def plot(self, polygon_label=True):
r"""
Returns a plot of the GraphicalPolygon.
EXAMPLES::
sage: from flatsurf import *
sage: s = similarity_surfaces.example()
sage: from flatsurf.graphical.surface import GraphicalSurface
sage: gs = GraphicalSurface(s)
sage: gs.graphical_polygon(0).set_fill_color("red")
sage: gs.graphical_polygon(0).plot()
Graphics object consisting of 5 graphics primitives
"""
from sage.plot.point import point2d
from sage.plot.polygon import polygon2d
from sage.plot.graphics import Graphics
from sage.plot.text import text
p = polygon2d(self._v, **self.polygon_options())
if self._label is not None and polygon_label:
p += text(str(self._label), sum(self._v) / len(self._v), **self.polygon_label_options())
if self._edge_labels:
opt = self.edge_label_options()
n = self.base_polygon().num_edges()
for i in range(n):
lab = str(i) if self._edge_labels is True else self._edge_labels[i]
if lab:
e = self._v[(i + 1) % n] - self._v[i]
no = V((-e[1], e[0]))
p += text(lab, self._v[i] + 0.3 * e + 0.05 * no, **self.edge_label_options())
return p
def _new_plot(self, M, color=None):
r"""
INPUT:
- ``M`` -- projection matrix
- ``color`` -- string or None
EXAMPLES::
sage: from EkEkstar import kFace, GeoSub
sage: sub = {1:[1,2], 2:[1,3], 3:[1]}
sage: geosub = GeoSub(sub,2, dual=True)
sage: M = geosub.projection()
sage: _ = kFace((10,21,33), (1,2), dual=True)._new_plot(M) # case C
"""
if color is None:
color = self._color
L = self.new_proj(M)
if self.face_dimension() == 1:
return line(L, color=color, thickness=3)
elif self.face_dimension() == 2:
return polygon2d(L, color=color, thickness=.1, alpha=.8)
else:
raise NotImplementedError(
"Plotting is implemented only for patches in two or three dimensions."
)
def plot(self):
"""
Plot the lattice polygon.
OUTPUT:
A graphics object.
EXAMPLES::
sage: from sage.geometry.polyhedron.ppl_lattice_polytope import LatticePolytope_PPL
sage: P = LatticePolytope_PPL((1,0), (0,1), (0,0), (2,2))
sage: P.plot()
Graphics object consisting of 6 graphics primitives
sage: LatticePolytope_PPL([0], [1]).plot()
Graphics object consisting of 3 graphics primitives
sage: LatticePolytope_PPL([0]).plot()
Graphics object consisting of 2 graphics primitives
"""
from sage.plot.point import point2d
from sage.plot.polygon import polygon2d
vertices = self.ordered_vertices()
points = self.integral_points()
if self.space_dimension() == 1:
vertices = [vector(ZZ, (v[0], 0)) for v in vertices]
points = [vector(ZZ, (p[0], 0)) for p in points]
point_plot = sum(
point2d(p, pointsize=100, color='red') for p in points)
polygon_plot = polygon2d(vertices,
alpha=0.2,
color='green',
zorder=-1,
thickness=2)
return polygon_plot + point_plot
def plot(self):
"""
Plot the lattice polygon.
OUTPUT:
A graphics object.
EXAMPLES::
sage: from sage.geometry.polyhedron.ppl_lattice_polytope import LatticePolytope_PPL
sage: P = LatticePolytope_PPL((1,0), (0,1), (0,0), (2,2))
sage: P.plot()
Graphics object consisting of 6 graphics primitives
sage: LatticePolytope_PPL([0], [1]).plot()
Graphics object consisting of 3 graphics primitives
sage: LatticePolytope_PPL([0]).plot()
Graphics object consisting of 2 graphics primitives
"""
from sage.plot.point import point2d
from sage.plot.polygon import polygon2d
vertices = self.ordered_vertices()
points = self.integral_points()
if self.space_dimension() == 1:
vertices = [vector(ZZ, (v[0], 0)) for v in vertices]
points = [vector(ZZ, (p[0], 0)) for p in points]
point_plot = sum(point2d(p, pointsize=100, color='red')
for p in points)
polygon_plot = polygon2d(vertices, alpha=0.2, color='green',
zorder=-1, thickness=2)
return polygon_plot + point_plot
def plot(self, **options):
r"""
Plot this cylinder in coordinates used by a graphical surface. This
plots this cylinder as a union of subpolygons. Only the intersections
with polygons visible in the graphical surface are shown.
