Remove the Function inheritance and keep concept

17 files changed, 81 insertions, 161 deletions

diff --git a/src/Coxeter_triangulation/example/manifold_tracing_custom_function.cpp b/src/Coxeter_triangulation/example/manifold_tracing_custom_function.cpp
index 7e3d95a4..a15756c6 100644
--- a/src/Coxeter_triangulation/example/manifold_tracing_custom_function.cpp
+++ b/src/Coxeter_triangulation/example/manifold_tracing_custom_function.cpp
@@ -19,8 +19,8 @@ using namespace Gudhi::coxeter_triangulation;
  * the equation of the manifold is x^3*y + y^3*z + z^3*x = 0.
  * The embedding consists of restricting the manifold to the affine subspace z = 1.
  */
-struct Function_surface_on_CP2_in_R4 : public Function {
-  virtual Eigen::VectorXd operator()(const Eigen::VectorXd& p) const override {
+struct Function_surface_on_CP2_in_R4 {
+  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
     // The real and imaginary parts of the variables x and y
     double xr = p(0), xi = p(1), yr = p(2), yi = p(3);
     Eigen::VectorXd result(cod_d());
@@ -36,10 +36,10 @@ struct Function_surface_on_CP2_in_R4 : public Function {
     return result;
   }
 
-  virtual std::size_t amb_d() const override { return 4; };
-  virtual std::size_t cod_d() const override { return 2; };
+  std::size_t amb_d() const { return 4; };
+  std::size_t cod_d() const { return 2; };
 
-  virtual Eigen::VectorXd seed() const override {
+  Eigen::VectorXd seed() const {
     Eigen::VectorXd result = Eigen::VectorXd::Zero(4);
     return result;
   }
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Cartesian_product.h b/src/Coxeter_triangulation/include/gudhi/Functions/Cartesian_product.h
index d1767eca..0533bb83 100644
--- a/src/Coxeter_triangulation/include/gudhi/Functions/Cartesian_product.h
+++ b/src/Coxeter_triangulation/include/gudhi/Functions/Cartesian_product.h
@@ -16,8 +16,6 @@
 #include <type_traits>  // for std::enable_if
 #include <cstdlib>      // for std::size_t
 
-#include <gudhi/Functions/Function.h>
-
 #include <Eigen/Dense>
 
 namespace Gudhi {
@@ -96,25 +94,25 @@ inline typename std::enable_if<I != sizeof...(T), void>::type get_value(const st
  * the concept FunctionForImplicitManifold.
  */
 template <class... Functions>
-struct Cartesian_product : public Function {
+struct Cartesian_product {
   /**
    * \brief Value of the function at a specified point.
    * @param[in] p The input point. The dimension needs to coincide with the ambient dimension.
    */
-  virtual Eigen::VectorXd operator()(const Eigen::VectorXd& p) const override {
+  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
     Eigen::VectorXd result(cod_d_);
     get_value(function_tuple_, p, result, 0, 0);
     return result;
   }
 
   /** \brief Returns the domain (ambient) dimension. */
-  virtual std::size_t amb_d() const override { return amb_d_; }
+  std::size_t amb_d() const { return amb_d_; }
 
   /** \brief Returns the codomain dimension. */
-  virtual std::size_t cod_d() const override { return cod_d_; }
+  std::size_t cod_d() const { return cod_d_; }
 
   /** \brief Returns a point on the zero-set. */
-  virtual Eigen::VectorXd seed() const override {
+  Eigen::VectorXd seed() const {
     Eigen::VectorXd result(amb_d_);
     get_seed(function_tuple_, result, 0);
     return result;
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Constant_function.h b/src/Coxeter_triangulation/include/gudhi/Functions/Constant_function.h
index 86533f81..0603afd8 100644
--- a/src/Coxeter_triangulation/include/gudhi/Functions/Constant_function.h
+++ b/src/Coxeter_triangulation/include/gudhi/Functions/Constant_function.h
@@ -13,8 +13,6 @@
 
