Coverage for local/lib/python2.7/site-packages/sage/geometry/polyhedron/plot.py: 97%

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(Image2)

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 ZZ^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 ZZ^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.

.. TODO::

Make it possible to draw Schlegel diagram for 4-polytopes. ::

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 ZZ^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-polytopes 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_dim < 2 or self.polyhedron_dim > 3:

raise NotImplementedError("The polytope has to be 2 or 3-dimensional.")

elif self.polyhedron_ambient_dim == 2: # self is a polygon in 2-space

return self._tikz_2d(scale, edge_color, facet_color, opacity,

vertex_color, axis)

elif self.polyhedron_dim == 2: # self is a polygon in 3-space

return self._tikz_2d_in_3d(view, angle, scale, edge_color,

facet_color, opacity, vertex_color, axis)

else: # self is a 3-polytope in 3-space

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):

r"""

Return a string ``tikz_pic`` consisting of a tikz picture of

``self``, which is assumed to be a polygon on the plane.

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)

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(Image) # not tested

Scientific notation is not used in the output (:trac:`16519`)::

sage: P=Polyhedron([[2*10^-10,0],[0,1],[1,0]],base_ring=QQ)

sage: tikzstr=P.projection().tikz()

sage: 'e-10' in tikzstr

False

.. 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 vert in self.points:

v = self.coords[vert]

v_vect = str(['%.5f' % i for i in v]).replace('\'','')

v_vect = v_vect.replace('[', '(')

v_vect = v_vect.replace(']', ')')

tag = '%s' %v_vect

node = "\\node[%s] at %s {};\n" % ('vertex', tag)

coord = '\coordinate %s at %s;\n' % (tag, tag)

dict_drawing[vert] = node, coord, tag

for index1, index2 in self.lines:

# v1 = self.coords[index1]

# v2 = self.coords[index2]

edges += "\\draw[%s] %s -- %s;\n" % ('edge',

dict_drawing[index1][2],

dict_drawing[index2][2])

# 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

vertices = list(self.parent_polyhedron.Vrep_generator())

tikz_pic += '%%\n%%\n%% Drawing the interior\n%%\n'

cyclic_vert = cyclic_sort_vertices_2d(list(self.parent_polyhedron.Vrep_generator()))

cyclic_indices = [vertices.index(v) for v in cyclic_vert]

tikz_pic += '\\fill[facet] '

for v in cyclic_indices:

if v in dict_drawing:

tikz_pic += '%s -- ' % dict_drawing[v][2]

tikz_pic += 'cycle {};\n'

# Draw the edges

tikz_pic += '%%\n%%\n%% Drawing edges\n%%\n'

tikz_pic += edges

# Finally, the vertices in front are drawn on top of everything.

tikz_pic += '%%\n%%\n%% Drawing the vertices\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):

r"""

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. ``self`` is

assumed to be a polygon in 3-space.

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 = Polyhedron(vertices=[[-1, -1, 2],[-1, 2, -1],[2, -1, -1]])

sage: P

A 2-dimensional polyhedron in ZZ^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(Image) # not tested

sage: p = Polyhedron(vertices=[[1,0,0],[0,1,0],[0,0,1]])

sage: proj = p.projection()

sage: Img = proj.tikz([1,1,1],130,axis=True)

sage: print('\n'.join(Img.splitlines()[21:25]))

%% Drawing the interior

\fill[facet] (1.00000, 0.00000, 0.00000) -- (0.00000, 0.00000, 1.00000) -- (0.00000, 1.00000, 0.00000) -- cycle {};

.. 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 vert in self.points:

v = self.coords[vert]

v_vect = str(['%.5f' % i for i in v]).replace('\'','')

v_vect = v_vect.replace('[','(')

v_vect = v_vect.replace(']',')')

tag = '%s' %v_vect

node = "\\node[%s] at %s {};\n" % ('vertex', tag)

coord = '\coordinate %s at %s;\n' % (tag, tag)

dict_drawing[vert] = node, coord, tag

for index1, index2 in self.lines:

# v1 = self.coords[index1]

# v2 = self.coords[index2]

edges += "\\draw[%s] %s -- %s;\n" % ('edge',

dict_drawing[index1][2],

dict_drawing[index2][2])

# 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

vertices = list(self.parent_polyhedron.Vrep_generator())

tikz_pic += '%%\n%%\n%% Drawing the interior\n%%\n'

cyclic_vert = cyclic_sort_vertices_2d(list(self.parent_polyhedron.Vrep_generator()))

cyclic_indices = [vertices.index(v) for v in cyclic_vert]

tikz_pic += '\\fill[facet] '

for v in cyclic_indices:

if v in dict_drawing:

tikz_pic += '%s -- ' % dict_drawing[v][2]

tikz_pic += 'cycle {};\n'

# Draw the edges in the front

tikz_pic += '%%\n%%\n%% Drawing edges\n%%\n'

tikz_pic += edges

# Finally, the vertices in front are drawn on top of everything.

tikz_pic += '%%\n%%\n%% Drawing the vertices\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):

r"""

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. ``self`` is

assumed to be a 3-polytope in 3-space.