Parameters other than `graphical_surface` are passed to `polygon2d`
which is called to render the polygons.
Parameters
----------
graphical_surface : a GraphicalSurface
If not provided or `None`, the plot method uses the default graphical
surface for the surface.
"""
if "graphical_surface" in options and options["graphical_surface"] is not None:
gs = options["graphical_surface"]
assert gs.get_surface() == self._s, "Graphical surface for the wrong surface."
del options["graphical_surface"]
else:
gs = self._s.graphical_surface()
plt = Graphics()
for l,p in self.polygons():
if gs.is_visible(l):
gp = gs.graphical_polygon(l)
t = gp.transformation()
pp = t(p)
poly = polygon2d(pp.vertices(), **options)
plt += poly.plot()
return plt
def plot(self, **options):
r"""
Plot this cylinder in coordinates used by a graphical surface. This
plots this cylinder as a union of subpolygons. Only the intersections
with polygons visible in the graphical surface are shown.
Parameters other than `graphical_surface` are passed to `polygon2d`
which is called to render the polygons.
Parameters
----------
graphical_surface : a GraphicalSurface
If not provided or `None`, the plot method uses the default graphical
surface for the surface.
"""
if "graphical_surface" in options and options[
"graphical_surface"] is not None:
gs = options["graphical_surface"]
assert gs.get_surface(
) == self._s, "Graphical surface for the wrong surface."
del options["graphical_surface"]
else:
gs = self._s.graphical_surface()
plt = Graphics()
for l, p in self.polygons():
if gs.is_visible(l):
gp = gs.graphical_polygon(l)
t = gp.transformation()
pp = t(p)
poly = polygon2d(pp.vertices(), **options)
plt += poly.plot()
return plt
def plot_towers(self, iterations, position=(0,0), colors=None):
"""
Plot the towers of this interval exchange obtained from Rauzy induction.
INPUT:
- ``nb_iterations`` -- the number of steps of Rauzy induction
- ``colors`` -- (optional) colors for the towers
EXAMPLES::
sage: from surface_dynamics.all import *
sage: p = iet.Permutation('A B', 'B A')
sage: T = iet.IntervalExchangeTransformation(p, [0.41510826, 0.58489174])
sage: T.plot_towers(iterations=5)
Graphics object consisting of 65 graphics primitives
"""
px,py = map(float, position)
T,_,towers = self.rauzy_move(iterations=iterations,data=True)
pi = T.permutation()
A = pi.alphabet()
lengths = map(float, T.lengths())
if colors is None:
from sage.plot.colors import rainbow
colors = {a:z for a,z in zip(A, rainbow(len(A)))}
from sage.plot.graphics import Graphics
from sage.plot.line import line2d
from sage.plot.polygon import polygon2d
from sage.plot.text import text
G = Graphics()
x = px
for letter in pi[0]:
y = x + lengths[A.rank(letter)]
tower = towers.image(letter)
h = tower.length()
G += line2d([(x,py),(x,py+h)], color='black')
G += line2d([(y,py),(y,py+h)], color='black')
for i,a in enumerate(tower):
G += line2d([(x,py+i),(y,py+i)], color='black')
G += polygon2d([(x,py+i),(y,py+i),(y,py+i+1),(x,py+i+1)], color=colors[a], alpha=0.4)
G += text(a, ((x+y)/2, py+i+.5), color='darkgray')
G += line2d([(x,py+h),(y,py+h)], color='black', linestyle='dashed')
G += text(letter, ((x+y)/2, py+h+.5), color='black', fontsize='large')
x = y
x = px
G += line2d([(px,py-.5),(px+sum(lengths),py-.5)], color='black')
for letter in pi[1]:
y = x + lengths[A.rank(letter)]
G += line2d([(x,py-.7),(x,py-.3)], color='black')
G += text(letter, ((x+y)/2, py-.5), color='black', fontsize='large')
x = y
G += line2d([(x,py-.7),(x,py-.3)], color='black')
return G
def plot_polygon(self, **options):
r"""
Returns only the filled polygon.
