Ticket #12083: trac_12083_unholy_rebase_to_sage-5.0.patch

sage/geometry/polyhedron/plot.py

@@ -17 +17 @@
 from sage.modules.free_module_element import vector
 from sage.matrix.constructor import matrix, identity_matrix
 from sage.misc.functional import norm
+from sage.misc.latex import LatexExpr
+from sage.symbolic.constants import pi
 from sage.structure.sequence import Sequence
 
 from sage.plot.all import point2d, line2d, arrow, polygon2d
 from sage.plot.plot3d.all import point3d, line3d, arrow3d, polygon3d
+from sage.plot.plot3d.transform import rotate_arbitrary
 from sage.graphs.graph import Graph
 
 from base import is_Polyhedron
@@ -402 +405 @@
             sage: proj.show()
             sage: TestSuite(proj).run(skip='_test_pickling')
         """
+        self.parent_polyhedron = polyhedron
         self.coords = Sequence([])
         self.points = Sequence([])
         self.lines  = Sequence([])
@@ -794 +798 @@
                     yield ineq
 
         faces = []
+        face_inequalities = []
         for facet_equation in defining_equation():
+            face_inequalities.append(facet_equation)
             vertices = [v for v in facet_equation.incident()]
             vertices = cyclic_sort_vertices_2d(vertices)
             coords = []
@@ -814 +820 @@
 
             faces.append(coords)
 
+        self.face_inequalities = face_inequalities
+
         if polyhedron.n_lines() == 0:
             assert len(faces)>0, "no vertices?"
             self.polygons.extend( [self.coord_indices_of(f) for f in faces] )
@@ -945 +953 @@
         """
         return sum([ polygon3d(self.coordinates_of(f), **kwds)
                      for f in self.polygons ])
+
+
+    def tikz(self, view=[0,0,1], angle=0, scale=2,
+             edge_color='blue!95!black', facet_color='blue!95!black',
+             opacity=0.8, vertex_color='green', axis=False):
+        """
+        Return a string ``tikz_pic`` consisting of a tikz picture of ``self``
+        according to a projection ``view`` and an angle ``angle``
+        obtained via Jmol through the current state property.
+
+        INPUT:
+
+        - ``view`` - list (default: [0,0,1]) representing the rotation axis (see note below).
+        - ``angle`` - integer (default: 0) angle of rotation in degree from 0 to 360 (see note
+          below).
+        - ``scale`` - integer (default: 2) specifying the scaling of the tikz picture.
+        - ``edge_color`` - string (default: 'blue!95!black') representing colors which tikz
+          recognize.
+        - ``facet_color`` - string (default: 'blue!95!black') representing colors which tikz
+          recognize.
+        - ``vertex_color`` - string (default: 'green') representing colors which tikz
+          recognize.
+        - ``opacity`` - real number (default: 0.8) between 0 and 1 giving the opacity of
+          the front facets.
+        - ``axis`` - Boolean (default: False) draw the axes at the origin or not.
+
+        OUTPUT:
+
+        - LatexExpr -- containing the TikZ picture.
+
+        .. NOTE::
+
+            The inputs ``view`` and ``angle`` can be obtained from the viewer
+            Jmol:
+
+            1) Right click on the image;
+            2) Select ``Console``;
+            3) Select the tab ``State``;
+            4) Scroll to the line ``moveto``
+
+            It read something like::
+
+            moveto 0.0 {x y z angle} Scale
+
+            The ``view`` is then [x,y,z] and ``angle`` is angle.
+            The following number is the scale.
+            Jmol performs a rotation of ``angle`` degrees along the vector [x,y,z] and show
+            the result from the z-axis.
