diff --git a/Packages/Triangulation_2/changes.txt b/Packages/Triangulation_2/changes.txt index 9b1b5108fe3..71adbb47f22 100644 --- a/Packages/Triangulation_2/changes.txt +++ b/Packages/Triangulation_2/changes.txt @@ -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 diff --git a/Packages/Triangulation_2/doc_tex/Triangulation_2/triangulation_user.tex b/Packages/Triangulation_2/doc_tex/Triangulation_2/triangulation_user.tex index c3f46a8d7ce..86bc15fc64f 100644 --- a/Packages/Triangulation_2/doc_tex/Triangulation_2/triangulation_user.tex +++ b/Packages/Triangulation_2/doc_tex/Triangulation_2/triangulation_user.tex @@ -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} and \ccc{Cartesian}, and the class \ccc{Triangulation_euclidean_traits_2} 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},\\ \ccc{Triangulation_euclidean_traits_yz_3}, and\\ \ccc{Triangulation_euclidean_traits_zx_3} \\ +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} 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} 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 diff --git a/Packages/Triangulation_2/doc_tex/basic/Triangulation_2/triangulation_user.tex b/Packages/Triangulation_2/doc_tex/basic/Triangulation_2/triangulation_user.tex index c3f46a8d7ce..86bc15fc64f 100644 --- a/Packages/Triangulation_2/doc_tex/basic/Triangulation_2/triangulation_user.tex +++ b/Packages/Triangulation_2/doc_tex/basic/Triangulation_2/triangulation_user.tex @@ -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} and \ccc{Cartesian}, and the class \ccc{Triangulation_euclidean_traits_2} 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},\\ \ccc{Triangulation_euclidean_traits_yz_3}, and\\ \ccc{Triangulation_euclidean_traits_zx_3} \\ +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} 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} 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