Fix doxygen warnings

4 files changed, 166 insertions, 69 deletions

diff --git a/biblio/bibliography.bib b/biblio/bibliography.bib
index 16fa29d0..579fa85e 100644
--- a/biblio/bibliography.bib
+++ b/biblio/bibliography.bib
@@ -1324,3 +1324,18 @@ year = "2011"
   doi =		{10.4230/LIPIcs.SoCG.2020.19},
   annote =	{Keywords: Computational Topology, Topological Data Analysis, Edge Collapse, Simple Collapse, Persistent homology}
 }
+
+@phdthesis{KachanovichThesis,
+  TITLE = {{Meshing submanifolds using Coxeter triangulations}},
+  AUTHOR = {Kachanovich, Siargey},
+  URL = {https://hal.inria.fr/tel-02419148},
+  NUMBER = {2019AZUR4072},
+  SCHOOL = {{COMUE Universit{\'e} C{\^o}te d'Azur (2015 - 2019)}},
+  YEAR = {2019},
+  MONTH = Oct,
+  KEYWORDS = {Mesh generation ; Coxeter triangulations ; Simplex quality ; Triangulations of the Euclidean space ; Freudenthal-Kuhn triangulations ; G{\'e}n{\'e}ration de maillages ; Triangulations de Coxeter ; Qualit{\'e} des simplexes ; Triangulations de l'espace euclidien ; Triangulations de Freudenthal-Kuhn},
+  TYPE = {Theses},
+  PDF = {https://hal.inria.fr/tel-02419148v2/file/2019AZUR4072.pdf},
+  HAL_ID = {tel-02419148},
+  HAL_VERSION = {v2},
+}
\ No newline at end of file
diff --git a/src/Coxeter_triangulation/doc/intro_coxeter_triangulation.h b/src/Coxeter_triangulation/doc/intro_coxeter_triangulation.h
index 80ca5b37..c883d904 100644
--- a/src/Coxeter_triangulation/doc/intro_coxeter_triangulation.h
+++ b/src/Coxeter_triangulation/doc/intro_coxeter_triangulation.h
@@ -1,7 +1,5 @@
-/*    This file is part of the Gudhi Library. The Gudhi library
- *    (Geometric Understanding in Higher Dimensions) is a generic C++
- *    library for computational topology.
- *
+/*    This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
+ *    See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
  *    Author(s):       Siargey Kachanovich
  *
  *    Copyright (C) 2019 Inria
@@ -10,8 +8,8 @@
  *      - YYYY/MM Author: Description of the modification
  */
 
-#ifndef DOC_TANGENTIAL_COMPLEX_INTRO_COXETER_TRIANGULATION_H_
-#define DOC_TANGENTIAL_COMPLEX_INTRO_COXETER_TRIANGULATION_H_
+#ifndef DOC_COXETER_TRIANGULATION_INTRO_COXETER_TRIANGULATION_H_
+#define DOC_COXETER_TRIANGULATION_INTRO_COXETER_TRIANGULATION_H_
 
 // needs namespaces for Doxygen to link on classes
 namespace Gudhi {
@@ -25,101 +23,184 @@ namespace tangential_complex {
 
 \section overview Module overview
 
-Coxeter triangulation module is designed to provide tools for constructing a piecewise-linear approximation of an \f$m\f$-dimensional smooth manifold embedded in \f$ \mathbb{R}^d \f$ using an ambient triangulation.
+Coxeter triangulation module is designed to provide tools for constructing a piecewise-linear approximation of an
+\f$m\f$-dimensional smooth manifold embedded in \f$ \mathbb{R}^d \f$ using an ambient triangulation.
 For a more detailed description of the module see \cite KachanovichThesis.
 
