= \{ p_i, i = 1, \ldots , n \}$ of center points
and whose vertices are a subset of ${ P}$.
and whose vertices form a subset of ${ P}$.
Such a triangulation is called a regular triangulation.
Three points $p_i, p_j$ and $p_k$ of ${ P}$
form a triangle in the regular triangulation of ${ PW}$
@ -687,8 +691,8 @@ The triangulation data structure has to be a model of the concept
\ccc{TriangulationDataStructure_2}.
The geometric traits class must provide a weighted point type
and a power test on these weighted points
and the concept for this parameter called
\ccc{RegularTriangulationTraits_2}
and the concept for this parameter, called
\ccc{RegularTriangulationTraits_2},
is a refinement of the concept
\ccc{TriangulationTraits_2}. \cgal\ provides
the class
@ -958,7 +962,8 @@ when it is built for Delaunay triangulations.
However it can be used as well for other triangulations
and the class \ccc{Triangulation_hierarchy_2<Tr>} is templated by a parameter
which is to be instantiated by one of the \cgal\ triangulation
classes.
classes. More precisely a triangulation hierarchy can be set for all
two dimensional triangulations of \cgal\ except for regular triangulations.
The class \ccc{Triangulation_hierarchy_2<Tr>} inherits from the
@ -974,8 +979,7 @@ the base class of a triangulation hierarchy
has to provide
some pointers to the corresponding vertices in the
triangulations of the next and preceeding levels.
Therefore the base vertex class of such a triangulation
the base class of a triangulation hierarchy
The base vertex class of a triangulation hierarchy
has to be a model of the
concept
\ccc{TriangulationHierarchyVertexBase_2} which extends

40
Packages/Triangulation_2/doc_tex/basic/Triangulation_2/triangulation_user.tex
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@ -51,7 +51,7 @@ are orientable triangulations
embedded in a plane or in a higher dimensional space.
Strictly speaking, the term {\em face} should be used
to design a face of any dimension
to design a face of any dimension,
and the two-dimensional faces of a triangulation
should be properly called {\em facets}.
However, following a common usage, we hereafter often call {\em
@ -104,14 +104,15 @@ surfaces, see Figure~\ref{I1_Fig_three_levels}. \\
The bottom layer is made of the base classes for vertices and faces.
These base classes store some
geometric informations such as the coordinate of vertices
and any other attribute (such as color, constraint edges etc.)
and any other attribute (such as a color, or boolean marks
for constrained edges etc.)
needed by the application.
The base classes handle
incidence and adjacency relations in term of \ccc{void*} pointers.
The use of \ccc{void*} pointers in the bottom layer
makes easy
the change one of the base
class, to deal with an extra attribute like a color for example.\\
the change of one of the base
classes, to deal with an extra attribute like a color for example.\\
The second layer is the \ccc{triangulation data structure}
which can be can be thought
of as a container for faces and vertices
@ -204,9 +205,8 @@ boundary of the convex hull are simpler to deal with.
In the following, we called {\it infinite} the infinite vertex
and any face or edge
incident to the infinite vertex. Any face or edge non incident
to the infinite vertex as well as any other vertex
is said
to be {\it finite}.
to the infinite vertex as well as any vertex different from
the infinite vertex is said to be {\it finite}.
Although it is convenient to draw a triangulation as in
figure~\ref{I1_Fig_infinite_vertex}, note that
the \ccc{infinite vertex} has no significant
@ -240,7 +240,7 @@ indexed with 0,1,2 in such a way that the neighbor indexed by \ccc{i}
is opposite to the vertex with the same index.
The edges are only implicitly represented
through the adjacency relations betwwen their two incident
through the adjacency relations between their two incident
faces. Each edge has two implicit representations : the edge
of a face \ccc{f} which is opposed to the vertex indexed \ccc{i},
can be represented as well as an edge of the \ccc{neighbor(i)} of
@ -376,7 +376,7 @@ for points located outside the convex hull.
Removal of a vertex is done by removing all adjacent triangles, and
retriangulating the hole. Removal takes a time at most proportionnal to
\ccTexHtml{$d^2$}{d^2} case, where
\ccTexHtml{$d^2$}{d^2}, where
\ccTexHtml{$d$}{d} is the degree of the removed vertex,
which is \ccTexHtml{$O(1)$}{O(1)} for a random vertex.
@ -535,12 +535,16 @@ The \cgal\ kernel classes \ccc{Homogeneous<Nt>} and
\ccc{Cartesian<Nt>}, and the class \ccc{Triangulation_euclidean_traits_2<R>}
are models of the concept \ccc{DelaunayTriangulationTraits_2}
for the euclidean metric.
Three traits classes are provided to deal with
the Delaunay triangulation of two dimensional points which are
the \ccc{xy}, \ccc{yz} or \ccc{zx} projections of three dimensional points:\\
\cgal\ also provides traits classes to deal with terrains,
that are two dimensional triangulated surfaces
embedded in the three dimensional space that have project on
a two dimensional Delaunay triangulation. Namely, the traits classes
\ccc{Triangulation_euclidean_traits_xy_3<R>},\\
\ccc{Triangulation_euclidean_traits_yz_3<R>}, and\\
\ccc{Triangulation_euclidean_traits_zx_3<R>} \\
are to be used to build a a triangulated surface
projecting on the Delaunay triangulation of respectively
the \ccc{xy}, \ccc{yz} or \ccc{zx} projections of its vertices:\\
The requirements for the duality functions and nearest vertex
queries are not yet satisfied by
these last three classes.
@ -612,7 +616,7 @@ in ${ PW}$. In the two-dimensional space,
the dual of this diagram is a triangulation
whose domain covers the convex hull of the set
${ P}= \{ p_i, i = 1, \ldots , n \}$ of center points
and whose vertices are a subset of ${ P}$.
and whose vertices form a subset of ${ P}$.
Such a triangulation is called a regular triangulation.
Three points $p_i, p_j$ and $p_k$ of ${ P}$
form a triangle in the regular triangulation of ${ PW}$
@ -687,8 +691,8 @@ The triangulation data structure has to be a model of the concept
\ccc{TriangulationDataStructure_2}.
The geometric traits class must provide a weighted point type
and a power test on these weighted points
and the concept for this parameter called
\ccc{RegularTriangulationTraits_2}
and the concept for this parameter, called
\ccc{RegularTriangulationTraits_2},
is a refinement of the concept
\ccc{TriangulationTraits_2}. \cgal\ provides
the class
@ -958,7 +962,8 @@ when it is built for Delaunay triangulations.
However it can be used as well for other triangulations
and the class \ccc{Triangulation_hierarchy_2<Tr>} is templated by a parameter
which is to be instantiated by one of the \cgal\ triangulation
classes.
classes. More precisely a triangulation hierarchy can be set for all
two dimensional triangulations of \cgal\ except for regular triangulations.
The class \ccc{Triangulation_hierarchy_2<Tr>} inherits from the
@ -974,8 +979,7 @@ the base class of a triangulation hierarchy
has to provide
some pointers to the corresponding vertices in the
triangulations of the next and preceeding levels.
Therefore the base vertex class of such a triangulation
the base class of a triangulation hierarchy
The base vertex class of a triangulation hierarchy
has to be a model of the
concept
\ccc{TriangulationHierarchyVertexBase_2} which extends