def plot(self, color=None):
r"""
EXAMPLES::
from flatsurf.geometry.similarity_surface_generators import SimilaritySurfaceGenerators
s=SimilaritySurfaceGenerators.example()
from flatsurf.graphical.surface import GraphicalSurface
gs=GraphicalSurface(s)
gs.make_visible(1)
from flatsurf.geometry.tangent_bundle import *
tb = SimilaritySurfaceTangentBundle(s)
V=tb.surface().vector_space()
v=SimilaritySurfaceTangentVector(tb, 0, V((1,-0.5)), V((3,-1)))
from flatsurf.geometry.straight_line_trajectory import *
seg = SegmentInPolygon(v)
from flatsurf.graphical.straight_line_trajectory import *
gseg = GraphicalSegmentInPolygon(gs, seg)
show(gs.plot()+gseg.plot())
"""
if self._gs.is_visible(self.polygon_label()):
if color==None:
color="black"
from sage.plot.line import line2d
return line2d([self.start(), self.end()],color=color)
else:
from sage.plot.graphics import Graphics
return Graphics()
def plot_function(self, **d):
r"""
Return a plot of the interval exchange transformation as a
function.
INPUT:
- Any option that is accepted by line2d
OUTPUT:
2d plot -- a plot of the iet as a function
EXAMPLES::
sage: t = iet.IntervalExchangeTransformation(('a b c d','d a c b'),[1,1,1,1])
sage: t.plot_function(rgbcolor=(0,1,0))
Graphics object consisting of 4 graphics primitives
"""
from sage.plot.all import Graphics
from sage.plot.line import line2d
G = Graphics()
l = self.singularities()
t = self._permutation._twin
for i in range(len(self._permutation)):
j = t[0][i]
G += line2d([(l[0][i], l[1][j]), (l[0][i + 1], l[1][j + 1])], **d)
return G
def plot(self, color=None):
r"""
EXAMPLES::
sage: from flatsurf import *
sage: s = similarity_surfaces.example()
sage: v = s.tangent_vector(0, (1,-0.5), (3,-1))
sage: from flatsurf.geometry.straight_line_trajectory import SegmentInPolygon
sage: seg = SegmentInPolygon(v)
sage: from flatsurf.graphical.straight_line_trajectory import *
sage: gseg = GraphicalSegmentInPolygon(s.graphical_surface(), seg)
sage: gseg.plot()
Graphics object consisting of 1 graphics primitive
sage: gseg.plot(color='red')
Graphics object consisting of 1 graphics primitive
"""
if self._gs.is_visible(self.polygon_label()):
if color is None:
if self._color is None:
color = "black"
else:
color = self._color
from sage.plot.line import line2d
return line2d([self.start(), self.end()],color=color)
else:
from sage.plot.graphics import Graphics
return Graphics()
def plot_function(self,**d):
r"""
Return a plot of the interval exchange transformation as a
function.
INPUT:
- Any option that is accepted by line2d
OUTPUT:
2d plot -- a plot of the iet as a function
EXAMPLES::
sage: t = iet.IntervalExchangeTransformation(('a b c d','d a c b'),[1,1,1,1])
sage: t.plot_function(rgbcolor=(0,1,0))
Graphics object consisting of 4 graphics primitives
"""
from sage.plot.all import Graphics
from sage.plot.line import line2d
G = Graphics()
l = self.singularities()
t = self._permutation._twin
for i in range(len(self._permutation)):
j = t[0][i]
G += line2d([(l[0][i],l[1][j]),(l[0][i+1],l[1][j+1])],**d)
return G
def plot_edge(self, e, color=None, dotted=False):
ne = self.base_polygon().num_edges()
if color is None:
color = self._outline_color
if color is None:
from sage.plot.graphics import Graphics
return Graphics()
from sage.plot.line import line2d
v = self._v[e]
w = self._v[(e + 1) % ne]
if dotted:
return line2d([v, w], color=color, linestyle=":")
else:
return line2d([v, w], color=color)
def plot_edge(self, e, **options):
r"""
Plot the edge e, with e a number 0,...,n-1 with n being the number
of edges of the polygon.
Options are processed as in sage.plot.line.line2d.
"""
return line2d([self._v[e], self._v[(e+1)%self.base_polygon().num_edges()]], \
**options)
def plot_edge(self, e, **options):
r"""
Plot the edge e, with e a number 0,...,n-1 with n being the number
of edges of the polygon.
Options are processed as in sage.plot.line.line2d.
"""
return line2d([self._v[e], self._v[(e+1)%self.base_polygon().num_edges()]], \
**options)
def plot_line(self):
from sage.plot.line import line2d
from sage.plot.point import point
p = line2d([[0, 0], [1, 0]])
for a in self._alpha:
p += point([a, 0], color='blue', size=100)
for b in self._beta:
p += point([b, 0], color='red', size=100)
p.show(axes=False, xmin=0, xmax=1, ymin=-.1, ymax=.1)
def plot_line(self):
from sage.plot.line import line2d
from sage.plot.point import point
p = line2d([[0,0],[1,0]])
for a in self._alpha:
p += point([a,0], color='blue', size=100)
for b in self._beta:
p += point([b,0], color='red', size=100)
p.show(axes=False, xmin=0, xmax=1, ymin=-.1, ymax=.1)
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_zero_flag(self, **options):
r"""
Draw a line segment from the zero vertex toward the baricenter.