 \section manifoldtracing Manifold tracing algorithm
-The central piece of the module is the manifold tracing algorithm represented by the class \ref Gudhi::coxeter_triangulation::Manifold_tracing "Manifold_tracing".
-The manifold tracing algorithm takes as input a manifold of some dimension \f$m\f$ embedded in \f$\mathbb{R}^d\f$ represented by an intersection oracle (see Section \ref intersectionoracle "Intersection oracle"), a point on the manifold and an ambient triangulation (see Section \ref ambienttriangulations "Ambient triangulations").
-The output consists of one map (or two maps in the case of manifolds with boundary) from the \f$(d-m)\f$-dimensional (and \f$(d-m+1)\f$-dimensional in the case of manifolds with boundary) simplices in the ambient triangulation that intersect the manifold to their intersection points.
-From this output, it is possible to construct the cell complex of the piecewise-linear approximation of the input manifold.
-
-There are two methods that execute the manifold tracing algorithm: the method \ref Gudhi::coxeter_triangulation::Manifold_tracing::manifold_tracing_algorithm() "Manifold_tracing::manifold_tracing_algorithm(seed_points, triangulation, oracle, out_simplex_map)" for manifolds without boundary and \ref Gudhi::coxeter_triangulation::Manifold_tracing::manifold_tracing_algorithm() "Manifold_tracing::manifold_tracing_algorithm(seed_points, triangulation, oracle, interior_simplex_map, boundary_simplex_map)" for manifolds with boundary.
+The central piece of the module is the manifold tracing algorithm represented by the class
+\ref Gudhi::coxeter_triangulation::Manifold_tracing "Manifold_tracing".
+The manifold tracing algorithm takes as input a manifold of some dimension \f$m\f$ embedded in \f$\mathbb{R}^d\f$
+represented by an intersection oracle (see Section \ref intersectionoracle "Intersection oracle"), a point on the
+manifold and an ambient triangulation (see Section \ref ambienttriangulations "Ambient triangulations").
+The output consists of one map (or two maps in the case of manifolds with boundary) from the \f$(d-m)\f$-dimensional
+(and \f$(d-m+1)\f$-dimensional in the case of manifolds with boundary) simplices in the ambient triangulation that
+intersect the manifold to their intersection points.
+From this output, it is possible to construct the cell complex of the piecewise-linear approximation of the input
+manifold.
+
+There are two methods that execute the manifold tracing algorithm: the method
+\ref Gudhi::coxeter_triangulation::Manifold_tracing::manifold_tracing_algorithm() "Manifold_tracing::manifold_tracing_algorithm(seed_points, triangulation, oracle, out_simplex_map)"
+for manifolds without boundary and
+\ref Gudhi::coxeter_triangulation::Manifold_tracing::manifold_tracing_algorithm() "Manifold_tracing::manifold_tracing_algorithm(seed_points, triangulation, oracle, interior_simplex_map, boundary_simplex_map)"
+for manifolds with boundary.
 The algorithm functions as follows.
-It starts at the specified seed points and inserts a \f$(d-m)\f$-dimensional simplices nearby each seed point that intersect the manifold into the output.
-Starting from this simplex, the algorithm propagates the search for other \f$(d-m)\f$-dimensional simplices that intersect the manifold by marching from a simplex to neighbouring simplices via their common cofaces.
-
-This class \ref Gudhi::coxeter_triangulation::Manifold_tracing "Manifold_tracing" has one template parameter Triangulation_ which specifies the ambient triangulation which is used by the algorithm.
-The template type Triangulation_ has to be a model of the concept \ref Gudhi::coxeter_triangulation::TriangulationForManifoldTracing "TriangulationForManifoldTracing".
-
-The module also provides two static methods: \ref Gudhi::coxeter_triangulation::manifold_tracing_algorithm() "manifold_tracing_algorithm(seed_points, triangulation, oracle, out_simplex_map)" for manifolds without boundary and \ref manifold_tracing_algorithm() "manifold_tracing_algorithm(seed_points, triangulation, oracle, interior_simplex_map, boundary_simplex_map)" for manifolds with boundary.
+It starts at the specified seed points and inserts a \f$(d-m)\f$-dimensional simplices nearby each seed point that
+intersect the manifold into the output.
+Starting from this simplex, the algorithm propagates the search for other \f$(d-m)\f$-dimensional simplices that
+intersect the manifold by marching from a simplex to neighbouring simplices via their common cofaces.
+
+This class \ref Gudhi::coxeter_triangulation::Manifold_tracing "Manifold_tracing" has one template parameter
+`Triangulation_` which specifies the ambient triangulation which is used by the algorithm.
+The template type `Triangulation_` has to be a model of the concept
+\ref Gudhi::coxeter_triangulation::TriangulationForManifoldTracing "TriangulationForManifoldTracing".
+
+The module also provides two static methods:
+\ref Gudhi::coxeter_triangulation::manifold_tracing_algorithm() "manifold_tracing_algorithm(seed_points, triangulation, oracle, out_simplex_map)"
+for manifolds without boundary and
+\ref manifold_tracing_algorithm() "manifold_tracing_algorithm(seed_points, triangulation, oracle, interior_simplex_map, boundary_simplex_map)"
+for manifolds with boundary.
 For these static methods it is not necessary to specify any template arguments.
 
