[zonotope] added operator+ and renamed center c

doc/manual/development/changelog.rst

@@ -3,6 +3,14 @@
 Changelog
 =========
 
+Upcoming version 
+****************
+
+Pull Request #379 from godardma (27/04)
+---------------------------------------
+
+``Zonotope`` and ``Parallelepiped`` center is now ``c`` instead of ``z`` to avoid ambiguity.
+
 Version 2.0.2
 *************
 

doc/manual/manual/geometry/zonotope.rst

@@ -16,13 +16,13 @@ A zonotope is a convex and symmetric polytope.
 It can be represented as the Minkowski sum of a finite number of line segments, which are called its generators.
 
 In Codac, zonotopes are represented by the class :class:`Zonotope`. A zonotope is defined by its center and its generators.
-The center is a :class:`Vector`, noted :math:`z`, and the generators are stored in a :class:`Matrix`, noted :math:`A`. 
+The center is a :class:`Vector`, noted :math:`\mathbf{c}`, and the generators are stored in a :class:`Matrix`, noted :math:`\mathbf{A}`. 
 Each column of the matrix corresponds to a generator.
 
 The resulting zonotope is:
 
 .. math::
-  Z = z + A \cdot [-1,1]^m
+  Z = \mathbf{c} + \mathbf{A} \cdot [-1,1]^m
 
 Where :math:`m` is the number of generators (i.e., the number of columns of the matrix :math:`A`).
 
@@ -37,24 +37,24 @@ It can be constructed in Codac as follows:
 
   .. code-tab:: py
 
-    z = Vector([1,2])
+    c = Vector([1,2])
     A = Matrix([[1,0,2],[0,1,1]])
 
-    Z = Zonotope(z, A)
+    Z = Zonotope(c, A)
 
   .. code-tab:: c++
 
-    Vector z({1,2});
+    Vector c({1,2});
     Matrix A({{1,0,2},{0,1,1}});
 
-    Zonotope Z(z, A);
+    Zonotope Z(c, A);
 
   .. code-tab:: matlab
 
-    z = Vector({1,2});
+    c = Vector({1,2});
     A = Matrix({{1,0,2},{0,1,1}});
 
-    Z = Zonotope(z,A);
+    Z = Zonotope(c,A);
 
 The resulting zonotope is represented in the figure below:
 

python/src/core/domains/zonotope/codac2_py_Zonotope.cpp

@@ -39,8 +39,12 @@ void export_Zonotope(py::module& m)
       ZONOTOPE_ZONOTOPE_PROJ_CONST_VECTOR_INDEX_REF_CONST,
       "indices"_a)
 
-    .def_readwrite("z", &Zonotope::z,
-      VECTOR_ZONOTOPE_Z)
+    .def("__add__", &Zonotope::operator+,
+      ZONOTOPE_ZONOTOPE_OPERATORPLUS_CONST_ZONOTOPE_REF,
+      py::is_operator())
+
+    .def_readwrite("c", &Zonotope::c,
+      VECTOR_ZONOTOPE_C)
 
     .def_readwrite("A", &Zonotope::A,
       MATRIX_ZONOTOPE_A)

python/src/graphics/figures/codac2_py_Figure3D.cpp

@@ -35,8 +35,8 @@ void export_Figure3D(py::module& m)
       CONST_STRING_REF_FIGURE3D_NAME_CONST)
 
     .def("draw_axes", &Figure3D::draw_axes,
-      VOID_FIGURE3D_DRAW_AXES_DOUBLE,
-      "size"_a=1.0)
+      VOID_FIGURE3D_DRAW_AXES_DOUBLE_CONST_VECTOR_REF,
+      "size"_a=1.0, "origin"_a=Vector::Zero(3))
 
     // Geometric shapes
     .def("draw_triangle", (void(Figure3D::*)(const Vector &c, const Matrix &A, const Vector &p1, const Vector &p2, const Vector &p3, const StyleProperties &s))&Figure3D::draw_triangle,

src/core/domains/zonotope/codac2_Parallelepiped.cpp

@@ -12,29 +12,29 @@
 
 using namespace codac2;
 