+
+        EXAMPLES::
+
+            sage: P1 = polytopes.small_rhombicuboctahedron()
+            sage: Image1 = P1.projection().tikz([1,3,5], 175, scale=4)
+            sage: type(Image1)
+            <class 'sage.misc.latex.LatexExpr'>
+            sage: print '\n'.join(Image1.splitlines()[:4])
+            \begin{tikzpicture}%
+                [x={(-0.939161cm, 0.244762cm)},
+                y={(0.097442cm, -0.482887cm)},
+                z={(0.329367cm, 0.840780cm)},
+            sage: open('polytope-tikz1.tex', 'w').write(Image1)    # not tested
+
+            sage: P2 = Polyhedron(vertices=[[1, 1],[1, 2],[2, 1]])
+            sage: Image2 = P2.projection().tikz(scale=3, edge_color='blue!95!black', facet_color='orange!95!black', opacity=0.4, vertex_color='yellow', axis=True)
+            sage: type(Image1)
+            <class 'sage.misc.latex.LatexExpr'>
+            sage: print '\n'.join(Image2.splitlines()[:4])
+            \begin{tikzpicture}%
+                [scale=3.000000,
+                back/.style={loosely dotted, thin},
+                edge/.style={color=blue!95!black, thick},
+            sage: open('polytope-tikz2.tex', 'w').write(Image2)    # not tested
+
+            sage: P3 = Polyhedron(vertices=[[-1, -1, 2],[-1, 2, -1],[2, -1, -1]])
+            sage: P3
+            A 2-dimensional polyhedron in QQ^3 defined as the convex hull of 3 vertices
+            sage: Image3 = P3.projection().tikz([0.5,-1,-0.1], 55, scale=3, edge_color='blue!95!black',facet_color='orange!95!black', opacity=0.7, vertex_color='yellow', axis=True)
+            sage: print '\n'.join(Image3.splitlines()[:4])
+            \begin{tikzpicture}%
+                [x={(0.658184cm, -0.242192cm)},
+                y={(-0.096240cm, 0.912008cm)},
+                z={(-0.746680cm, -0.331036cm)},
+            sage: open('polytope-tikz3.tex', 'w').write(Image3)    # not tested
+
+            sage: P=Polyhedron(vertices=[[1,1,0,0],[1,2,0,0],[2,1,0,0],[0,0,1,0],[0,0,0,1]])
+            sage: P
+            A 4-dimensional polyhedron in QQ^4 defined as the convex hull of 5 vertices
+            sage: P.projection().tikz()
+            Traceback (most recent call last):
+            ...
+            NotImplementedError: The polytope has to live in 2 or 3 dimensions.
+
+        .. TO DO::
+
+            Make it possible to draw Schlegel diagram for 4-polytope.
+
+                sage: P=Polyhedron(vertices=[[1,1,0,0],[1,2,0,0],[2,1,0,0],[0,0,1,0],[0,0,0,1]])
+                sage: P
+                A 4-dimensional polyhedron in QQ^4 defined as the convex hull of 5 vertices
+                sage: P.projection().tikz()
+                Traceback (most recent call last):
+                ...
+                NotImplementedError: The polytope has to live in 2 or 3 dimensions.
+
+            Make it possible to draw 3-polytope living in higher dimension.
+
+        """
+        if self.polyhedron_ambient_dim > 3 or self.polyhedron_ambient_dim < 2:
+            raise NotImplementedError("The polytope has to live in 2 or 3 dimensions.")
+        elif self.polyhedron_ambient_dim == 2:
+            return self._tikz_2d(scale, edge_color, facet_color, opacity,
+                                 vertex_color, axis)
+        elif self.dimension == 2:
+            return self._tikz_2d_in_3d(view, angle, scale, edge_color,
+                                       facet_color, opacity, vertex_color, axis)
+        else:
+            return self._tikz_3d_in_3d(view, angle, scale, edge_color,
+                                       facet_color, opacity, vertex_color, axis)
+
+    def _tikz_2d(self, scale, edge_color, facet_color, opacity, vertex_color, axis):
+        """
+        Return a string ``tikz_pic`` consisting of a tikz picture of ``self``
+
+        INPUT:
+
+        - ``scale`` - integer specifying the scaling of the tikz picture.
+        - ``edge_color`` - string representing colors which tikz
+          recognize.
+        - ``facet_color`` - string representing colors which tikz
+          recognize.
+        - ``vertex_color`` - string representing colors which tikz
+          recognize.
+        - ``opacity`` - real number between 0 and 1 giving the opacity of
+          the front facets.
+        - ``axis`` - Boolean (default: False) draw the axes at the origin or not.
+
+        OUTPUT:
+
+        - LatexExpr -- containing the TikZ picture.