Options are processed as in sage.plot.polygon.polygon2d except
that by default axes=False.
"""
if not "axes" in options:
options["axes"] = False
return polygon2d(self._v, **options)
def plot_polygon(self, **options):
r"""
Returns only the filled polygon.
Options are processed as in sage.plot.polygon.polygon2d except
that by default axes=False.
"""
if not "axes" in options:
options["axes"] = False
return polygon2d(self._v, **options)
def plot(self, translation=None):
r"""
Plot the polygon with the origin at ``translation``.
"""
from sage.plot.point import point2d
from sage.plot.line import line2d
from sage.plot.polygon import polygon2d
from sage.modules.free_module import VectorSpace
V = VectorSpace(RR,2)
P = self.vertices(translation)
return point2d(P, color='red') + line2d(P + (P[0],), color='orange') + polygon2d(P, alpha=0.3)
def plot(self, **kwds):
r"""
Plot the initial triangulation associated to ``self``.
INPUT:
- ``radius`` - the radius of the disk; by default the length of
the circle is the number of vertices
- ``points_color`` - the color of the vertices; default 'black'
- ``points_size`` - the size of the vertices; default 7
- ``triangulation_color`` - the color of the arcs; default 'black'
- ``triangulation_thickness`` - the thickness of the arcs; default 0.5
- ``shading_color`` - the color of the shading used on neuter
intervals; default 'lightgray'
- ``reflections_color`` - the color of the reflection axes; default
'blue'
- ``reflections_thickness`` - the thickness of the reflection axes;
default 1
EXAMPLES::
sage: Y = SineGordonYsystem('A',(6,4,3))
sage: Y.plot() # long time 2s
Graphics object consisting of 219 graphics primitives
"""
# Set up plotting options
if 'radius' in kwds:
radius = kwds['radius']
else:
radius = ceil(self.r() / (2 * pi))
points_opts = {}
if 'points_color' in kwds:
points_opts['color'] = kwds['points_color']
else:
points_opts['color'] = 'black'
if 'points_size' in kwds:
points_opts['size'] = kwds['points_size']
else:
points_opts['size'] = 7
triangulation_opts = {}
if 'triangulation_color' in kwds:
triangulation_opts['color'] = kwds['triangulation_color']
else:
triangulation_opts['color'] = 'black'
if 'triangulation_thickness' in kwds:
triangulation_opts['thickness'] = kwds['triangulation_thickness']
else:
triangulation_opts['thickness'] = 0.5
shading_opts = {}
if 'shading_color' in kwds:
shading_opts['color'] = kwds['shading_color']
else:
shading_opts['color'] = 'lightgray'
reflections_opts = {}
if 'reflections_color' in kwds:
reflections_opts['color'] = kwds['reflections_color']
else:
reflections_opts['color'] = 'blue'
if 'reflections_thickness' in kwds:
reflections_opts['thickness'] = kwds['reflections_thickness']
else:
reflections_opts['thickness'] = 1
# Helper functions
def triangle(x):
(a, b) = sorted(x[:2])
for p in self.vertices():
if (p, a) in self.triangulation() or (a, p) in self.triangulation():
if (p, b) in self.triangulation() or (b, p) in self.triangulation():
if p < a or p > b:
return sorted((a, b, p))
def plot_arc(radius, p, q, **opts):