-Parallelepiped::Parallelepiped(const Vector& z_, const Matrix& A_)
-  : Zonotope(z_, A_)
+Parallelepiped::Parallelepiped(const Vector& c_, const Matrix& A_)
+  : Zonotope(c_, A_)
 {
-  assert_release(A.cols() <= z.size() && "too many vectors, you are describing a zonotope");
+  assert_release(A.cols() <= c.size() && "too many vectors, you are describing a zonotope");
 }
 
-void generate_vertices(Index i, Index n, const Vector& z, const Matrix& A, std::vector<Vector>& L_v)
+void generate_vertices(Index i, Index n, const Vector& c, const Matrix& A, std::vector<Vector>& L_v)
 {
   if (i == n)
   {
-    L_v.push_back(z);
+    L_v.push_back(c);
   }
   else if (i<n)
   {
-    generate_vertices(i+1, n, z + A.col(i), A, L_v);
-    generate_vertices(i+1, n, z - A.col(i), A, L_v);
+    generate_vertices(i+1, n, c + A.col(i), A, L_v);
+    generate_vertices(i+1, n, c - A.col(i), A, L_v);
   }
 }
 
 std::vector<Vector> Parallelepiped::vertices() const
 {
   std::vector<Vector> L_v;
-  generate_vertices(0, z.size(),z,A,L_v);
+  generate_vertices(0, c.size(),c,A,L_v);
   return L_v;
 }
 
@@ -46,9 +46,9 @@ BoolInterval Parallelepiped::contains(const Vector& v) const
 BoolInterval Parallelepiped::is_superset(const IntervalVector& x) const
 {
   assert_release(A.rows() == A.cols() && "Matrix A must be square to check containment.");
-  assert_release(x.size() == z.size() && "Point dimension must match parallelepiped dimension.");
+  assert_release(x.size() == c.size() && "Point dimension must match parallelepiped dimension.");
 
-  IntervalVector B = inverse_enclosure(A)*(x - z);
+  IntervalVector B = inverse_enclosure(A)*(x - c);
   IntervalVector IV = IntervalVector::constant(A.cols(),{-1,1});
 
   if (!(B.intersects(IV)))

src/core/domains/zonotope/codac2_Parallelepiped.h

@@ -21,9 +21,9 @@ namespace codac2
   /**
    * \class Parallelepiped
    * 
-   * \brief Class representing a parallelepiped \f$\mathbf{z} + \mathbf{A}\cdot[-1,1]^m\f$
+   * \brief Class representing a parallelepiped \f$\mathbf{c} + \mathbf{A}\cdot[-1,1]^m\f$
    * 
-   * This class represents a parallelepiped in n-dimensional space, defined by a center point \f$\mathbf{z}\f$ and a shape matrix \f$\mathbf{A}\f$.
+   * This class represents a parallelepiped in n-dimensional space, defined by a center point \f$\mathbf{c}\f$ and a shape matrix \f$\mathbf{A}\f$.
    * 
    * A parallelepiped is a special case of a zonotope where the shape matrix \f$\mathbf{A}\f$ has \f$m\f$ columns with \f$m \leqslant n\f$.
    */
@@ -34,10 +34,10 @@ namespace codac2
       /**
        * \brief Constructs a n-parallelepiped object with a given center and shape matrix
        * 
-       * \param z Center of the parallelepiped (n-dimensional vector)
+       * \param c Center of the parallelepiped (n-dimensional vector)
        * \param A Shape matrix of the parallelepiped (\f$n\times m\f$ matrix with \f$m \leqslant n\f$)
        */
-      Parallelepiped(const Vector& z, const Matrix& A);
+      Parallelepiped(const Vector& c, const Matrix& A);
 
       /**
        * \brief Computes the vertices of the parallelepiped

src/core/domains/zonotope/codac2_Zonotope.cpp

@@ -11,31 +11,42 @@
 
 using namespace codac2;
 