+
+        EXAMPLES::
+
+            sage: P = Polyhedron(vertices=[[1, 1],[1, 2],[2, 1]])
+            sage: Image = P.projection()._tikz_2d(scale=3, edge_color='black', facet_color='orange', opacity=0.75, vertex_color='yellow', axis=True)
+            sage: type(Image)
+            <class 'sage.misc.latex.LatexExpr'>
+            sage: print '\n'.join(Image.splitlines()[:4])
+            \begin{tikzpicture}%
+                [scale=3.000000,
+                back/.style={loosely dotted, thin},
+                edge/.style={color=black, thick},
+            sage: open('polytope-tikz2.tex', 'w').write(Image2)    # not tested
+
+        .. NOTE::
+
+            The ``facet_color`` is the filing color of the polytope (polygon).
+        """
+
+        # Creates the nodes, coordinate and tag for every vertex of the polytope.
+        # The tag is used to draw the front facets later on.
+        dict_drawing = {}
+        edges = ''
+        for index1,index2 in self.lines:
+            v = self.coords[index1]
+            v_vect = str([i.n(digits=3) for i in v])
+            v_vect = v_vect.replace('[','(')
+            v_vect = v_vect.replace(']',')')
+            tag = '%s' %v_vect
+            node = "\\node[%s] at %s     {};\n" %('vertex',tag)
+
+            nei = self.coords[index2]
+            nei_vect = str([i.n(digits=3) for i in nei])
+            nei_vect = nei_vect.replace('[','(')
+            nei_vect = nei_vect.replace(']',')')
+            tag_nei = '%s' %nei_vect
+            edges += "\\draw[%s] %s -- %s;\n" %('edge',tag,tag_nei)
+
+            coord = '\coordinate %s at %s;\n' %(tag,tag)
+            dict_drawing[tuple(v)] = node,coord,tag
+
+        # Start to write the output
+        tikz_pic = ''
+        tikz_pic += '\\begin{tikzpicture}%\n'
+        tikz_pic += '\t[scale=%f,\n' %scale
+        tikz_pic += '\tback/.style={loosely dotted, thin},\n'
+        tikz_pic += '\tedge/.style={color=%s, thick},\n' %edge_color
+        tikz_pic += '\tfacet/.style={fill=%s,fill opacity=%f},\n' %(facet_color,opacity)
+        tikz_pic += '\tvertex/.style={inner sep=1pt,circle,draw=%s!25!black,' %vertex_color
+        tikz_pic += 'fill=%s!75!black,thick,anchor=base}]\n%%\n%%\n' %vertex_color
+
+        # Draws the axes if True
+        if axis:
+            tikz_pic += '\\draw[color=black,thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};\n'
+            tikz_pic += '\\draw[color=black,thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};\n'
+
+        # Create the coordinate of the vertices:
+        tikz_pic += '%% Coordinate of the vertices:\n%%\n'
+        for v in dict_drawing:
+            tikz_pic += dict_drawing[v][1]
+
+        # Draw the interior by going in a cycle
+        tikz_pic += '%%\n%%\n%% Drawing the interior\n%%\n'
+        cyclic_vert = cyclic_sort_vertices_2d(list(self.parent_polyhedron.Vrep_generator()))
+        tikz_pic += '\\fill[facet] '
+        for v in cyclic_vert:
+            if tuple(v) in dict_drawing:
+                tikz_pic += '%s -- ' %dict_drawing[tuple(v)][2]
+        tikz_pic += 'cycle {};\n'
+
+        # Draw the edges in the front
+        tikz_pic += '%%\n%%\n%% Drawing edges in the front\n%%\n'
+        tikz_pic += edges
+
+        # Finally, the vertices in front are drawn on top of everything.
+        tikz_pic += '%%\n%%\n%% Drawing the vertices in the front\n%%\n'
+        for v in dict_drawing:
+            tikz_pic += dict_drawing[v][0]
+        tikz_pic += '%%\n%%\n\\end{tikzpicture}'
+
+        return LatexExpr(tikz_pic)
+
+    def _tikz_2d_in_3d(self, view, angle, scale, edge_color, facet_color,
+                       opacity, vertex_color, axis):
+        """
+        Return a string ``tikz_pic`` consisting of a tikz picture of ``self``
+        according to a projection ``view`` and an angle ``angle``
+        obtained via Jmol through the current state property.
+
+        INPUT:
+
+        - ``view`` - list (default: [0,0,1]) representing the rotation axis.
+        - ``angle`` - integer angle of rotation in degree from 0 to 360.
+        - ``scale`` - integer specifying the scaling of the tikz picture.
+        - ``edge_color`` - string representing colors which tikz
+          recognize.
+        - ``facet_color`` - string representing colors which tikz
+          recognize.