 \section ambienttriangulations Ambient triangulations
 
-The ambient triangulations supported by the manifold tracing algorithm have to be models of the concept \ref Gudhi::coxeter_triangulation::TriangulationForManifoldTracing "TriangulationForManifoldTracing". 
-This module offers two such models: the class \ref Gudhi::coxeter_triangulation::Freudenthal_triangulation "Freudenthal_triangulation" and the derived class \ref Gudhi::coxeter_triangulation::Coxeter_triangulation "Coxeter_triangulation". 
+The ambient triangulations supported by the manifold tracing algorithm have to be models of the concept
+\ref Gudhi::coxeter_triangulation::TriangulationForManifoldTracing "TriangulationForManifoldTracing". 
+This module offers two such models: the class
+\ref Gudhi::coxeter_triangulation::Freudenthal_triangulation "Freudenthal_triangulation" and the derived class
+\ref Gudhi::coxeter_triangulation::Coxeter_triangulation "Coxeter_triangulation". 
 
 Both these classes encode affine transformations of the so-called Freudenthal-Kuhn triangulation of \f$\mathbb{R}^d\f$.
-The Freudenthal-Kuhn triangulation of \f$\mathbb{R}^d\f$ is defined as the simplicial subdivision of the unit cubic partition of \f$\mathbb{R}^d\f$.
-Each simplex is encoded using the permutahedral representation, which consists of an integer-valued vector \f$y\f$ that positions the simplex in a specific cube in the cubical partition and an ordered partition \f$\omega\f$ of the set \f$\{1,\ldots,d+1\}\f$, which positions the simplex in the simplicial subdivision of the cube.
-The default constructor \ref Gudhi::coxeter_triangulation::Freudenthal_triangulation::Freudenthal_triangulation(std::size_t) "Freudenthal_triangulation(d)" the Freudenthal-Kuhn triangulation of \f$\mathbb{R}^d\f$.
-The class \ref Gudhi::coxeter_triangulation::Freudenthal_triangulation "Freudenthal_triangulation" can also encode any affine transformation of the Freudenthal-Kuhn triangulation of \f$\mathbb{R}^d\f$ using an invertible matrix \f$\Lambda\f$ and an offset vector \f$b\f$ that can be specified in the constructor and which can be changed using the methods change_matrix and change_offset.
-The class \ref Gudhi::coxeter_triangulation::Coxeter_triangulation "Coxeter_triangulation" is derived from \ref Gudhi::coxeter_triangulation::Freudenthal_triangulation "Freudenthal_triangulation" and its default constructor \ref Gudhi::coxeter_triangulation::Coxeter_triangulation::Coxeter_triangulation(std::size_t) "Coxeter_triangulation(d)" builds a Coxeter triangulation of type \f$\tilde{A}_d\f$, which has the best simplex quality of all linear transformations of the Freudenthal-Kuhn triangulation of \f$\mathbb{R}^d\f$.
-
-\image html two_triangulations.png "On the left: Coxeter triangulation of type \f$\tilde{A}_2\f$. On the right: Freudenthal-Kuhn triangulation of \f$\mathbb{R}^d\f$."
+The Freudenthal-Kuhn triangulation of \f$\mathbb{R}^d\f$ is defined as the simplicial subdivision of the unit cubic
+partition of \f$\mathbb{R}^d\f$.
+Each simplex is encoded using the permutahedral representation, which consists of an integer-valued vector \f$y\f$ that
+positions the simplex in a specific cube in the cubical partition and an ordered partition \f$\omega\f$ of the set
+\f$\{1,\ldots,d+1\}\f$, which positions the simplex in the simplicial subdivision of the cube.
+The default constructor
+\ref Gudhi::coxeter_triangulation::Freudenthal_triangulation::Freudenthal_triangulation(std::size_t) "Freudenthal_triangulation(d)"
+the Freudenthal-Kuhn triangulation of \f$\mathbb{R}^d\f$.
+The class \ref Gudhi::coxeter_triangulation::Freudenthal_triangulation "Freudenthal_triangulation" can also encode any
+affine transformation of the Freudenthal-Kuhn triangulation of \f$\mathbb{R}^d\f$ using an invertible matrix
+\f$\Lambda\f$ and an offset vector \f$b\f$ that can be specified in the constructor and which can be changed using the
+methods change_matrix and change_offset.
+The class \ref Gudhi::coxeter_triangulation::Coxeter_triangulation "Coxeter_triangulation" is derived from
+\ref Gudhi::coxeter_triangulation::Freudenthal_triangulation "Freudenthal_triangulation" and its default constructor
+\ref Gudhi::coxeter_triangulation::Coxeter_triangulation::Coxeter_triangulation(std::size_t) "Coxeter_triangulation(d)"
+builds a Coxeter triangulation of type \f$\tilde{A}_d\f$, which has the best simplex quality of all linear
+transformations of the Freudenthal-Kuhn triangulation of \f$\mathbb{R}^d\f$.
+
+\image html two_triangulations.png "Coxeter (on the left) and Freudenthal-Kuhn triangulation (on the right)"
 