# TODO: THIS SHOULD USE THE EXISTING PLOT OF ARCS!
# plot the arc from p to q differently depending on the type of self
p = ZZ(p)
q = ZZ(q)
t = var('t')
if p - q in [1, -1]:
def f(t):
return (radius * cos(t), radius * sin(t))
(p, q) = sorted([p, q])
angle_p = vertex_to_angle(p)
angle_q = vertex_to_angle(q)
return parametric_plot(f(t), (t, angle_q, angle_p), **opts)
if self.type() == 'A':
angle_p = vertex_to_angle(p)
angle_q = vertex_to_angle(q)
if angle_p < angle_q:
angle_p += 2 * pi
internal_angle = angle_p - angle_q
if internal_angle > pi:
(angle_p, angle_q) = (angle_q + 2 * pi, angle_p)
internal_angle = angle_p - angle_q
angle_center = (angle_p+angle_q) / 2
hypotenuse = radius / cos(internal_angle / 2)
radius_arc = hypotenuse * sin(internal_angle / 2)
center = (hypotenuse * cos(angle_center),
hypotenuse * sin(angle_center))
center_angle_p = angle_p + pi / 2
center_angle_q = angle_q + 3 * pi / 2
def f(t):
return (radius_arc * cos(t) + center[0],
radius_arc * sin(t) + center[1])
return parametric_plot(f(t), (t, center_angle_p,
center_angle_q), **opts)
elif self.type() == 'D':
if p >= q:
q += self.r()
px = -2 * pi * p / self.r() + pi / 2
qx = -2 * pi * q / self.r() + pi / 2
arc_radius = (px - qx) / 2
arc_center = qx + arc_radius
def f(t):
return exp(I * ((cos(t) + I * sin(t)) *
arc_radius + arc_center)) * radius
return parametric_plot((real_part(f(t)), imag_part(f(t))),
(t, 0, pi), **opts)
def vertex_to_angle(v):
# v==0 corresponds to pi/2
return -2 * pi * RR(v) / self.r() + 5 * pi / 2
# Begin plotting
P = Graphics()
# Shade neuter intervals
neuter_intervals = [x for x in flatten(self.intervals()[:-1],
max_level=1)
if x[2] in ["NR", "NL"]]
shaded_triangles = map(triangle, neuter_intervals)
for (p, q, r) in shaded_triangles:
points = list(plot_arc(radius, p, q)[0])
points += list(plot_arc(radius, q, r)[0])
points += list(reversed(plot_arc(radius, p, r)[0]))
P += polygon2d(points, **shading_opts)
# Disk boundary
P += circle((0, 0), radius, **triangulation_opts)
# Triangulation
for (p, q) in self.triangulation():
P += plot_arc(radius, p, q, **triangulation_opts)
if self.type() == 'D':
s = radius / 50.0
P += polygon2d([(s, 5 * s), (s, 7 * s),
(3 * s, 5 * s), (3 * s, 7 * s)],
color=triangulation_opts['color'])
P += bezier_path([[(0, 0), (2 * s, 1 * s), (2 * s, 6 * s)],
[(2 * s, 10 * s), (s, 20 * s)],
[(0, 30 * s), (0, radius)]],
**triangulation_opts)
P += bezier_path([[(0, 0), (-2 * s, 1 * s), (-2 * s, 6 * s)],
[(-2 * s, 10 * s), (-s, 20 * s)],
[(0, 30 * s), (0, radius)]],
**triangulation_opts)
P += point((0, 0), zorder=len(P), **points_opts)
# Vertices
v_points = {x: (radius * cos(vertex_to_angle(x)),
radius * sin(vertex_to_angle(x)))
for x in self.vertices()}
for v in v_points:
P += point(v_points[v], zorder=len(P), **points_opts)
# Reflection axes
P += line([(0, 1.1 * radius), (0, -1.1 * radius)],
zorder=len(P), **reflections_opts)
axis_angle = vertex_to_angle(-0.5 * (self.rk() + (1, 1))[1])
(a, b) = (1.1 * radius * cos(axis_angle),
1.1 * radius * sin(axis_angle))
P += line([(a, b), (-a, -b)], zorder=len(P), **reflections_opts)
# Wrap up
P.set_aspect_ratio(1)
P.axes(False)
return P
def plot(self, **kwds):
r"""
Plot the initial triangulation associated to ``self``.