 #include <cstdlib>  // for std::size_t
 
-#include <gudhi/Functions/Function.h>
-
 #include <Eigen/Dense>
 
 namespace Gudhi {
@@ -26,22 +24,22 @@ namespace coxeter_triangulation {
  * \brief A class that encodes a constant function from R^d to R^k.
  * This class does not have any implicit manifold in correspondence.
  */
-struct Constant_function : public Function {
+struct Constant_function {
   /** \brief Value of the function at a specified point. The value is constant.
    * @param[in] p The input point. The dimension needs to coincide with the ambient dimension.
    */
-  virtual Eigen::VectorXd operator()(const Eigen::VectorXd& p) const override {
+  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
     return value_;
   }
 
   /** \brief Returns the domain dimension. Same as the ambient dimension of the sphere. */
-  virtual std::size_t amb_d() const override { return d_; };
+  std::size_t amb_d() const { return d_; };
 
   /** \brief Returns the codomain dimension. Same as the codimension of the sphere. */
-  virtual std::size_t cod_d() const override { return k_; };
+  std::size_t cod_d() const { return k_; };
 
   /** \brief No seed point is available. Throws an exception on evocation. */
-  virtual Eigen::VectorXd seed() const override { throw "Seed invoked on a constant function.\n"; }
+  Eigen::VectorXd seed() const { throw "Seed invoked on a constant function.\n"; }
 
   Constant_function() {}
 
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Embed_in_Rd.h b/src/Coxeter_triangulation/include/gudhi/Functions/Embed_in_Rd.h
index bfeda2c3..e1fe868f 100644
--- a/src/Coxeter_triangulation/include/gudhi/Functions/Embed_in_Rd.h
+++ b/src/Coxeter_triangulation/include/gudhi/Functions/Embed_in_Rd.h
@@ -13,8 +13,6 @@
 
 #include <cstdlib>  // for std::size_t
 
-#include <gudhi/Functions/Function.h>
-
 #include <Eigen/Dense>
 
 namespace Gudhi {
@@ -29,12 +27,12 @@ namespace coxeter_triangulation {
  * the concept FunctionForImplicitManifold.
  */
 template <class Function_>
-struct Embed_in_Rd : public Function {
+struct Embed_in_Rd {
   /**
    * \brief Value of the function at a specified point.
    * @param[in] p The input point. The dimension needs to coincide with the ambient dimension.
    */
-  virtual Eigen::VectorXd operator()(const Eigen::VectorXd& p) const override {
+  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
     Eigen::VectorXd x = p;
     Eigen::VectorXd x_k(fun_.amb_d()), x_rest(d_ - fun_.amb_d());
     for (std::size_t i = 0; i < fun_.amb_d(); ++i) x_k(i) = x(i);
@@ -46,13 +44,13 @@ struct Embed_in_Rd : public Function {
   }
 
   /** \brief Returns the domain (ambient) dimension. */
-  virtual std::size_t amb_d() const override { return d_; }
+  std::size_t amb_d() const { return d_; }
 
   /** \brief Returns the codomain dimension. */
-  virtual std::size_t cod_d() const override { return d_ - (fun_.amb_d() - fun_.cod_d()); }
+  std::size_t cod_d() const { return d_ - (fun_.amb_d() - fun_.cod_d()); }
 
   /** \brief Returns a point on the zero-set of the embedded function. */
-  virtual Eigen::VectorXd seed() const override {
+  Eigen::VectorXd seed() const {
     Eigen::VectorXd result = fun_.seed();
     result.conservativeResize(d_);
     for (std::size_t l = fun_.amb_d(); l < d_; ++l) result(l) = 0;
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Function.h b/src/Coxeter_triangulation/include/gudhi/Functions/Function.h
deleted file mode 100644
index eddfedf5..00000000
--- a/src/Coxeter_triangulation/include/gudhi/Functions/Function.h
+++ /dev/null
@@ -1,50 +0,0 @@
-/*    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
- *
- *    Modification(s):
- *      - YYYY/MM Author: Description of the modification
- */
-
-#ifndef FUNCTIONS_FUNCTION_H_
-#define FUNCTIONS_FUNCTION_H_
-
-#include <Eigen/Dense>
-
-namespace Gudhi {
-
-namespace coxeter_triangulation {
-
-/**
- * \class Function
- * \brief The parent class for all functions implemented in the module.
- *  Contains virtual methods needed to be a model of the concept FunctionForImplicitManifold.
- *
- * \ingroup coxeter_triangulation
- */
-struct Function {
-  /** \brief Virtual method for the value of the function at a specified point.
-   * @param[in] p The input point.
-   */
-  virtual Eigen::VectorXd operator()(const Eigen::VectorXd& p) const = 0;
-
-  /** \brief Virtual method for the domain dimension. */
-  virtual std::size_t amb_d() const = 0;
-
-  /** \brief Virtual method for the codomain dimension. */
-  virtual std::size_t cod_d() const = 0;
-
-  /** \brief Virtual method for the seed point. */
-  virtual Eigen::VectorXd seed() const = 0;
-
-  /** \brief Virtual destructor. */
-  virtual ~Function() {}
-};
-
-}  // namespace coxeter_triangulation
-
-}  // namespace Gudhi
-
-#endif
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Function_Sm_in_Rd.h b/src/Coxeter_triangulation/include/gudhi/Functions/Function_Sm_in_Rd.h
index d901e832..8911f990 100644
--- a/src/Coxeter_triangulation/include/gudhi/Functions/Function_Sm_in_Rd.h
+++ b/src/Coxeter_triangulation/include/gudhi/Functions/Function_Sm_in_Rd.h
@@ -13,8 +13,6 @@
 