 
 \section intersectionoracle Intersection oracle
 
-The input \f$m\f$-dimensional manifold in \f$\mathbb{R}^d\f$ needs to be given via the intersection oracle that answers the following query: given a \f$(d-m)\f$-dimensional simplex, does it intersect the manifold?
-The concept \ref Gudhi::coxeter_triangulation::IntersectionOracle "IntersectionOracle" describes all requirements for an intersection oracle class to be compatible with the class \ref Gudhi::coxeter_triangulation::Manifold_tracing "Manifold_tracing".
-This module offers one model of the concept \ref Gudhi::coxeter_triangulation::IntersectionOracle "IntersectionOracle", which is the class \ref Gudhi::coxeter_triangulation::Implicit_manifold_intersection_oracle "Implicit_manifold_intersection_oracle".
-This class represents a manifold given as the zero-set of a specified function \f$F: \mathbb{R}^d \rightarrow \mathbb{R}^{d-m}\f$.
-The function \f$F\f$ is given by a class which is a model of the concept \ref Gudhi::coxeter_triangulation::FunctionForImplicitManifold "FunctionForImplicitManifold".
+The input \f$m\f$-dimensional manifold in \f$\mathbb{R}^d\f$ needs to be given via the intersection oracle that answers
+the following query: given a \f$(d-m)\f$-dimensional simplex, does it intersect the manifold?
+The concept \ref Gudhi::coxeter_triangulation::IntersectionOracle "IntersectionOracle" describes all requirements for
+an intersection oracle class to be compatible with the class
+\ref Gudhi::coxeter_triangulation::Manifold_tracing "Manifold_tracing".
+This module offers one model of the concept
+\ref Gudhi::coxeter_triangulation::IntersectionOracle "IntersectionOracle", which is the class
+\ref Gudhi::coxeter_triangulation::Implicit_manifold_intersection_oracle "Implicit_manifold_intersection_oracle".
+This class represents a manifold given as the zero-set of a specified function
+\f$F: \mathbb{R}^d \rightarrow \mathbb{R}^{d-m}\f$.
+The function \f$F\f$ is given by a class which is a model of the concept
+\ref Gudhi::coxeter_triangulation::FunctionForImplicitManifold "FunctionForImplicitManifold".
 There are multiple function classes that are already implemented in this module.
 