A real parameter ``t`` can be provided. If t=1, then the segment will
go all the way to the baricenter. The value of ``t`` is linear in the
length of the segment. Defaults to t=0.5.
Other options are processed as in sage.plot.line.line2d.
"""
if "t" in options:
t = RDF(options.pop("t"))
else:
t = 0.5
return line2d([self._v[0], self._v[0] + t*(sum(self._v) / len(self._v) - self._v[0])],
**options)
def plot_profile(self):
from sage.plot.line import line2d
from sage.plot.point import point
from sage.plot.text import text
p_color, p_number, p_ev = self.profile()
d = len(p_color)
color = lambda i: 'blue' if p_color[i] else 'red'
p = lambda i: [0,0] if i == -1 else [i+1,p_number[i]]
plt = point([0,0],marker='x',size=100)
for i in range(d):
plt += line2d([p(i-1),p(i)],alpha=.5)
plt += point(p(i), color=color(i), size=100)
if p_color[i]:
[x,y] = p(i)
plt += text(r"$\alpha_%i$"%(self._i_alpha[p_ev[i]]+1), [x,y+.2], fontsize = 40)
else:
[x,y] = p(i)
plt += text(r"$\beta_%i$"%(self._i_beta[p_ev[i]]+1), [x,y+.2], fontsize = 40)
plt.show(axes=False, ymin=0, xmin=0, xmax=d)
def plot_zero_flag(self, **options):
r"""
Draw a line segment from the zero vertex toward the baricenter.
A real parameter ``t`` can be provided. If t=1, then the segment will
go all the way to the baricenter. The value of ``t`` is linear in the
length of the segment. Defaults to t=0.5.
Other options are processed as in sage.plot.line.line2d.
"""
if "t" in options:
t = RDF(options.pop("t"))
else:
t = 0.5
return line2d([
self._v[0], self._v[0] + t *
(sum(self._v) / len(self._v) - self._v[0])
], **options)
def plot(self, **options):
r"""
EXAMPLES::
sage: from flatsurf import *
sage: s = similarity_surfaces.example()
sage: v = s.tangent_vector(0, (1,-0.5), (3,-1))
sage: from flatsurf.geometry.straight_line_trajectory import SegmentInPolygon
sage: seg = SegmentInPolygon(v)
sage: from flatsurf.graphical.straight_line_trajectory import *
sage: gseg = GraphicalSegmentInPolygon(seg, s.graphical_surface())
sage: gseg.plot() # not tested (problem with matplotlib font caches on Travis)
Graphics object consisting of 1 graphics primitive
sage: gseg.plot(color='red') # not tested (problem with matplotlib font caches on Travis)
Graphics object consisting of 1 graphics primitive
"""
if self._gs.is_visible(self.polygon_label()):
from sage.plot.line import line2d
return line2d([self.start(), self.end()],**options)
else:
from sage.plot.graphics import Graphics
return Graphics()
def plot_profile(self):
from sage.plot.line import line2d
from sage.plot.point import point
from sage.plot.text import text
p_color, p_number, p_ev = self.profile()
d = len(p_color)
color = lambda i: 'blue' if p_color[i] else 'red'
p = lambda i: [0, 0] if i == -1 else [i + 1, p_number[i]]
plt = point([0, 0], marker='x', size=100)
for i in range(d):
plt += line2d([p(i - 1), p(i)], alpha=.5)
plt += point(p(i), color=color(i), size=100)
if p_color[i]:
[x, y] = p(i)
plt += text(r"$\alpha_%i$" % (self._i_alpha[p_ev[i]] + 1),
[x, y + .2],
fontsize=40)
else:
[x, y] = p(i)
plt += text(r"$\beta_%i$" % (self._i_beta[p_ev[i]] + 1),
[x, y + .2],
fontsize=40)
plt.show(axes=False, ymin=0, xmin=0, xmax=d)
def make_chart(self, region=None):
G = Graphics()
smin, smax, nmin, nmax = [], [], [], []
for d in self.chartgens(region):
x, y = self.get_coords(d)
G += point2d((x, y), zorder=10)
smin.append(y)
smax.append(y)
nmin.append(x)
nmax.append(x)
smin = [
min(smin),
]
smax = [
max(smax),
]
nmin = [
min(nmin),
]
nmax = [
max(nmax),
]
for l in self.chartlines():
try:
pts, lineargs = self.lineinfo[l["line"]]
x1, y1 = self.get_coords(self.geninfo(int(l["src"])))
x2, y2 = self.get_coords(self.geninfo(int(l["tar"])))
G += line2d([(x1, y1), (x2, y2)], **lineargs)
except:
print("line not understood:", l)
off = 0.5
G.ymin(smin[0] - off)
G.ymax(smax[0] + off)
G.xmin(nmin[0] - off)
G.xmax(nmax[0] + off)
return G
def plot_two_intervals(self,
position=(0,0),
vertical_alignment='center',
horizontal_alignment='left',
interval_height=0.1,
labels_height=0.05,
fontsize=14,
labels=True,
colors=None):
r"""
Returns a picture of the interval exchange transformation.