 #include <cstdlib>  // for std::size_t
 
-#include <gudhi/Functions/Function.h>
-
 #include <Eigen/Dense>
 
 namespace Gudhi {
@@ -26,11 +24,11 @@ namespace coxeter_triangulation {
  * \brief A class for the function that defines an m-dimensional implicit sphere embedded
  * in the d-dimensional Euclidean space.
  */
-struct Function_Sm_in_Rd : public Function {
+struct Function_Sm_in_Rd {
   /** \brief Value of the function at a specified point.
    * @param[in] p The input point. The dimension needs to coincide with the ambient dimension.
    */
-  virtual Eigen::VectorXd operator()(const Eigen::VectorXd& p) const override {
+  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
     Eigen::VectorXd x = p;
     for (std::size_t i = 0; i < d_; ++i) x(i) -= center_[i];
     Eigen::VectorXd result = Eigen::VectorXd::Zero(k_);
@@ -41,13 +39,13 @@ struct Function_Sm_in_Rd : public Function {
   }
 
   /** \brief Returns the domain dimension. Same as the ambient dimension of the sphere. */
-  virtual std::size_t amb_d() const override { return d_; };
+  std::size_t amb_d() const { return d_; };
 
   /** \brief Returns the codomain dimension. Same as the codimension of the sphere. */
-  virtual std::size_t cod_d() const override { return k_; };
+  std::size_t cod_d() const { return k_; };
 
   /** \brief Returns a point on the sphere. */
-  virtual Eigen::VectorXd seed() const override {
+  Eigen::VectorXd seed() const {
     Eigen::VectorXd result = Eigen::VectorXd::Zero(d_);
     result(0) += r_;
     for (std::size_t i = 0; i < d_; ++i) result(i) += center_[i];
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Function_affine_plane_in_Rd.h b/src/Coxeter_triangulation/include/gudhi/Functions/Function_affine_plane_in_Rd.h
index b7414cda..b29f0906 100644
--- a/src/Coxeter_triangulation/include/gudhi/Functions/Function_affine_plane_in_Rd.h
+++ b/src/Coxeter_triangulation/include/gudhi/Functions/Function_affine_plane_in_Rd.h
@@ -13,8 +13,6 @@
 
 #include <cstdlib>  // for std::size_t
 
-#include <gudhi/Functions/Function.h>
-
 #include <Eigen/Dense>
 
 namespace Gudhi {
@@ -26,24 +24,24 @@ namespace coxeter_triangulation {
  * \brief A class for the function that defines an m-dimensional implicit affine plane
  * embedded in d-dimensional Euclidean space.
  */
-struct Function_affine_plane_in_Rd : public Function {
+struct Function_affine_plane_in_Rd {
   /**
    * \brief Value of the function at a specified point.
    * @param[in] p The input point. The dimension needs to coincide with the ambient dimension.
    */
-  virtual Eigen::VectorXd operator()(const Eigen::VectorXd& p) const override {
+  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
     Eigen::VectorXd result = normal_matrix_.transpose() * (p - off_);
     return result;
   }
 