-\li \ref Gudhi::coxeter_triangulation::Constant_function(std::size_t, std::size_t, Eigen::VectorXd) "Constant_function(d,k,v)" defines a constant function \f$F\f$ such that for all \f$x \in \mathbb{R}^d\f$, we have \f$F(x) = v \in \mathbb{R}^k\f$.
-  The class Constant_function does not define an implicit manifold, but is useful as the domain function when defining boundaryless implicit manifolds.
-\li \ref Gudhi::coxeter_triangulation::Function_affine_plane_in_Rd(N,b) "Function_affine_plane_in_Rd(N,b)" defines an \f$m\f$-dimensional implicit affine plane in the \f$d\f$-dimensional Euclidean space given by a normal matrix \f$N\f$ and an offset vector \f$b\f$.
-\li \ref Gudhi::coxeter_triangulation::Function_Sm_in_Rd(r,m,d,center) "Function_Sm_in_Rd(r,m,d,center)" defines an \f$m\f$-dimensional implicit sphere embedded in the \f$d\f$-dimensional Euclidean space of radius \f$r\f$ centered at the point 'center'.
-\li \ref Gudhi::coxeter_triangulation::Function_moment_curve_in_Rd(r,d) "Function_moment_curve(r,d)" defines the moment curve in the \f$d\f$-dimensional Euclidean space of radius \f$r\f$ given as the parameterized curve (but implemented as an implicit curve):
+\li \ref Gudhi::coxeter_triangulation::Constant_function(std::size_t, std::size_t, Eigen::VectorXd) "Constant_function(d,k,v)"
+  defines a constant function \f$F\f$ such that for all \f$x \in \mathbb{R}^d\f$, we have
+  \f$F(x) = v \in \mathbb{R}^k\f$.
+  The class Constant_function does not define an implicit manifold, but is useful as the domain function when defining
+  boundaryless implicit manifolds.
+\li \ref Gudhi::coxeter_triangulation::Function_affine_plane_in_Rd(N,b) "Function_affine_plane_in_Rd(N,b)" defines an
+  \f$m\f$-dimensional implicit affine plane in the \f$d\f$-dimensional Euclidean space given by a normal matrix \f$N\f$
+  and an offset vector \f$b\f$.
+\li \ref Gudhi::coxeter_triangulation::Function_Sm_in_Rd(r,m,d,center) "Function_Sm_in_Rd(r,m,d,center)" defines an
+  \f$m\f$-dimensional implicit sphere embedded in the \f$d\f$-dimensional Euclidean space of radius \f$r\f$ centered at
+  the point 'center'.
+\li \ref Gudhi::coxeter_triangulation::Function_moment_curve_in_Rd(r,d) "Function_moment_curve(r,d)" defines the moment
+  curve in the \f$d\f$-dimensional Euclidean space of radius \f$r\f$ given as the parameterized curve (but implemented
+  as an implicit curve):
   \f[ (r, rt, \ldots, rt^{d-1}) \in \mathbb{R}^d,\text{ for $t \in \mathbb{R}$.} \f]
-\li \ref Gudhi::coxeter_triangulation::Function_torus_in_R3(R, r) "Function_torus_in_R3(R, r)" defines a torus in \f$\mathbb{R}^3\f$ with the outer radius \f$R\f$ and the inner radius, given by the equation:
+\li \ref Gudhi::coxeter_triangulation::Function_torus_in_R3(R, r) "Function_torus_in_R3(R, r)" defines a torus in
+  \f$\mathbb{R}^3\f$ with the outer radius \f$R\f$ and the inner radius, given by the equation:
   \f[ z^2 + (\sqrt{x^2 + y^2} - r)^2 - R^2 = 0. \f]
-\li \ref Gudhi::coxeter_triangulation::Function_chair_in_R3(a, b, k) "Function_chair_in_R3(a, b, k)" defines the ``Chair'' surface in \f$\mathbb{R}^3\f$ defined by the equation:
+\li \ref Gudhi::coxeter_triangulation::Function_chair_in_R3(a, b, k) "Function_chair_in_R3(a, b, k)" defines the
+  \"Chair\" surface in \f$\mathbb{R}^3\f$ defined by the equation:
   \f[ (x^2 + y^2 + z^2 - ak^2)^2 - b((z-k)^2 - 2x^2)((z+k)^2 - 2y^2) = 0. \f]
-\li \ref Gudhi::coxeter_triangulation::Function_iron_in_R3() "Function_iron_in_R3()" defines the ``Iron'' surface in \f$\mathbb{R}^3\f$ defined by the equation:
+\li \ref Gudhi::coxeter_triangulation::Function_iron_in_R3() "Function_iron_in_R3()" defines the \"Iron\" surface in
+  \f$\mathbb{R}^3\f$ defined by the equation:
   \f[ \frac{-x^6-y^6-z^6}{300} + \frac{xy^2z}{2.1} + y^2 + (z-2)^2 = 1. \f]
-\li \ref Gudhi::coxeter_triangulation::Function_lemniscate_revolution_in_R3(a) "Function_lemniscate_revolution_in_R3(a)" defines a revolution surface in \f$\mathbb{R}^3\f$ obtained from the lemniscate of Bernoulli defined by the equation:
+\li \ref Gudhi::coxeter_triangulation::Function_lemniscate_revolution_in_R3(a) "Function_lemniscate_revolution_in_R3(a)"
+  defines a revolution surface in \f$\mathbb{R}^3\f$ obtained from the lemniscate of Bernoulli defined by the equation:
   \f[ (x^2 + y^2 + z^2)^2 - 2a^2(x^2 - y^2 - z^2) = 0. \f]
-\li \ref Gudhi::coxeter_triangulation::Function_whitney_umbrella_in_R3() "Function_whitney_umbrella_in_R3()" defines the Whitney umbrella surface in \f$\mathbb{R}^3\f$ defined by the equation:
+\li \ref Gudhi::coxeter_triangulation::Function_whitney_umbrella_in_R3() "Function_whitney_umbrella_in_R3()" defines
+  the Whitney umbrella surface in \f$\mathbb{R}^3\f$ defined by the equation:
   \f[ x^2 - y^2z = 0. \f]
 