INPUT:
- ``radius`` - the radius of the disk; by default the length of
the circle is the number of vertices
- ``points_color`` - the color of the vertices; default 'black'
- ``points_size`` - the size of the vertices; default 7
- ``triangulation_color`` - the color of the arcs; default 'black'
- ``triangulation_thickness`` - the thickness of the arcs; default 0.5
- ``shading_color`` - the color of the shading used on neuter
intervals; default 'lightgray'
- ``reflections_color`` - the color of the reflection axes; default
'blue'
- ``reflections_thickness`` - the thickness of the reflection axes;
default 1
EXAMPLES::
sage: Y = SineGordonYsystem('A',(6,4,3));
sage: Y.plot() # not tested
"""
# Set up plotting options
if 'radius' in kwds:
radius = kwds['radius']
else:
radius = ceil(self.r() / (2 * pi))
points_opts = {}
if 'points_color' in kwds:
points_opts['color'] = kwds['points_color']
else:
points_opts['color'] = 'black'
if 'points_size' in kwds:
points_opts['size'] = kwds['points_size']
else:
points_opts['size'] = 7
triangulation_opts = {}
if 'triangulation_color' in kwds:
triangulation_opts['color'] = kwds['triangulation_color']
else:
triangulation_opts['color'] = 'black'
if 'triangulation_thickness' in kwds:
triangulation_opts['thickness'] = kwds['triangulation_thickness']
else:
triangulation_opts['thickness'] = 0.5
shading_opts = {}
if 'shading_color' in kwds:
shading_opts['color'] = kwds['shading_color']
else:
shading_opts['color'] = 'lightgray'
reflections_opts = {}
if 'reflections_color' in kwds:
reflections_opts['color'] = kwds['reflections_color']
else:
reflections_opts['color'] = 'blue'
if 'reflections_thickness' in kwds:
reflections_opts['thickness'] = kwds['reflections_thickness']
else:
reflections_opts['thickness'] = 1
# Helper functions
def triangle(x):
(a, b) = sorted(x[:2])
for p in self.vertices():
if (p, a) in self.triangulation() or (a, p) in self.triangulation():
if (p, b) in self.triangulation() or (b, p) in self.triangulation():
if p < a or p > b:
return sorted((a, b, p))
def plot_arc(radius, p, q, **opts):
# plot the arc from p to q differently depending on the type of self
p = ZZ(p)
q = ZZ(q)
t = var('t')
if p - q in [1, -1]:
def f(t):
return (radius * cos(t), radius * sin(t))
(p, q) = sorted([p, q])
angle_p = vertex_to_angle(p)
angle_q = vertex_to_angle(q)
return parametric_plot(f(t), (t, angle_q, angle_p), **opts)
if self.type() == 'A':
angle_p = vertex_to_angle(p)
angle_q = vertex_to_angle(q)
if angle_p < angle_q:
angle_p += 2 * pi
internal_angle = angle_p - angle_q
if internal_angle > pi:
(angle_p, angle_q) = (angle_q + 2 * pi, angle_p)
internal_angle = angle_p - angle_q
angle_center = (angle_p+angle_q) / 2
hypotenuse = radius / cos(internal_angle / 2)
radius_arc = hypotenuse * sin(internal_angle / 2)
center = (hypotenuse * cos(angle_center),
hypotenuse * sin(angle_center))
center_angle_p = angle_p + pi / 2
center_angle_q = angle_q + 3 * pi / 2
def f(t):
return (radius_arc * cos(t) + center[0],
radius_arc * sin(t) + center[1])
return parametric_plot(f(t), (t, center_angle_p,
center_angle_q), **opts)
elif self.type() == 'D':