-Zonotope::Zonotope(const Vector& z_, const Matrix& A_)
-  : z(z_), A(A_)
+Zonotope::Zonotope(const Vector& c_, const Matrix& A_)
+  : c(c_), A(A_)
 {
-  assert_release(z.size() == A.rows());
+  assert_release(c.size() == A.rows());
 }
 
 IntervalVector Zonotope::box() const
 {
-  return z + (A.template cast<Interval>())*IntervalVector::constant(A.cols(),{-1,1});
+  return c + (A.template cast<Interval>())*IntervalVector::constant(A.cols(),{-1,1});
 }
 
 Zonotope Zonotope::proj(const std::vector<Index>& indices) const
 {
   assert_release(*std::min_element(indices.begin(), indices.end()) >= 0 && "indices out of range");
-  assert_release(*std::max_element(indices.begin(), indices.end()) <= z.size() && "indices out of range");
+  assert_release(*std::max_element(indices.begin(), indices.end()) <= c.size() && "indices out of range");
 
   Matrix A_cropped (indices.size(), A.cols());
-  Vector z_cropped (indices.size());
+  Vector c_cropped (indices.size());
 
   for (size_t i = 0; i < indices.size(); ++i)
   {
     A_cropped.row(i) = A.row(indices[i]);
-    z_cropped[i] = z[indices[i]];
+    c_cropped[i] = c[indices[i]];
   }
 
-  return Zonotope(z_cropped, A_cropped);
+  return Zonotope(c_cropped, A_cropped);
 }
 
+Zonotope Zonotope::operator+(const Zonotope& zonotope)
+{
+  assert_release(c.size() == zonotope.c.size() && "Zonotopes must have the same dimension");
+
+  Vector c_sum = c + zonotope.c;
+  Matrix A_sum (A.rows(), A.cols() + zonotope.A.cols());
+
+  A_sum << A, zonotope.A;
+
+  return Zonotope(c_sum, A_sum);
+}

src/core/domains/zonotope/codac2_Zonotope.h

@@ -18,11 +18,11 @@ namespace codac2
 {
   /**
    * \class Zonotope
-   * \brief Class representing a zonotope \f$\mathbf{z} + \mathbf{A}\cdot[-1,1]^m\f$
+   * \brief Class representing a zonotope \f$\mathbf{c} + \mathbf{A}\cdot[-1,1]^m\f$
    * 
-   * This class represents a zonotope in n-dimensional space, defined by a center point \f$\mathbf{z}\f$ and a shape matrix \f$\mathbf{A}\f$.
+   * This class represents a zonotope in n-dimensional space, defined by a center point \f$\mathbf{c}\f$ and a shape matrix \f$\mathbf{A}\f$.
    * 
-   * The vector \f$\mathbf{z}\f$ and each column of the matrix \f$\mathbf{A}\f$ must have the same dimension \f$n\f$, but the matrix \f$\mathbf{A}\f$ can have any number of columns \f$m\f$.
+   * The vector \f$\mathbf{c}\f$ and each column of the matrix \f$\mathbf{A}\f$ must have the same dimension \f$n\f$, but the matrix \f$\mathbf{A}\f$ can have any number of columns \f$m\f$.
    */
   class Zonotope
   {
@@ -31,10 +31,10 @@ namespace codac2
       /**
        * \brief Constructs a n-zonotope object with a given center and shape matrix
        * 
-       * \param z Center of the zonotope (n-dimensional vector)
+       * \param c Center of the zonotope (n-dimensional vector)
        * \param A Shape matrix of the zonotope (\f$n\times m\f$ matrix)
        */
-      Zonotope(const Vector& z, const Matrix& A);
+      Zonotope(const Vector& c, const Matrix& A);
 
       /**
        * \brief Computes the axis-aligned bounding box of the zonotope
@@ -52,10 +52,19 @@ namespace codac2
        */
       Zonotope proj(const std::vector<Index>& indices) const;
 
+      /**
+       * \brief Computes the Minkowski sum of this Zonotope with another Zonotope
+       * 
+       * \param zonotope The other Zonotope to add to this one
+       * 
+       * \return A new Zonotope object representing the Minkowski sum of the two Zonotopes
+       */
+      Zonotope operator+(const Zonotope& zonotope);
+
       /**
        * \brief Center of the zonotope
        */
-      Vector z;
+      Vector c;
 