+        - ``vertex_color`` - string representing colors which tikz
+          recognize.
+        - ``opacity`` - real number between 0 and 1 giving the opacity of
+          the front facets.
+        - ``axis`` - Boolean draw the axes at the origin or not.
+
+        OUTPUT:
+
+        - LatexExpr -- containing the TikZ picture.
+
+        EXAMPLE::
+
+            sage: P = Polyhedron(vertices=[[-1, -1, 2],[-1, 2, -1],[2, -1, -1]])
+            sage: P
+            A 2-dimensional polyhedron in QQ^3 defined as the convex hull of 3 vertices
+            sage: Image = P.projection()._tikz_2d_in_3d(view=[0.5,-1,-0.5], angle=55, scale=3, edge_color='blue!95!black', facet_color='orange', opacity=0.5, vertex_color='yellow', axis=True)
+            sage: print '\n'.join(Image.splitlines()[:4])
+            \begin{tikzpicture}%
+                [x={(0.644647cm, -0.476559cm)},
+                y={(0.192276cm, 0.857859cm)},
+                z={(-0.739905cm, -0.192276cm)},
+            sage: open('polytope-tikz3.tex', 'w').write(Image3)    # not tested
+
+        .. NOTE::
+
+            The ``facet_color`` is the filing color of the polytope (polygon).
+
+        """
+
+        view_vector = vector(RDF, view)
+        rot = rotate_arbitrary(view_vector,-(angle/360)*2*pi)
+        rotation_matrix = rot[:2].transpose()
+
+        # Creates the nodes, coordinate and tag for every vertex of the polytope.
+        # The tag is used to draw the front facets later on.
+        dict_drawing = {}
+        edges = ''
+        for index1, index2 in self.lines:
+            v = self.coords[index1]
+            v_vect = str([i.n(digits=3) for i in v])
+            v_vect = v_vect.replace('[','(')
+            v_vect = v_vect.replace(']',')')
+            tag = '%s' %v_vect
+            node = "\\node[%s] at %s     {};\n" %('vertex',tag)
+
+            nei = self.coords[index2]
+            nei_vect = str([i.n(digits=3) for i in nei])
+            nei_vect = nei_vect.replace('[','(')
+            nei_vect = nei_vect.replace(']',')')
+            tag_nei = '%s' %nei_vect
+            edges += "\\draw[%s] %s -- %s;\n" %('edge',tag,tag_nei)
+
+            coord = '\coordinate %s at %s;\n' %(tag,tag)
+            dict_drawing[tuple(v)] = node,coord,tag
+
+        # Start to write the output
+        tikz_pic = ''
+        tikz_pic += '\\begin{tikzpicture}%\n'
+        tikz_pic += '\t[x={(%fcm, %fcm)},\n' %(RDF(rotation_matrix[0][0]),RDF(rotation_matrix[0][1]))
+        tikz_pic += '\ty={(%fcm, %fcm)},\n' %(RDF(rotation_matrix[1][0]),RDF(rotation_matrix[1][1]))
+        tikz_pic += '\tz={(%fcm, %fcm)},\n' %(RDF(rotation_matrix[2][0]),RDF(rotation_matrix[2][1]))
+        tikz_pic += '\tscale=%f,\n' %scale
+        tikz_pic += '\tback/.style={loosely dotted, thin},\n'
+        tikz_pic += '\tedge/.style={color=%s, thick},\n' %edge_color
+        tikz_pic += '\tfacet/.style={fill=%s,fill opacity=%f},\n' %(facet_color,opacity)
+        tikz_pic += '\tvertex/.style={inner sep=1pt,circle,draw=%s!25!black,' %vertex_color
+        tikz_pic += 'fill=%s!75!black,thick,anchor=base}]\n%%\n%%\n' %vertex_color
+
+        # Draws the axes if True
+        if axis:
+            tikz_pic += '\\draw[color=black,thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};\n'
+            tikz_pic += '\\draw[color=black,thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};\n'
+            tikz_pic += '\\draw[color=black,thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};\n'
+
+        # Create the coordinate of the vertices:
+        tikz_pic += '%% Coordinate of the vertices:\n%%\n'
+        for v in dict_drawing:
+            tikz_pic += dict_drawing[v][1]
+
+        # Draw the interior by going in a cycle
+        tikz_pic += '%%\n%%\n%% Drawing the interior\n%%\n'
+        cyclic_vert = cyclic_sort_vertices_2d(list(self.parent_polyhedron.Vrep_generator()))
+        tikz_pic += '\\fill[facet] '
+        for v in cyclic_vert:
+            if tuple(v) in dict_drawing:
+                tikz_pic += '%s -- ' %dict_drawing[tuple(v)][2]
+        tikz_pic += 'cycle {};\n'
+
+        # Draw the edges in the front
+        tikz_pic += '%%\n%%\n%% Drawing edges in the front\n%%\n'
+        tikz_pic += edges
+
+        # Finally, the vertices in front are drawn on top of everything.
