Spell check.

Surface_mesh_parameterization/doc_tex/Surface_mesh_parameterization/complexity_and_guarantees.tex

@@ -35,8 +35,8 @@
 
     \item Non-singularity of the matrix
 
-        For LSCM, the matrix of the system is the Gramm matrix of a matrix with maximal rank,
-        and is therefore non-singular (Gramm theorem).
+        For LSCM, the matrix of the system is the Gram matrix of a matrix with maximal rank,
+        and is therefore non-singular (Gram theorem).
 
     \end{itemize}
 

Surface_mesh_parameterization/doc_tex/Surface_mesh_parameterization/introduction.tex

@@ -18,7 +18,7 @@ approximating surfaces and remeshing.
 This \cgal\ package implements some of the state-of-the-art
 surface parameterization methods, such as least squares conformal maps,
 discrete conformal map, discrete authalic
-parameterization, Floater mean value coordinates or tutte barycentric
+parameterization, Floater mean value coordinates or Tutte barycentric
 mapping. These methods mainly distinguish by the distortion they
 minimize (angles vs. areas), by the constrained border onto the
 planar domain (convex polygon vs. free border) and by the guarantees

Surface_mesh_parameterization/doc_tex/Surface_mesh_parameterization_ref/BorderParameterizer_3.tex

@@ -76,7 +76,7 @@ Construction and destruction are undefined.
 
 \ccMethod{Error_code parameterize_border(Adaptor& mesh);}
 {
-Assign to mesh's border vertices a 2D position (ie a (u,v) pair) on border's shape. Mark them as {\em parameterized}. Return false on error.
+Assign to mesh's border vertices a 2D position (i.e. a (u,v) pair) on border's shape. Mark them as {\em parameterized}. Return false on error.
 }
 \ccGlue
 \ccMethod{bool is_border_convex();}

Surface_mesh_parameterization/doc_tex/Surface_mesh_parameterization_ref/Circular_border_parameterizer_3.tex

@@ -97,7 +97,7 @@ Export \ccc{ParameterizationMesh_3} template parameter.
 
 \ccMethod{Parameterizer_traits_3<Adaptor>::Error_code parameterize_border(Adaptor& mesh);}
 {
-Assign to mesh's border vertices a 2D position (ie a (u,v) pair) on border's shape. Mark them as {\em parameterized}.
+Assign to mesh's border vertices a 2D position (i.e. a (u,v) pair) on border's shape. Mark them as {\em parameterized}.
 }
 \ccGlue
 \ccMethod{bool is_border_convex();}

Surface_mesh_parameterization/doc_tex/Surface_mesh_parameterization_ref/Fixed_border_parameterizer_3.tex

@@ -135,9 +135,9 @@ Check parameterize() preconditions:\begin{itemize}
 \ccGlue
 \ccMethod{void initialize_system_from_mesh_border(Matrix& A, Vector& Bu, Vector& Bv, const Adaptor& mesh);}
 {
-Initialize A, Bu and Bv after border parameterization. Fill the border vertices' lines in both linear systems: {\em u = constant} and {\em v = constant}.
+Initialize A, Bu and \ccc{Bv} after border parameterization. Fill the border vertices' lines in both linear systems: {\em u = constant} and {\em v = constant}.
 Preconditions:\begin{itemize}
-\item vertices must be indexed.\item A, Bu and Bv must be allocated.\item border vertices must be parameterized. \end{itemize}
+\item vertices must be indexed.\item A, Bu and \ccc{Bv} must be allocated.\item border vertices must be parameterized. \end{itemize}
 }
 \ccGlue
 \ccMethod{virtual NT compute_w_ij(const Adaptor& mesh, Vertex_const_handle main_vertex_v_i, Vertex_around_vertex_const_circulator neighbor_vertex_v_j);}
@@ -150,12 +150,12 @@ Compute \ccc{w_ij} = (i, j) coefficient of matrix A for j neighbor vertex of i.
 Compute the line i of matrix A for i inner vertex:\begin{itemize}
 \item call \ccc{compute_w_ij}() to compute the A coefficient \ccc{w_ij} for each neighbor \ccc{v_j}.\item compute \ccc{w_ii} = - sum of \ccc{w_ijs}.\end{itemize}
 Preconditions:\begin{itemize}
-\item vertices must be indexed.\item vertex i musn't be already parameterized.\item line i of A must contain only zeros. \end{itemize}
+\item vertices must be indexed.\item vertex i mustn't be already parameterized.\item line i of A must contain only zeros. \end{itemize}
 }
 \ccGlue
 \ccMethod{void set_mesh_uv_from_system(Adaptor& mesh, const Vector& Xu, const Vector& Xv);}
 {
-Copy Xu and Xv coordinates into the (u,v) pair of each surface vertex.
+Copy \ccc{Xu} and Xv coordinates into the (u,v) pair of each surface vertex.
 }
 \ccGlue
 \ccMethod{Parameterizer_traits_3<Adaptor>::Error_code check_parameterize_postconditions(const Adaptor& mesh, const Matrix& A, const Vector& Bu, const Vector& Bv);}

Surface_mesh_parameterization/doc_tex/Surface_mesh_parameterization_ref/ParameterizationPatchableMesh_3.tex