   /** \brief Returns the domain dimension. Same as the ambient dimension of the sphere. */
-  virtual std::size_t amb_d() const override { return d_; };
+  std::size_t amb_d() const { return d_; };
 
   /** \brief Returns the codomain dimension. Same as the codimension of the sphere. */
-  virtual std::size_t cod_d() const override { return k_; };
+  std::size_t cod_d() const { return k_; };
 
   /** \brief Returns a point on the affine plane. */
-  virtual Eigen::VectorXd seed() const override {
+  Eigen::VectorXd seed() const {
     Eigen::VectorXd result = off_;
     return result;
   }
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Function_chair_in_R3.h b/src/Coxeter_triangulation/include/gudhi/Functions/Function_chair_in_R3.h
index b30f964f..620446da 100644
--- a/src/Coxeter_triangulation/include/gudhi/Functions/Function_chair_in_R3.h
+++ b/src/Coxeter_triangulation/include/gudhi/Functions/Function_chair_in_R3.h
@@ -14,8 +14,6 @@
 #include <cstdlib>  // for std::size_t
 #include <cmath>    // for std::pow
 
-#include <gudhi/Functions/Function.h>
-
 #include <Eigen/Dense>
 
 namespace Gudhi {
@@ -27,12 +25,12 @@ namespace coxeter_triangulation {
  * \brief A class that encodes the function, the zero-set of which is a so-called
  * "chair" surface embedded in R^3.
  */
-struct Function_chair_in_R3 : public Function {
+struct Function_chair_in_R3 {
   /**
    * \brief Value of the function at a specified point.
    * @param[in] p The input point. The dimension needs to coincide with the ambient dimension.
    */
-  virtual Eigen::VectorXd operator()(const Eigen::VectorXd& p) const override {
+  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
     double x = p(0) - off_[0], y = p(1) - off_[1], z = p(2) - off_[2];
     Eigen::VectorXd result(cod_d());
     result(0) = std::pow(x * x + y * y + z * z - a_ * k_ * k_, 2) -
@@ -41,13 +39,13 @@ struct Function_chair_in_R3 : public Function {
   }
 
   /** \brief Returns the domain (ambient) dimension. */
-  virtual std::size_t amb_d() const override { return 3; }
+  std::size_t amb_d() const { return 3; }
 
   /** \brief Returns the codomain dimension. */
-  virtual std::size_t cod_d() const override { return 1; }
+  std::size_t cod_d() const { return 1; }
 
   /** \brief Returns a point on the surface. */
-  virtual Eigen::VectorXd seed() const override {
+  Eigen::VectorXd seed() const {
     double t1 = a_ - b_;
     double discr = t1 * t1 - (1.0 - b_) * (a_ * a_ - b_);
     double z0 = k_ * std::sqrt((t1 + std::sqrt(discr)) / (1 - b_));
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Function_iron_in_R3.h b/src/Coxeter_triangulation/include/gudhi/Functions/Function_iron_in_R3.h
index def2a99c..f73c4280 100644
--- a/src/Coxeter_triangulation/include/gudhi/Functions/Function_iron_in_R3.h
+++ b/src/Coxeter_triangulation/include/gudhi/Functions/Function_iron_in_R3.h
@@ -14,8 +14,6 @@
 #include <cstdlib>  // for std::size_t
 #include <cmath>    // for std::pow
 
-#include <gudhi/Functions/Function.h>
-
 #include <Eigen/Dense>
 
 namespace Gudhi {
@@ -27,12 +25,12 @@ namespace coxeter_triangulation {
  * \brief A class that encodes the function, the zero-set of which is a surface
  * embedded in R^3 that ressembles an iron.
  */
-struct Function_iron_in_R3 : public Function {
+struct Function_iron_in_R3 {
   /**
    * \brief Value of the function at a specified point.
    * @param[in] p The input point. The dimension needs to coincide with the ambient dimension.
    */
-  virtual Eigen::VectorXd operator()(const Eigen::VectorXd& p) const override {
+  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
     double x = p(0), y = p(1), z = p(2);
     Eigen::VectorXd result(cod_d());
     result(0) = -std::pow(x, 6) / 300. - std::pow(y, 6) / 300. - std::pow(z, 6) / 300. + x * y * y * z / 2.1 + y * y +
@@ -41,13 +39,13 @@ struct Function_iron_in_R3 : public Function {
   }
 