+        tikz_pic += '%%\n%%\n%% Drawing the vertices in the front\n%%\n'
+        for v in dict_drawing:
+            tikz_pic += dict_drawing[v][0]
+        tikz_pic += '%%\n%%\n\\end{tikzpicture}'
+
+        return LatexExpr(tikz_pic)
+
+    def _tikz_3d_in_3d(self, view, angle, scale, edge_color,
+                       facet_color, opacity, vertex_color, axis):
+        """
+        Return a string ``tikz_pic`` consisting of a tikz picture of ``self``
+        according to a projection ``view`` and an angle ``angle``
+        obtained via Jmol through the current state property.
+
+        INPUT:
+
+        - ``view`` - list (default: [0,0,1]) representing the rotation axis.
+        - ``angle`` - integer angle of rotation in degree from 0 to 360.
+        - ``scale`` - integer specifying the scaling of the tikz picture.
+        - ``edge_color`` - string representing colors which tikz
+          recognize.
+        - ``facet_color`` - string representing colors which tikz
+          recognize.
+        - ``vertex_color`` - string representing colors which tikz
+          recognize.
+        - ``opacity`` - real number between 0 and 1 giving the opacity of
+          the front facets.
+        - ``axis`` - Boolean draw the axes at the origin or not.
+
+        OUTPUT:
+
+        - LatexExpr -- containing the TikZ picture.
+
+        EXAMPLES::
+
+            sage: P = polytopes.small_rhombicuboctahedron()
+            sage: Image = P.projection()._tikz_3d_in_3d([3,7,5], 100, scale=3, edge_color='blue', facet_color='orange', opacity=0.5, vertex_color='green', axis=True)
+            sage: type(Image)
+            <class 'sage.misc.latex.LatexExpr'>
+            sage: print '\n'.join(Image.splitlines()[:4])
+            \begin{tikzpicture}%
+                [x={(-0.046385cm, 0.837431cm)},
+                y={(-0.243536cm, 0.519228cm)},
+                z={(0.968782cm, 0.170622cm)},
+            sage: open('polytope-tikz1.tex', 'w').write(Image1)    # not tested
+
+        """
+
+        view_vector = vector(RDF, view)
+        rot = rotate_arbitrary(view_vector,-(angle/360)*2*pi)
+        rotation_matrix = rot[:2].transpose()
+        proj_vector = (rot**(-1))*vector(RDF, [0,0,1])
+
+        # First compute the back and front vertices and facets
+        front_facets = []
+        back_facets = []
+        for facet in self.face_inequalities:
+            A = facet.vector()[1:]
+            B = facet.vector()[0]
+            if A*(2000*proj_vector)+B<0:
+                front_facets += [facet]
+            else:
+                back_facets += [facet]
+
+        front_vertices = []
+        for facet in front_facets:
+            A = facet.vector()[1:]
+            B = facet.vector()[0]
+            for v in self.coords:
+                if A*v+B<0.0005:
+                    front_vertices += [v]
+
+        back_vertices = []
+        for facet in back_facets:
+            A = facet.vector()[1:]
+            B = facet.vector()[0]
+            for v in self.coords:
+                if A*v+B<0.0005:
+                    back_vertices += [v]
+
+        # Creates the nodes, coordinate and tag for every vertex of the polytope.
+        # The tag is used to draw the front facets later on.