 The base function classes above can be composed or modified into new functions using the following classes and methods:
 
-\li \ref Gudhi::coxeter_triangulation::Cartesian_product "Cartesian_product(functions...)" expresses the Cartesian product \f$F_1^{-1}(0) \times \ldots \times F_k^{-1}(0)\f$ of multiple implicit manifolds as an implicit manifold.
-  For convenience, a static function \ref Gudhi::coxeter_triangulation::make_product_function() "make_product_function(functions...)" is provided that takes a pack of function-typed objects as the argument.
-\li \ref Gudhi::coxeter_triangulation::Embed_in_Rd "Embed_in_Rd(F, d)" expresses an implicit manifold given as the zero-set of a function \f$F\f$ embedded in a higher-dimensional Euclidean space \f$\mathbb{R}^d\f$.
-  For convenience, a static function \ref Gudhi::coxeter_triangulation::make_embedding() "make_embedding(F, d)" is provided.
-\li \ref Gudhi::coxeter_triangulation::Linear_transformation "Linear_transformation(F, M)" applies a linear transformation given by a matrix \f$M\f$ on an implicit manifold given as the zero-set of the function \f$F\f$.
-  For convenience, a static function \ref Gudhi::coxeter_triangulation::linear_transformation() "linear_transformation(F, M)" is provided.
-\li \ref Gudhi::coxeter_triangulation::Translate "Translate(F, v)" translates an implicit manifold given as the zero-set of ththe function \f$F\f$ by a vector \f$v\f$.
-  For convenience, a static function \ref Gudhi::coxeter_triangulation::translate(F, v) "translate(F, v)" is provided.
+\li \ref Gudhi::coxeter_triangulation::Cartesian_product "Cartesian_product(functions...)" expresses the Cartesian
+  product \f$F_1^{-1}(0) \times \ldots \times F_k^{-1}(0)\f$ of multiple implicit manifolds as an implicit manifold.
+  For convenience, a static function
+  \ref Gudhi::coxeter_triangulation::make_product_function() "make_product_function(functions...)" is provided that
+  takes a pack of function-typed objects as the argument.
+\li \ref Gudhi::coxeter_triangulation::Embed_in_Rd "Embed_in_Rd(F, d)" expresses an implicit manifold given as the
+  zero-set of a function \f$F\f$ embedded in a higher-dimensional Euclidean space \f$\mathbb{R}^d\f$.
+  For convenience, a static function \ref Gudhi::coxeter_triangulation::make_embedding() "make_embedding(F, d)" is
+  provided.
+\li \ref Gudhi::coxeter_triangulation::Linear_transformation "Linear_transformation(F, M)" applies a linear
+  transformation given by a matrix \f$M\f$ on an implicit manifold given as the zero-set of the function \f$F\f$.
+  For convenience, a static function
+  \ref Gudhi::coxeter_triangulation::make_linear_transformation() "make_linear_transformation(F, M)" is provided.
+\li \ref Gudhi::coxeter_triangulation::Translate "Translate(F, v)" translates an implicit manifold given as the
+  zero-set of ththe function \f$F\f$ by a vector \f$v\f$.
+  For convenience, a static function \ref Gudhi::coxeter_triangulation::translate() "translate(F, v)" is provided.
 \li \ref Gudhi::coxeter_triangulation::Negation() "Negation(F)" defines the negative of the given function \f$F\f$.
   This class is useful to define the complementary of a given domain, when defining a manifold with boundary.
   For convenience, a static function \ref Gudhi::coxeter_triangulation::negation() "negation(F)" is provided.
-\li \ref Gudhi::coxeter_triangulation::PL_approximation "PL_approximation(F, T)" defines a piecewise-linear approximation of a given function \f$F\f$ induced by an ambient triangulation \f$T\f$.
-  The purpose of this class is to define a piecewise-linear function that is compatible with the requirements for the domain function \f$D\f$ when defining a manifold with boundary.
-  For convenience, a static function \ref Gudhi::coxeter_triangulation::make_pl_approximation() "make_pl_approximation(F, T)" is provided.
-  The type of \f$T\f$ is required to be a model of the concept \ref Gudhi::coxeter_triangulation::TriangulationForManifoldTracing "TriangulationForManifoldTracing".
+\li \ref Gudhi::coxeter_triangulation::PL_approximation "PL_approximation(F, T)" defines a piecewise-linear
+  approximation of a given function \f$F\f$ induced by an ambient triangulation \f$T\f$.
+  The purpose of this class is to define a piecewise-linear function that is compatible with the requirements for the
+  domain function \f$D\f$ when defining a manifold with boundary.
+  For convenience, a static function
+  \ref Gudhi::coxeter_triangulation::make_pl_approximation() "make_pl_approximation(F, T)" is provided.
+  The type of \f$T\f$ is required to be a model of the concept
+  \ref Gudhi::coxeter_triangulation::TriangulationForManifoldTracing "TriangulationForManifoldTracing".
 