INPUT:
- ``position`` - a 2-uple of the position
- ``horizontal_alignment`` - left (default), center or right
- ``labels`` - boolean (default: True)
- ``fontsize`` - the size of the label
OUTPUT:
2d plot -- a plot of the two intervals (domain and range)
EXAMPLES::
sage: t = iet.IntervalExchangeTransformation(('a b','b a'),[1,1])
sage: t.plot_two_intervals()
Graphics object consisting of 8 graphics primitives
"""
from sage.plot.all import Graphics
from sage.plot.line import line2d
from sage.plot.text import text
from sage.plot.colors import rainbow
G = Graphics()
lengths = [float(_) for _ in self._lengths]
total_length = sum(lengths)
if colors is None:
colors = rainbow(len(self._permutation), 'rgbtuple')
if horizontal_alignment == 'left':
s = position[0]
elif horizontal_alignment == 'center':
s = position[0] - total_length / 2
elif horizontal_alignment == 'right':
s = position[0] - total_length
else:
raise ValueError("horizontal_alignement must be left, center or right")
top_height = position[1] + interval_height
for i in self._permutation._intervals[0]:
G += line2d([(s,top_height), (s+lengths[i],top_height)],
rgbcolor=colors[i])
if labels:
G += text(str(self._permutation._alphabet.unrank(i)),
(s+float(lengths[i])/2, top_height+labels_height),
horizontal_alignment='center',
rgbcolor=colors[i],
fontsize=fontsize)
s += lengths[i]
if horizontal_alignment == 'left':
s = position[0]
elif horizontal_alignment == 'center':
s = position[0] - total_length / 2
elif horizontal_alignment == 'right':
s = position[0] - total_length
else:
raise ValueError("horizontal_alignement must be left, center or right")
bottom_height = position[1] - interval_height
for i in self._permutation._intervals[1]:
G += line2d([(s,bottom_height), (s+lengths[i],bottom_height)],
rgbcolor=colors[i])
if labels:
G += text(str(self._permutation._alphabet.unrank(i)),
(s+float(lengths[i])/2, bottom_height-labels_height),
horizontal_alignment='center',
rgbcolor=colors[i],
fontsize=fontsize)
s += lengths[i]
return G
def plot_two_intervals(self,
position=(0, 0),
vertical_alignment='center',
horizontal_alignment='left',
interval_height=0.1,
labels_height=0.05,
fontsize=14,
labels=True,
colors=None):
r"""
Returns a picture of the interval exchange transformation.
INPUT:
- ``position`` - a 2-uple of the position
- ``horizontal_alignment`` - left (default), center or right
- ``labels`` - boolean (default: True)
- ``fontsize`` - the size of the label
OUTPUT:
2d plot -- a plot of the two intervals (domain and range)
EXAMPLES::
sage: t = iet.IntervalExchangeTransformation(('a b','b a'),[1,1])
sage: t.plot_two_intervals()
Graphics object consisting of 8 graphics primitives
"""
from sage.plot.all import Graphics
from sage.plot.line import line2d
from sage.plot.text import text
from sage.plot.colors import rainbow
G = Graphics()
lengths = [float(_) for _ in self._lengths]
total_length = sum(lengths)
if colors is None:
colors = rainbow(len(self._permutation), 'rgbtuple')
if horizontal_alignment == 'left':
s = position[0]
elif horizontal_alignment == 'center':
s = position[0] - total_length / 2
elif horizontal_alignment == 'right':
s = position[0] - total_length
else:
raise ValueError(
"horizontal_alignement must be left, center or right")
top_height = position[1] + interval_height
for i in self._permutation._intervals[0]:
G += line2d([(s, top_height), (s + lengths[i], top_height)],
rgbcolor=colors[i])
if labels:
G += text(
str(self._permutation._alphabet.unrank(i)),
(s + float(lengths[i]) / 2, top_height + labels_height),
horizontal_alignment='center',
rgbcolor=colors[i],
fontsize=fontsize)
s += lengths[i]
if horizontal_alignment == 'left':
s = position[0]
elif horizontal_alignment == 'center':
s = position[0] - total_length / 2
elif horizontal_alignment == 'right':
s = position[0] - total_length
else:
raise ValueError(
"horizontal_alignement must be left, center or right")
bottom_height = position[1] - interval_height
for i in self._permutation._intervals[1]:
G += line2d([(s, bottom_height), (s + lengths[i], bottom_height)],
rgbcolor=colors[i])
if labels:
G += text(
str(self._permutation._alphabet.unrank(i)),
(s + float(lengths[i]) / 2, bottom_height - labels_height),
horizontal_alignment='center',
rgbcolor=colors[i],
fontsize=fontsize)
s += lengths[i]
return G