+        dict_drawing = {}
+        first_part = ''
+        second_part = ''
+        for index1, index2 in self.lines:
+            v = self.coords[index1]
+            v_vect = str([i.n(digits=3) for i in v])
+            v_vect = v_vect.replace('[','(')
+            v_vect = v_vect.replace(']',')')
+            tag = '%s' %v_vect
+            node = "\\node[%s] at %s     {};\n" %('vertex',tag)
+            nei = self.coords[index2]
+            nei_vect = str([i.n(digits=3) for i in nei])
+            nei_vect = nei_vect.replace('[','(')
+            nei_vect = nei_vect.replace(']',')')
+            tag_nei = '%s' %nei_vect
+            H_v = set(self.parent_polyhedron.vertex_incidences()[index1][1])
+            H_nei = set(self.parent_polyhedron.vertex_incidences()[index2][1])
+            H_v_nei = [h in back_facets for h in H_v.intersection(H_nei)]
+
+            # The back edge has to be between two vertices in the Back
+            # AND such that the 2 facets touching them are in the Back
+            if v in back_vertices and nei in back_vertices and sum(H_v_nei)==2:
+                first_part += "\\draw[%s,back] %s -- %s;\n" %('edge',tag,tag_nei)
+            else:
+                second_part += "\\draw[%s] %s -- %s;\n" %('edge',tag,tag_nei)
+            coord = '\coordinate %s at %s;\n' %(tag,tag)
+            dict_drawing[tuple(v)] = node,coord,tag
+
+        # Start to write the output
+        tikz_pic = ''
+        tikz_pic += '\\begin{tikzpicture}%\n'
+        tikz_pic += '\t[x={(%fcm, %fcm)},\n' %(RDF(rotation_matrix[0][0]),RDF(rotation_matrix[0][1]))
+        tikz_pic += '\ty={(%fcm, %fcm)},\n' %(RDF(rotation_matrix[1][0]),RDF(rotation_matrix[1][1]))
+        tikz_pic += '\tz={(%fcm, %fcm)},\n' %(RDF(rotation_matrix[2][0]),RDF(rotation_matrix[2][1]))
+        tikz_pic += '\tscale=%f,\n' %scale
+        tikz_pic += '\tback/.style={loosely dotted, thin},\n'
+        tikz_pic += '\tedge/.style={color=%s, thick},\n' %edge_color
+        tikz_pic += '\tfacet/.style={fill=%s,fill opacity=%f},\n' %(facet_color,opacity)
+        tikz_pic += '\tvertex/.style={inner sep=1pt,circle,draw=%s!25!black,' %vertex_color
+        tikz_pic += 'fill=%s!75!black,thick,anchor=base}]\n%%\n%%\n' %vertex_color
+
+        # Draws the axes if True
+        if axis:
+            tikz_pic += '\\draw[color=black,thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};\n'
+            tikz_pic += '\\draw[color=black,thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};\n'
+            tikz_pic += '\\draw[color=black,thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};\n'
+
+        # Create the coordinate of the vertices
+        tikz_pic += '%% Coordinate of the vertices:\n%%\n'
+        for v in dict_drawing:
+            tikz_pic += dict_drawing[v][1]
+
+        # Draw the edges in the back
+        tikz_pic += '%%\n%%\n%% Drawing edges in the back\n%%\n'
+        tikz_pic += first_part
+
+        # Draw the vertices on top of the back-edges
+        tikz_pic += '%%\n%%\n%% Drawing vertices in the back\n%%\n'
+        for v in back_vertices:
+            if not v in front_vertices and tuple(v) in dict_drawing:
+                tikz_pic += dict_drawing[tuple(v)][0]
+
+        # Draw the facets in the front by going in cycles for every facet.
+        tikz_pic += '%%\n%%\n%% Drawing the facets\n%%\n'
+        for facet in front_facets:
+            cyclic_vert = cyclic_sort_vertices_2d(list(facet.incident()))
+            tikz_pic += '\\fill[facet] '
+            for v in cyclic_vert:
+                if tuple(v) in dict_drawing:
+                    tikz_pic += '%s -- ' %dict_drawing[tuple(v)][2]
+            tikz_pic += 'cycle {};\n'
+
+        # Draw the edges in the front
+        tikz_pic += '%%\n%%\n%% Drawing edges in the front\n%%\n'
+        tikz_pic += second_part
+
+        # Finally, the vertices in front are drawn on top of everything.
+        tikz_pic += '%%\n%%\n%% Drawing the vertices in the front\n%%\n'
+        for v in self.coords:
+            if v in front_vertices:
+                if tuple(v) in dict_drawing:
+                    tikz_pic += dict_drawing[tuple(v)][0]
+        tikz_pic += '%%\n%%\n\\end{tikzpicture}'
+
+        return LatexExpr(tikz_pic)