Source code for flatsurf.graphical.straight_line_trajectory
r"""
.. jupyter-execute::
:hide-code:
# Allow jupyter-execute blocks in this module to contain doctests
import jupyter_doctest_tweaks
"""
# ****************************************************************************
# This file is part of sage-flatsurf.
#
# Copyright (C) 2013-2019 Vincent Delecroix
# 2013-2019 W. Patrick Hooper
# 2022-2023 Julian Rüth
#
# sage-flatsurf is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 2 of the License, or
# (at your option) any later version.
#
# sage-flatsurf is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with sage-flatsurf. If not, see <https://www.gnu.org/licenses/>.
# ****************************************************************************
[docs]
class GraphicalSegmentInPolygon:
def __init__(self, segment, graphical_surface):
r"""
Create a graphical segment from a graphical surface and a SegmentInPolygon.
"""
self._gs = graphical_surface
self._seg = segment
label = self.polygon_label()
self._start = self._gs.graphical_polygon(label).transform(
segment.start().point()
)
if self._seg.is_edge():
self._end = self._gs.graphical_polygon(label).transform(
self._seg.start().polygon().vertex(self._seg.edge() + 1)
)
else:
self._end = self._gs.graphical_polygon(label).transform(
segment.end().point()
)
[docs]
def polygon_label(self):
return self._seg.polygon_label()
[docs]
def start(self):
r"""Return the start point as a RDF Vector."""
return self._start
[docs]
def end(self):
r"""Return the end point as a RDF Vector."""
return self._end
[docs]
def plot(self, **options):
r"""
EXAMPLES:
.. jupyter-execute::
sage: from flatsurf import similarity_surfaces
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 GraphicalSegmentInPolygon
sage: gseg = GraphicalSegmentInPolygon(seg, s.graphical_surface())
sage: gseg.plot()
...Graphics object consisting of 1 graphics primitive
.. jupyter-execute::
sage: gseg.plot(color='red')
...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()
[docs]
class GraphicalStraightLineTrajectory:
r"""
Allows for the rendering of a straight-line trajectory through a graphical surface.
"""
def __init__(self, trajectory, graphical_surface=None):
if graphical_surface is None:
self._gs = trajectory.surface().graphical_surface()
else:
if trajectory.surface() != graphical_surface.get_surface():
raise ValueError
self._gs = graphical_surface
self._traj = trajectory
self._segments = [
GraphicalSegmentInPolygon(s, self._gs) for s in self._traj.segments()
]
[docs]
def plot(self, **options):
r"""
EXAMPLES:
.. jupyter-execute::
sage: from flatsurf import similarity_surfaces
sage: K.<sqrt2>=NumberField(x^2-2,embedding=1)
sage: s = similarity_surfaces.example().change_ring(K)
sage: gs = s.graphical_surface()
sage: v = s.tangent_vector(0, (1,-1), (sqrt2,-1),ring=K)
sage: traj = v.straight_line_trajectory()
sage: traj.flow(100)
sage: traj.flow(-5)
sage: gtraj = traj.graphical_trajectory(gs)
sage: gs.plot() + gtraj.plot()
...Graphics object consisting of 119 graphics primitives
"""
from sage.plot.graphics import Graphics
p = Graphics()
for seg in self._segments:
p += seg.plot(**options)
return p