if p >= q:
q += self.r()
px = -2 * pi * p / self.r() + pi / 2
qx = -2 * pi * q / self.r() + pi / 2
arc_radius = (px - qx) / 2
arc_center = qx + arc_radius
def f(t):
return exp(I * ((cos(t) + I * sin(t)) *
arc_radius + arc_center)) * radius
return parametric_plot((real_part(f(t)), imag_part(f(t))),
(t, 0, pi), **opts)
def vertex_to_angle(v):
# v==0 corresponds to pi/2
return -2 * pi * RR(v) / self.r() + 5 * pi / 2
# Begin plotting
P = Graphics()
# Shade neuter intervals
neuter_intervals = [x for x in flatten(self.intervals()[:-1],
max_level=1)
if x[2] in ["NR", "NL"]]
shaded_triangles = map(triangle, neuter_intervals)
for (p, q, r) in shaded_triangles:
points = list(plot_arc(radius, p, q)[0])
points += list(plot_arc(radius, q, r)[0])
points += list(reversed(plot_arc(radius, p, r)[0]))
P += polygon2d(points, **shading_opts)
# Disk boundary
P += circle((0, 0), radius, **triangulation_opts)
# Triangulation
for (p, q) in self.triangulation():
P += plot_arc(radius, p, q, **triangulation_opts)
if self.type() == 'D':
s = radius / 50.0
P += polygon2d([(s, 5 * s), (s, 7 * s),
(3 * s, 5 * s), (3 * s, 7 * s)],
color=triangulation_opts['color'])
P += bezier_path([[(0, 0), (2 * s, 1 * s), (2 * s, 6 * s)],
[(2 * s, 10 * s), (s, 20 * s)],
[(0, 30 * s), (0, radius)]],
**triangulation_opts)
P += bezier_path([[(0, 0), (-2 * s, 1 * s), (-2 * s, 6 * s)],
[(-2 * s, 10 * s), (-s, 20 * s)],
[(0, 30 * s), (0, radius)]],
**triangulation_opts)
P += point((0, 0), zorder=len(P), **points_opts)
# Vertices
v_points = {x: (radius * cos(vertex_to_angle(x)),
radius * sin(vertex_to_angle(x)))
for x in self.vertices()}
for v in v_points:
P += point(v_points[v], zorder=len(P), **points_opts)
# Reflection axes
P += line([(0, 1.1 * radius), (0, -1.1 * radius)],
zorder=len(P), **reflections_opts)
axis_angle = vertex_to_angle(-0.5 * (self.rk() + (1, 1))[1])
(a, b) = (1.1 * radius * cos(axis_angle),
1.1 * radius * sin(axis_angle))
P += line([(a, b), (-a, -b)], zorder=len(P), **reflections_opts)
# Wrap up
P.set_aspect_ratio(1)
P.axes(False)
return P
def _plot(self, geosub, color=None):
r"""
EXAMPLES::
sage: from EkEkstar import kFace, GeoSub
sage: sub = {1:[1,2], 2:[1,3], 3:[1]}
sage: geosub = GeoSub(sub,2, dual=True)
sage: _ = kFace((10,21,33), (1,))._plot(geosub) # case A
sage: _ = kFace((10,21,33), (1,2), dual=True)._plot(geosub) # case C
sage: _ = kFace((10,21,33), (1,), dual=True)._plot(geosub) # case E
::
sage: sub = {1: [1, 3, 2, 3], 2: [2, 3], 3: [3, 2, 3, 1, 3, 2, 3]}
sage: geosub = GeoSub(sub, 2, dual=True)
sage: _ = kFace((10,21,33), (1,2), dual=True)._plot(geosub) # case B
::
sage: sub = {1:[1,2,3,3,3,3], 2:[1,3], 3:[1]}
sage: geosub = GeoSub(sub,2, dual=True)
sage: _ = kFace((0,0,0),(1,2), dual=True)._plot(geosub) # case A
"""
v = self.vector()
t = self.type()
if color != None:
col = color
else:
col = self._color
G = Graphics()
K = geosub.field()
b = K.gen()
num = geosub._sigma_dict.keys()
if self.is_dual():
h = list(set(num) - set(t))
B = b
vec = geosub.dominant_left_eigenvector()
emb = geosub.contracting_eigenvalues_indices()
else:
h = list(t)
B = b**(-1) # TODO: this seems useless (why?)