 \section cellcomplex Cell complex construction
 
-The output of the manifold tracing algorithm can be transformed into the Hasse diagram of a cell complex that approximates the input manifold using the class \ref Gudhi::coxeter_triangulation::Cell_complex "Cell_complex".
-The type of the cells in the Hasse diagram is \ref Gudhi::Hasse_diagram::Hasse_diagram_cell "Hasse_cell<int, double, bool>" provided by the module Hasse diagram.
-The cells in the cell complex given by an object of the class \ref Gudhi::coxeter_triangulation::Cell_complex "Cell_complex" are accessed through several maps that are accessed through the following methods.
-
-\li The method \ref Gudhi::coxeter_triangulation::Cell_complex::interior_simplex_cell_maps() "interior_simplex_cell_maps()" returns a vector of maps from the cells of various dimensions in the interior of the cell complex to the permutahedral representations of the corresponding simplices in the ambient triangulation.
-Each individual map for cells of a specific dimension \f$l\f$ can be accessed using the method \ref Gudhi::coxeter_triangulation::Cell_complex::interior_simplex_cell_map() "interior_simplex_cell_map(l)".
-\li The method \ref Gudhi::coxeter_triangulation::Cell_complex::boundary_simplex_cell_maps() "boundary_simplex_cell_maps()" returns a vector of maps from the cells of various dimensions on the boundary of the cell complex to the permutahedral representations of the corresponding simplices in the ambient triangulation.
-Each individual map for cells of a specific dimension \f$l\f$ can be accessed using the method \ref Gudhi::coxeter_triangulation::Cell_complex::boundary_simplex_cell_map() "boundary_simplex_cell_map(l)".
-\li The method \ref Gudhi::coxeter_triangulation::Cell_complex::cell_simplex_map() "cell_simplex_map()" returns a map from the cells in the cell complex to the permutahedral representations of the corresponding simplices in the ambient triangulation.
-\li The method \ref Gudhi::coxeter_triangulation::Cell_complex::cell_point_map() "cell_point_map()" returns a map from the vertex cells in the cell complex to their Cartesian coordinates.
+The output of the manifold tracing algorithm can be transformed into the Hasse diagram of a cell complex that
+approximates the input manifold using the class \ref Gudhi::coxeter_triangulation::Cell_complex "Cell_complex".
+The type of the cells in the Hasse diagram is
+\ref Gudhi::Hasse_diagram::Hasse_diagram_cell "Hasse_cell<int, double, bool>" provided by the module Hasse diagram.
+The cells in the cell complex given by an object of the class
+\ref Gudhi::coxeter_triangulation::Cell_complex "Cell_complex" are accessed through several maps that are accessed
+through the following methods.
+
+\li The method
+\ref Gudhi::coxeter_triangulation::Cell_complex::interior_simplex_cell_maps() "interior_simplex_cell_maps()"
+returns a vector of maps from the cells of various dimensions in the interior of the cell complex to the permutahedral
+representations of the corresponding simplices in the ambient triangulation.
+Each individual map for cells of a specific dimension \f$l\f$ can be accessed using the method
+\ref Gudhi::coxeter_triangulation::Cell_complex::interior_simplex_cell_map() "interior_simplex_cell_map(l)".
+\li The method
+\ref Gudhi::coxeter_triangulation::Cell_complex::boundary_simplex_cell_maps() "boundary_simplex_cell_maps()"
+returns a vector of maps from the cells of various dimensions on the boundary of the cell complex to the permutahedral
+representations of the corresponding simplices in the ambient triangulation.
+Each individual map for cells of a specific dimension \f$l\f$ can be accessed using the method
+\ref Gudhi::coxeter_triangulation::Cell_complex::boundary_simplex_cell_map() "boundary_simplex_cell_map(l)".
+\li The method \ref Gudhi::coxeter_triangulation::Cell_complex::cell_simplex_map() "cell_simplex_map()" returns a map
+from the cells in the cell complex to the permutahedral representations of the corresponding simplices in the ambient
+triangulation.
+\li The method \ref Gudhi::coxeter_triangulation::Cell_complex::cell_point_map() "cell_point_map()" returns a map from
+the vertex cells in the cell complex to their Cartesian coordinates.
 