   /** \brief Returns the domain (ambient) dimension. */
-  virtual std::size_t amb_d() const override { return 3; };
+  std::size_t amb_d() const { return 3; };
 
   /** \brief Returns the codomain dimension. */
-  virtual std::size_t cod_d() const override { return 1; };
+  std::size_t cod_d() const { return 1; };
 
   /** \brief Returns a point on the surface. */
-  virtual Eigen::VectorXd seed() const override {
+  Eigen::VectorXd seed() const {
     Eigen::Vector3d result(std::pow(4500, 1. / 6), 0, 0);
     return result;
   }
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Function_lemniscate_revolution_in_R3.h b/src/Coxeter_triangulation/include/gudhi/Functions/Function_lemniscate_revolution_in_R3.h
index f36ccd3c..beb41e00 100644
--- a/src/Coxeter_triangulation/include/gudhi/Functions/Function_lemniscate_revolution_in_R3.h
+++ b/src/Coxeter_triangulation/include/gudhi/Functions/Function_lemniscate_revolution_in_R3.h
@@ -14,8 +14,6 @@
 #include <cstdlib>  // for std::size_t
 #include <cmath>    // for std::sqrt
 
-#include <gudhi/Functions/Function.h>
-
 #include <Eigen/Dense>
 
 namespace Gudhi {
@@ -27,12 +25,12 @@ namespace coxeter_triangulation {
  * \brief A class that encodes the function, the zero-set of which is a surface of revolution
  * around the x axis based on the lemniscate of Bernoulli embedded in R^3.
  */
-struct Function_lemniscate_revolution_in_R3 : public Function {
+struct Function_lemniscate_revolution_in_R3 {
   /**
    * \brief Value of the function at a specified point.
    * @param[in] p The input point. The dimension needs to coincide with the ambient dimension.
    */
-  virtual Eigen::VectorXd operator()(const Eigen::VectorXd& p) const override {
+  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
     double x = p(0) - off_[0], y = p(1) - off_[1], z = p(2) - off_[2];
     Eigen::VectorXd result(cod_d());
     double x2 = x * x, y2 = y * y, z2 = z * z, a2 = a_ * a_;
@@ -42,16 +40,16 @@ struct Function_lemniscate_revolution_in_R3 : public Function {
   }
 
   /** \brief Returns the (ambient) domain dimension.*/
-  virtual std::size_t amb_d() const override { return 3; };
+  std::size_t amb_d() const { return 3; };
 
   /** \brief Returns the codomain dimension. */
-  virtual std::size_t cod_d() const override { return 1; };
+  std::size_t cod_d() const { return 1; };
 
   /** \brief Returns a point on the surface. This seed point is only one of
    * two necessary seed points for the manifold tracing algorithm.
    * See the method seed2() for the other point.
    */
-  virtual Eigen::VectorXd seed() const override {
+  Eigen::VectorXd seed() const {
     Eigen::Vector3d result(std::sqrt(2 * a_) + off_[0], off_[1], off_[2]);
     return result;
   }
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Function_moment_curve_in_Rd.h b/src/Coxeter_triangulation/include/gudhi/Functions/Function_moment_curve_in_Rd.h
index 0db8289b..11b379f3 100644
--- a/src/Coxeter_triangulation/include/gudhi/Functions/Function_moment_curve_in_Rd.h
+++ b/src/Coxeter_triangulation/include/gudhi/Functions/Function_moment_curve_in_Rd.h
@@ -13,8 +13,6 @@
 
 #include <cstdlib>  // for std::size_t
 
-#include <gudhi/Functions/Function.h>
-
 #include <Eigen/Dense>
 
 namespace Gudhi {
@@ -26,24 +24,24 @@ namespace coxeter_triangulation {
  * \brief A class for the function that defines an implicit moment curve
  * in the d-dimensional Euclidean space.
  */
-struct Function_moment_curve_in_Rd : public Function {
+struct Function_moment_curve_in_Rd {
   /** \brief Value of the function at a specified point.
    * @param[in] p The input point. The dimension needs to coincide with the ambient dimension.
    */
-  virtual Eigen::VectorXd operator()(const Eigen::VectorXd& p) const override {
+  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
     Eigen::VectorXd result(k_);
     for (std::size_t i = 1; i < d_; ++i) result(i - 1) = p(i) - p(0) * p(i - 1);
     return result;
   }
 