vec = -geosub.dominant_left_eigenvector()
emb = geosub.dilating_eigenvalues_indices()
el = v * vec
iter = 0
conjugates = geosub.complex_embeddings()
if len(h) == 1:
if conjugates[emb[0]].is_real() == True:
bp = zero_vector(CC, len(emb))
for i in range(len(emb)):
bp[i] = K(el).complex_embeddings()[emb[i]]
bp1 = zero_vector(CC, len(emb))
for i in range(len(emb)):
bp1[i] = K(
(el + vec[h[0] - 1])).complex_embeddings()[emb[i]]
if len(emb) == 1:
return line([bp[0], bp1[0]], color=col, thickness=3)
else:
return line([bp, bp1], color=col, thickness=3)
else:
bp = K(el).complex_embeddings()[emb[0]]
bp1 = K((el + vec[h[0] - 1])).complex_embeddings()[emb[0]]
return line([bp, bp1], color=col, thickness=3)
elif len(h) == 2:
if conjugates[emb[0]].is_real() == True:
bp = (K(el).complex_embeddings()[emb[0]],
K(el).complex_embeddings()[emb[1]])
bp1 = (K(el + vec[h[0] - 1]).complex_embeddings()[emb[0]],
K(el + vec[h[0] - 1]).complex_embeddings()[emb[1]])
bp2 = (K(el + vec[h[0] - 1] +
vec[h[1] - 1]).complex_embeddings()[emb[0]],
K(el + vec[h[0] - 1] +
vec[h[1] - 1]).complex_embeddings()[emb[1]])
bp3 = (K(el + vec[h[1] - 1]).complex_embeddings()[emb[0]],
K(el + vec[h[1] - 1]).complex_embeddings()[emb[1]])
return polygon2d([bp, bp1, bp2, bp3],
color=col,
thickness=.1,
alpha=0.8)
else:
bp = K(el).complex_embeddings()[emb[0]]
bp1 = K(el + vec[h[0] - 1]).complex_embeddings()[emb[0]]
bp2 = K(el + vec[h[0] - 1] +
vec[h[1] - 1]).complex_embeddings()[emb[0]]
bp3 = K(el + vec[h[1] - 1]).complex_embeddings()[emb[0]]
return polygon2d([[bp[0], bp[1]], [bp1[0], bp1[1]],
[bp2[0], bp2[1]], [bp3[0], bp3[1]]],
color=col,
thickness=.1,
alpha=0.8)
else:
raise NotImplementedError(
"Plotting is implemented only for patches in two or three dimensions."
)
return G
def plot_towers(self, iterations, position=(0, 0), colors=None):
"""
Plot the towers of this interval exchange obtained from Rauzy induction.
INPUT:
- ``nb_iterations`` -- the number of steps of Rauzy induction
- ``colors`` -- (optional) colors for the towers
EXAMPLES::
sage: from surface_dynamics.all import *
sage: p = iet.Permutation('A B', 'B A')
sage: T = iet.IntervalExchangeTransformation(p, [0.41510826, 0.58489174])
sage: T.plot_towers(iterations=5) # not tested (problem with matplotlib font cache)
Graphics object consisting of 65 graphics primitives
"""
px, py = map(float, position)
T, _, towers = self.rauzy_move(iterations=iterations, data=True)
pi = T.permutation()
A = pi.alphabet()
lengths = map(float, T.lengths())
if colors is None:
from sage.plot.colors import rainbow
colors = {a: z for a, z in zip(A, rainbow(len(A)))}
from sage.plot.graphics import Graphics
from sage.plot.line import line2d
from sage.plot.polygon import polygon2d
from sage.plot.text import text
G = Graphics()
x = px
for letter in pi[0]:
y = x + lengths[A.rank(letter)]
tower = towers.image(letter)
h = tower.length()
G += line2d([(x, py), (x, py + h)], color='black')
G += line2d([(y, py), (y, py + h)], color='black')
for i, a in enumerate(tower):
G += line2d([(x, py + i), (y, py + i)], color='black')
G += polygon2d([(x, py + i), (y, py + i), (y, py + i + 1),
(x, py + i + 1)],
color=colors[a],
alpha=0.4)
G += text(a, ((x + y) / 2, py + i + .5), color='darkgray')
G += line2d([(x, py + h), (y, py + h)],
color='black',
linestyle='dashed')
G += text(letter, ((x + y) / 2, py + h + .5),
color='black',
fontsize='large')
x = y
x = px
G += line2d([(px, py - .5), (px + sum(lengths), py - .5)],
color='black')
for letter in pi[1]:
y = x + lengths[A.rank(letter)]
G += line2d([(x, py - .7), (x, py - .3)], color='black')
G += text(letter, ((x + y) / 2, py - .5),
color='black',
fontsize='large')
x = y
G += line2d([(x, py - .7), (x, py - .3)], color='black')
return G