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)

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(Image) # not tested

sage: Associahedron = Polyhedron(vertices=[[1,0,1],[1,0,0],[1,1,0],[0,0,-1],[0,1,0],[-1,0,0],[0,1,1],[0,0,1],[0,-1,0]]).polar()

sage: ImageAsso = Associahedron.projection().tikz([-15,-755,-655], 116, scale=1)

sage: print('\n'.join(ImageAsso.splitlines()[29:41]))

%% Drawing edges in the back

\draw[edge,back] (-0.50000, -0.50000, -0.50000) -- (-1.00000, 0.00000, 0.00000);

\draw[edge,back] (-0.50000, -0.50000, -0.50000) -- (0.00000, -1.00000, 0.00000);

\draw[edge,back] (-0.50000, -0.50000, -0.50000) -- (0.00000, 0.00000, -1.00000);

\draw[edge,back] (-1.00000, 0.00000, 0.00000) -- (-1.00000, 0.00000, 1.00000);

\draw[edge,back] (-1.00000, 0.00000, 0.00000) -- (-1.00000, 1.00000, 0.00000);

\draw[edge,back] (0.00000, -1.00000, 0.00000) -- (0.00000, -1.00000, 1.00000);

\draw[edge,back] (0.00000, -1.00000, 0.00000) -- (1.00000, -1.00000, 0.00000);

\draw[edge,back] (0.00000, 0.00000, -1.00000) -- (0.00000, 1.00000, -1.00000);

\draw[edge,back] (0.00000, 0.00000, -1.00000) -- (1.00000, 0.00000, -1.00000);

"""

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

facets = self.face_inequalities

front_facets = []

back_facets = []

for index_facet in range(len(facets)):

A = facets[index_facet].vector()[1:]

B = facets[index_facet].vector()[0]

if A*(2000*proj_vector)+B < 0:

front_facets += [index_facet]

else:

back_facets += [index_facet]

vertices = list(self.parent_polyhedron.Vrep_generator())

front_vertices = []

for index_facet in front_facets:

A = facets[index_facet].vector()[1:]

B = facets[index_facet].vector()[0]

for v in self.points:

if A*self.coords[v]+B < 0.0005 and v not in front_vertices:

front_vertices += [v]

back_vertices = []

for index_facet in back_facets:

A = facets[index_facet].vector()[1:]

B = facets[index_facet].vector()[0]

for v in self.points:

if A*self.coords[v]+B < 0.0005 and v not in back_vertices:

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 = {}

back_part = ''

front_part = ''

for vert in self.points:

v = self.coords[vert]

v_vect = str(['%.5f' % i for i in v]).replace('\'','')

v_vect = v_vect.replace('[','(')

v_vect = v_vect.replace(']',')')

tag = '%s' %v_vect

node = "\\node[%s] at %s {};\n" % ('vertex', tag)

coord = '\coordinate %s at %s;\n' %(tag, tag)

dict_drawing[vert] = node, coord, tag

# Separate the edges between back and front

for index1, index2 in self.lines:

# v1 = self.coords[index1]

# v2 = self.coords[index2]

H_v1 = set(self.parent_polyhedron.Vrepresentation(index1).incident())

H_v2 = set(self.parent_polyhedron.Vrepresentation(index2).incident())

H_v12 = [h for h in H_v1.intersection(H_v2) if facets.index(h) in back_facets]

# 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 index1 in back_vertices and index2 in back_vertices and len(H_v12)==2:

back_part += "\\draw[%s,back] %s -- %s;\n" % ('edge', dict_drawing[index1][2], dict_drawing[index2][2])

else:

front_part += "\\draw[%s] %s -- %s;\n" % ('edge',dict_drawing[index1][2],dict_drawing[index2][2])

# 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 += back_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 v in dict_drawing:

tikz_pic += dict_drawing[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 index_facet in front_facets:

cyclic_vert = cyclic_sort_vertices_2d(list(facets[index_facet].incident()))

cyclic_indices = [vertices.index(v) for v in cyclic_vert]

tikz_pic += '\\fill[facet] '

for v in cyclic_indices:

if v in dict_drawing:

tikz_pic += '%s -- ' % dict_drawing[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 += front_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.points:

if v in front_vertices:

if v in dict_drawing:

tikz_pic += dict_drawing[v][0]

tikz_pic += '%%\n%%\n\\end{tikzpicture}'

return LatexExpr(tikz_pic)

Coverage for local/lib/python2.7/site-packages/sage/geometry/polyhedron/plot.py : 97%

576 statements 557 run 19 missing 0 excluded