 \section example Examples
 
-Here is an example of constructing a piecewise-linear approximation of a flat torus embedded in \f$\mathbb{R}^4\f$, rotated by a random rotation in \f$\mathbb{R}^4\f$ and cut by a hyperplane.
+Here is an example of constructing a piecewise-linear approximation of a flat torus embedded in \f$\mathbb{R}^4\f$,
+rotated by a random rotation in \f$\mathbb{R}^4\f$ and cut by a hyperplane.
 
 \include Coxeter_triangulation/manifold_tracing_flat_torus_with_boundary.cpp
 
@@ -143,4 +224,4 @@ The output in medit looks as follows:
 
 }  // namespace Gudhi
 
-#endif  // DOC_TANGENTIAL_COMPLEX_INTRO_TANGENTIAL_COMPLEX_H_
+#endif  // DOC_COXETER_TRIANGULATION_INTRO_COXETER_TRIANGULATION_H_
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Linear_transformation.h b/src/Coxeter_triangulation/include/gudhi/Functions/Linear_transformation.h
index 5f7485e7..89bef379 100644
--- a/src/Coxeter_triangulation/include/gudhi/Functions/Linear_transformation.h
+++ b/src/Coxeter_triangulation/include/gudhi/Functions/Linear_transformation.h
@@ -82,6 +82,8 @@ private:
  *
  * \tparam Function_ The function template parameter. Should be a model of 
  * the concept FunctionForImplicitManifold.
+ *
+ * \ingroup coxeter_triangulation
  */
 template <class Function_>
 Linear_transformation<Function_> make_linear_transformation(const Function_& function,
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Negation.h b/src/Coxeter_triangulation/include/gudhi/Functions/Negation.h
index e28d9ddb..6752ec3f 100644
--- a/src/Coxeter_triangulation/include/gudhi/Functions/Negation.h
+++ b/src/Coxeter_triangulation/include/gudhi/Functions/Negation.h
@@ -72,7 +72,6 @@ struct Negation : public Function {
  * \brief Static constructor of the negative function.
  *
  * @param[in] function The function to be translated.
- * @param[in] off The offset vector. The dimension should correspond to the 
  * domain (ambient) dimension of 'function'.
  *
  * \tparam Function_ The function template parameter. Should be a model of