       /**
        * \brief Shape matrix of the zonotope

src/core/functions/analytic/codac2_AnalyticFunction.h

@@ -220,17 +220,17 @@ namespace codac2
                     "Parallelepiped evaluation requires at least one input.");
 
         IntervalVector Y = this->eval(((typename Wrapper<Args>::Domain)(x)).mid()...);
-        Vector z = Y.mid();
+        Vector c = Y.mid();
 
         Matrix A = this->diff(((typename Wrapper<Args>::Domain)(x)).mid()...).mid();
 
         // Maximum error computation
-        double rho = error_peibos(Y, z, this->diff(x...), A, cart_prod(x...));
+        double rho = error_peibos(Y, c, this->diff(x...), A, cart_prod(x...));
 
         // Inflation of the parallelepiped
         Matrix A_inf = inflate_flat_parallelepiped(A, (cart_prod(x...).template cast<Interval>()).rad(), rho);
 
-        return Parallelepiped(z, A_inf);
+        return Parallelepiped(c, A_inf);
       }
 
       Index output_size() const

src/graphics/figures/codac2_Figure2D.cpp

@@ -255,7 +255,7 @@ void Figure2D::draw_zonotope(const Zonotope& z, const StyleProperties& style)
        }
    }
    vector<Vector> vertices;
-   Vector point=z.z;
+   Vector point=z.c;
    // Start from v[1] maximum (and v[0] min for horizontal side)
    for (const auto& a : sides) {
        point+=a.second;
@@ -277,17 +277,17 @@ void Figure2D::draw_zonotope(const Zonotope& z, const StyleProperties& style)
 
 void Figure2D::draw_parallelepiped(const Parallelepiped& p, const StyleProperties& style)
 {
-  assert_release(p.A.is_squared() && p.A.rows() == p.z.size());
-  assert_release(p.z.size() == 2);
+  assert_release(p.A.is_squared() && p.A.rows() == p.c.size());
+  assert_release(p.c.size() == 2);
 
   auto a1 = p.A.col(0), a2 = p.A.col(1);
 
   if (a1.isZero() || a2.isZero())
-      draw_polyline({p.z-a1-a2,p.z+a1+a2}, style);
+      draw_polyline({p.c-a1-a2,p.c+a1+a2}, style);
   else
     draw_polygon({
-        p.z+a1+a2, p.z-a1+a2,
-        p.z-a1-a2, p.z+a1-a2
+        p.c+a1+a2, p.c-a1+a2,
+        p.c-a1-a2, p.c+a1-a2
       }, style);
 }
 

src/graphics/figures/codac2_Figure2D.h

@@ -310,7 +310,7 @@ namespace codac2
       void draw_parallelepiped(const Parallelepiped& p, const StyleProperties& style = StyleProperties());
 
       /**
-       * \brief Draws a zonotope z+sum_i [-1,1] A_i on the figure
+       * \brief Draws a zonotope c+sum_i [-1,1] A_i on the figure
        * 
        * \param z Zonotope to draw (center and shape matrix)
        * \param style Style of the zonotope (edge color and fill color)
@@ -856,15 +856,15 @@ namespace codac2
       }
 
       /**
-       * \brief Draws a zonotope z+sum_i [-1,1] A_i on the figure
+       * \brief Draws a zonotope c+sum_i [-1,1] A_i on the figure
        * 
-       * \param z Zonotope to draw (center and shape matrix)
+       * \param c Zonotope to draw (center and shape matrix)
        * \param style Style of the zonotope (edge color and fill color)
        */
-      static void draw_zonotope(const Zonotope& z, const StyleProperties& style = StyleProperties())
+      static void draw_zonotope(const Zonotope& c, const StyleProperties& style = StyleProperties())
       {
         auto_init();
-        selected_fig()->draw_zonotope(z,style);
+        selected_fig()->draw_zonotope(c,style);
       }
 
       /**