   /** \brief Returns the domain (ambient) dimension.. */
-  virtual std::size_t amb_d() const override { return d_; };
+  std::size_t amb_d() const { return d_; };
 
   /** \brief Returns the codomain dimension. */
-  virtual std::size_t cod_d() const override { return k_; };
+  std::size_t cod_d() const { return k_; };
 
   /** \brief Returns a point on the moment curve. */
-  virtual Eigen::VectorXd seed() const override {
+  Eigen::VectorXd seed() const {
     Eigen::VectorXd result = Eigen::VectorXd::Zero(d_);
     return result;
   }
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Function_torus_in_R3.h b/src/Coxeter_triangulation/include/gudhi/Functions/Function_torus_in_R3.h
index 4aa50cfd..b54d3c74 100644
--- a/src/Coxeter_triangulation/include/gudhi/Functions/Function_torus_in_R3.h
+++ b/src/Coxeter_triangulation/include/gudhi/Functions/Function_torus_in_R3.h
@@ -14,8 +14,6 @@
 #include <cstdlib>  // for std::size_t
 #include <cmath>    // for std::sqrt
 
-#include <gudhi/Functions/Function.h>
-
 #include <Eigen/Dense>
 
 namespace Gudhi {
@@ -27,12 +25,12 @@ namespace coxeter_triangulation {
  * \brief A class that encodes the function, the zero-set of which is a torus
  * surface embedded in R^3.
  */
-struct Function_torus_in_R3 : public Function {
+struct Function_torus_in_R3 {
   /**
    * \brief Value of the function at a specified point.
    * @param[in] p The input point. The dimension needs to coincide with the ambient dimension.
    */
-  virtual Eigen::VectorXd operator()(const Eigen::VectorXd& p) const override {
+  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
     double x = p(0) - off_[0], y = p(1) - off_[1], z = p(2) - off_[2];
     Eigen::VectorXd result(cod_d());
     result(0) = (z * z + (std::sqrt(x * x + y * y) - r_) * (std::sqrt(x * x + y * y) - r_) - R_ * R_);
@@ -40,13 +38,13 @@ struct Function_torus_in_R3 : public Function {
   }
 
   /** \brief Returns the domain (ambient) dimension. */
-  virtual std::size_t amb_d() const override { return 3; };
+  std::size_t amb_d() const { return 3; };
 
   /** \brief Returns the codomain dimension. */
-  virtual std::size_t cod_d() const override { return 1; };
+  std::size_t cod_d() const { return 1; };
 
   /** \brief Returns a point on the surface. */
-  virtual Eigen::VectorXd seed() const override {
+  Eigen::VectorXd seed() const {
     Eigen::Vector3d result(R_ + r_ + off_[0], off_[1], off_[2]);
     return result;
   }
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Function_whitney_umbrella_in_R3.h b/src/Coxeter_triangulation/include/gudhi/Functions/Function_whitney_umbrella_in_R3.h
index a37fec1c..df1f1eec 100644
--- a/src/Coxeter_triangulation/include/gudhi/Functions/Function_whitney_umbrella_in_R3.h
+++ b/src/Coxeter_triangulation/include/gudhi/Functions/Function_whitney_umbrella_in_R3.h
@@ -13,8 +13,6 @@
 
 #include <cstdlib>  // for std::size_t
 
-#include <gudhi/Functions/Function.h>
-
 #include <Eigen/Dense>
 
 namespace Gudhi {
@@ -26,12 +24,12 @@ namespace coxeter_triangulation {
  * \brief A class that encodes the function, the zero-set of which is the Whitney umbrella
  * surface embedded in R^3.
  */
-struct Function_whitney_umbrella_in_R3 : public Function {
+struct Function_whitney_umbrella_in_R3 {
   /**
    * \brief Value of the function at a specified point.
    * @param[in] p The input point. The dimension needs to coincide with the ambient dimension.
    */
-  virtual Eigen::VectorXd operator()(const Eigen::VectorXd& p) const override {
+  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
     double x = p(0) - off_[0], y = p(1) - off_[1], z = p(2) - off_[2];
     Eigen::VectorXd result(cod_d());
     result(0) = x * x - y * y * z;
@@ -39,16 +37,16 @@ struct Function_whitney_umbrella_in_R3 : public Function {
   }
 