@@ -92,7 +92,7 @@ Get/set vertex seaming flag. Default value is undefined.
 \ccGlue
 \ccMethod{int get_halfedge_seaming(Vertex_const_handle source, Vertex_const_handle target) const;}
 {
-Get/set oriented edge's seaming flag, ie position of the oriented edge wrt to the UNIQUE main border.
+Get/set oriented edge's seaming flag, i.e. position of the oriented edge wrt to the UNIQUE main border.
 }
 \ccGlue
 \ccMethod{void set_halfedge_seaming(Vertex_handle source, Vertex_handle target, int seaming);}

Surface_mesh_parameterization/doc_tex/Surface_mesh_parameterization_ref/Parameterization_mesh_patch_3.tex

@@ -197,7 +197,7 @@ Clockwise circulator over the vertices incident to a vertex. Model of the Bidire
 {
 Create a Decorator for an existing \ccc{ParameterizationPatchableMesh_3} mesh. The input mesh can be of any genus, but it has to come with a {\em seam} that describes the border of a topological disc. This border may be an actual border of the mesh or a virtual border.
 Preconditions:\begin{itemize}
-\item \ccc{first_seam_vertex} -$>$ \ccc{end_seam_vertex} defines the outer seam, ie \ccc{Parameterization_mesh_patch_3} will export the {\em right} of the seam.\item The {\em seam} is given as a container of \ccc{Adaptor::Vertex_handle} elements.\item The {\em seam} is implicitely a loop. The first vertex should $\ast$not$\ast$ be duplicated at the end. \end{itemize}
+\item \ccc{first_seam_vertex} -$>$ \ccc{end_seam_vertex} defines the outer seam, ie \ccc{Parameterization_mesh_patch_3} will export the {\em right} of the seam.\item The {\em seam} is given as a container of \ccc{Adaptor::Vertex_handle} elements.\item The {\em seam} is implicitly a loop. The first vertex should $\ast$not$\ast$ be duplicated at the end. \end{itemize}
 }
 \ccGlue
 

Surface_mesh_parameterization/doc_tex/Surface_mesh_parameterization_ref/Parameterization_polyhedron_adaptor_3.tex

@@ -405,7 +405,7 @@ Return true if a vertex belongs to ANY mesh's border.
 \ccGlue
 \ccMethod{bool is_vertex_on_main_border(Vertex_const_handle vertex) const;}
 {
-Return true if a vertex belongs to the UNIQUE mesh's main border, ie the mesh's LONGEST border.
+Return true if a vertex belongs to the UNIQUE mesh's main border, i.e. the mesh's LONGEST border.
 }
 \ccGlue
 \ccMethod{Vertex_around_vertex_circulator vertices_around_vertex_begin(Vertex_handle vertex, Vertex_handle start_position = Vertex_handle());}
@@ -428,7 +428,7 @@ Get/set vertex seaming flag. Default value is undefined.
 \ccGlue
 \ccMethod{int get_halfedge_seaming(Vertex_const_handle source, Vertex_const_handle target) const;}
 {
-Get/set oriented edge's seaming flag, ie position of the oriented edge wrt to the UNIQUE main border.
+Get/set oriented edge's seaming flag, i.e. position of the oriented edge wrt to the UNIQUE main border.
 }
 \ccGlue
 \ccMethod{void set_halfedge_seaming(Vertex_handle source, Vertex_handle target, int seaming);}

Surface_mesh_parameterization/doc_tex/Surface_mesh_parameterization_ref/Parameterizer_traits_3.tex

@@ -134,7 +134,7 @@ Preconditions:\begin{itemize}
 \ccGlue
 \ccMethod{static const char* get_error_message(int error_code);}
 {
-Get message (in english) corresponding to an error code 
+Get message (in English) corresponding to an error code 
 }
 \ccGlue
 \begin{description}

Surface_mesh_parameterization/doc_tex/Surface_mesh_parameterization_ref/Square_border_parameterizer_3.tex

@@ -99,7 +99,7 @@ Export \ccc{ParameterizationMesh_3} template parameter.
 
 \ccMethod{Parameterizer_traits_3<Adaptor>::Error_code parameterize_border(Adaptor& mesh);}
 {
-Assign to mesh's border vertices a 2D position (ie a (u,v) pair) on border's shape. Mark them as {\em parameterized}.
+Assign to mesh's border vertices a 2D position (i.e. a (u,v) pair) on border's shape. Mark them as {\em parameterized}.
 }
 \ccGlue
 \ccMethod{bool is_border_convex();}

Surface_mesh_parameterization/doc_tex/Surface_mesh_parameterization_ref/parameterize.tex

@@ -23,7 +23,7 @@
 It computes a one-to-one mapping from a 3D triangle surface 'mesh' to a simple 2D domain.
 The mapping is piecewise linear on the triangle mesh.
 The result is a pair (u,v) of parameter coordinates for each vertex of the input mesh.
-One-to-one mapping may be guaranteed or not, depending on the chosen ParametizerTraits algorithm.
+One-to-one mapping may be guaranteed or not, depending on the chosen \ccc{ParametizerTraits} algorithm.
 
 The \ccc{CGAL::parameterize()} function exists in two flavors, to provide a default parameterization algorithm
 of Floater Mean Value Coordinates.