   /** \brief Returns the (ambient) domain dimension.*/
-  virtual std::size_t amb_d() const override { return 3; };
+  std::size_t amb_d() const { return 3; };
 
   /** \brief Returns the codomain dimension. */
-  virtual std::size_t cod_d() const override { return 1; };
+  std::size_t cod_d() const { return 1; };
 
   /** \brief Returns a point on the surface. This seed point is only one of
    * two necessary seed points for the manifold tracing algorithm.
    * See the method seed2() for the other point.
    */
-  virtual Eigen::VectorXd seed() const override {
+  Eigen::VectorXd seed() const {
     Eigen::Vector3d result(1 + off_[0], 1 + off_[1], 1 + off_[2]);
     return result;
   }
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Linear_transformation.h b/src/Coxeter_triangulation/include/gudhi/Functions/Linear_transformation.h
index 9228d487..82e25bb9 100644
--- a/src/Coxeter_triangulation/include/gudhi/Functions/Linear_transformation.h
+++ b/src/Coxeter_triangulation/include/gudhi/Functions/Linear_transformation.h
@@ -13,8 +13,6 @@
 
 #include <cstdlib>  // for std::size_t
 
-#include <gudhi/Functions/Function.h>
-
 #include <Eigen/Dense>
 
 namespace Gudhi {
@@ -29,24 +27,24 @@ namespace coxeter_triangulation {
  * the concept FunctionForImplicitManifold.
  */
 template <class Function_>
-struct Linear_transformation : public Function {
+struct Linear_transformation {
   /**
    * \brief Value of the function at a specified point.
    * @param[in] p The input point. The dimension needs to coincide with the ambient dimension.
    */
-  virtual Eigen::VectorXd operator()(const Eigen::VectorXd& p) const override {
+  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
     Eigen::VectorXd result = fun_(matrix_.householderQr().solve(p));
     return result;
   }
 
   /** \brief Returns the domain (ambient) dimension. */
-  virtual std::size_t amb_d() const override { return fun_.amb_d(); }
+  std::size_t amb_d() const { return fun_.amb_d(); }
 
   /** \brief Returns the codomain dimension. */
-  virtual std::size_t cod_d() const override { return fun_.cod_d(); }
+  std::size_t cod_d() const { return fun_.cod_d(); }
 
   /** \brief Returns a point on the zero-set. */
-  virtual Eigen::VectorXd seed() const override {
+  Eigen::VectorXd seed() const {
     Eigen::VectorXd result = fun_.seed();
     result = matrix_ * result;
     return result;
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Negation.h b/src/Coxeter_triangulation/include/gudhi/Functions/Negation.h
index 1c202cd5..fdf07f27 100644
--- a/src/Coxeter_triangulation/include/gudhi/Functions/Negation.h
+++ b/src/Coxeter_triangulation/include/gudhi/Functions/Negation.h
@@ -13,8 +13,6 @@
 
 #include <cstdlib>  // for std::size_t
 
-#include <gudhi/Functions/Function.h>
-
 #include <Eigen/Dense>
 
 namespace Gudhi {
@@ -30,24 +28,24 @@ namespace coxeter_triangulation {
  * the concept FunctionForImplicitManifold.
  */
 template <class Function_>
-struct Negation : public Function {
+struct Negation {
   /**
    * \brief Value of the function at a specified point.
    * @param[in] p The input point. The dimension needs to coincide with the ambient dimension.
    */
-  virtual Eigen::VectorXd operator()(const Eigen::VectorXd& p) const override {
+  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
     Eigen::VectorXd result = -fun_(p);
     return result;
   }
 
   /** \brief Returns the domain (ambient) dimension. */
-  virtual std::size_t amb_d() const override { return fun_.amb_d(); }
+  std::size_t amb_d() const { return fun_.amb_d(); }
 
   /** \brief Returns the codomain dimension. */
-  virtual std::size_t cod_d() const override { return fun_.cod_d(); }
+  std::size_t cod_d() const { return fun_.cod_d(); }
 
   /** \brief Returns a point on the zero-set. */
-  virtual Eigen::VectorXd seed() const override {
+  Eigen::VectorXd seed() const {
     Eigen::VectorXd result = fun_.seed();
     return result;
   }
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/PL_approximation.h b/src/Coxeter_triangulation/include/gudhi/Functions/PL_approximation.h
index 20d4e6a8..22071d6d 100644
--- a/src/Coxeter_triangulation/include/gudhi/Functions/PL_approximation.h
+++ b/src/Coxeter_triangulation/include/gudhi/Functions/PL_approximation.h
@@ -13,8 +13,6 @@
 
 #include <cstdlib>  // for std::size_t
 
-#include <gudhi/Functions/Function.h>
-
 #include <Eigen/Dense>
 
 namespace Gudhi {
@@ -26,18 +24,18 @@ namespace coxeter_triangulation {
  * \brief Constructs a piecewise-linear approximation of a function induced by
  * an ambient triangulation.
  *
- * \tparam Function The function template parameter. Should be a model of
+ * \tparam Function_ The function template parameter. Should be a model of
  * the concept FunctionForImplicitManifold.
  * \tparam Triangulation The triangulation template parameter. Should be a model of
  * the concept TriangulationForManifoldTracing.
  */
 template <class Function_, class Triangulation_>
-struct PL_approximation : public Function {
+struct PL_approximation {
   /**
    * \brief Value of the function at a specified point.
    * @param[in] p The input point. The dimension needs to coincide with the ambient dimension.
    */
-  virtual Eigen::VectorXd operator()(const Eigen::VectorXd& p) const override {
+  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
     std::size_t cod_d = this->cod_d();
     std::size_t amb_d = this->amb_d();
     auto s = tr_.locate_point(p);
@@ -62,13 +60,13 @@ struct PL_approximation : public Function {
   }
 
   /** \brief Returns the domain (ambient) dimension. */
-  virtual std::size_t amb_d() const override { return fun_.amb_d(); }
+  std::size_t amb_d() const { return fun_.amb_d(); }
 
   /** \brief Returns the codomain dimension. */
-  virtual std::size_t cod_d() const override { return fun_.cod_d(); }
+  std::size_t cod_d() const { return fun_.cod_d(); }
 
   /** \brief Returns a point on the zero-set. */
-  virtual Eigen::VectorXd seed() const override {
+  Eigen::VectorXd seed() const {
     // TODO: not finished. Should use an oracle.
     return Eigen::VectorXd(amb_d());
   }
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Translate.h b/src/Coxeter_triangulation/include/gudhi/Functions/Translate.h
index fc91a118..cbe65abe 100644
--- a/src/Coxeter_triangulation/include/gudhi/Functions/Translate.h
+++ b/src/Coxeter_triangulation/include/gudhi/Functions/Translate.h
@@ -13,8 +13,6 @@
 
 #include <cstdlib>  // for std::size_t
 
-#include <gudhi/Functions/Function.h>
-
 #include <Eigen/Dense>
 
 namespace Gudhi {
@@ -30,24 +28,24 @@ namespace coxeter_triangulation {
  * the concept FunctionForImplicitManifold.
  */
 template <class Function_>
-struct Translate : public Function {
+struct Translate {
   /**
    * \brief Value of the function at a specified point.
    * @param[in] p The input point. The dimension needs to coincide with the ambient dimension.
    */
-  virtual Eigen::VectorXd operator()(const Eigen::VectorXd& p) const override {
+  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
     Eigen::VectorXd result = fun_(p - off_);
     return result;
   }
 
   /** \brief Returns the domain (ambient) dimension. */
-  virtual std::size_t amb_d() const override { return fun_.amb_d(); }
+  std::size_t amb_d() const { return fun_.amb_d(); }
 
   /** \brief Returns the codomain dimension. */
-  virtual std::size_t cod_d() const override { return fun_.cod_d(); }
+  std::size_t cod_d() const { return fun_.cod_d(); }
 
   /** \brief Returns a point on the zero-set. */
-  virtual Eigen::VectorXd seed() const override {
+  Eigen::VectorXd seed() const {
     Eigen::VectorXd result = fun_.seed();
     result += off_;
     return result;