def plot3d(self):
"""
Plots the braid in 3d.
EXAMPLES::
sage: B = BraidGroup(4, 's')
sage: b = B([1, 2, 3, 1, 2, 1])
sage: b.plot3d()
"""
from sage.plot.plot3d.shapes2 import bezier3d
b = []
braid = self.Tietze()
n = self.strands()
for i in range(len(braid)):
m = braid[i]
for j in range(n):
if m==j+1:
b.append(bezier3d([[(0, j, i), (0, j, i+0.25), (0.25, j, i+0.25), (0.25, j+0.5, i+0.5)],
[(0.25, j+1, i+0.75), (0, j+1, i+0.75), (0, j+1, i+1)]]))
elif -m==j+1:
b.append(bezier3d([[(0, j, i), (0, j, i+0.25), (-0.25, j, i+0.25), (-0.25, j+0.5, i+0.5)],
[(-0.25, j+1, i+0.75), (0, j+1, i+0.75), (0, j+1, i+1)]]))
elif m==j:
b.append(bezier3d([[(0, j, i), (0, j, i+0.25), (-0.25, j, i+0.25), (-0.25, j-0.5, i+0.5)],
[(-0.25, j-1, i+0.75), (0, j-1, i+0.75), (0, j-1, i+1)]]))
elif -m==j:
b.append(bezier3d([[(0, j, i), (0, j, i+0.25), (0.25, j, i+0.25), (0.25, j-0.5, i+0.5)],
[(0.25, j-1, i+0.75), (0, j-1, i+0.75), (0, j-1, i+1)]]))
else:
b.append(bezier3d([[(0, j, i), (0, j, i+1)]]))
return sum(b)
def plot3d(self):
"""
Plots the braid in 3d.
EXAMPLES::
sage: B = BraidGroup(4, 's')
sage: b = B([1, 2, 3, 1, 2, 1])
sage: b.plot3d()
"""
from sage.plot.plot3d.shapes2 import bezier3d
b = []
braid = self.Tietze()
n = self.strands()
for i in range(len(braid)):
m = braid[i]
for j in range(n):
if m==j+1:
b.append(bezier3d([[(0, j, i), (0, j, i+0.25), (0.25, j, i+0.25), (0.25, j+0.5, i+0.5)],
[(0.25, j+1, i+0.75), (0, j+1, i+0.75), (0, j+1, i+1)]]))
elif -m==j+1:
b.append(bezier3d([[(0, j, i), (0, j, i+0.25), (-0.25, j, i+0.25), (-0.25, j+0.5, i+0.5)],
[(-0.25, j+1, i+0.75), (0, j+1, i+0.75), (0, j+1, i+1)]]))
elif m==j:
b.append(bezier3d([[(0, j, i), (0, j, i+0.25), (-0.25, j, i+0.25), (-0.25, j-0.5, i+0.5)],
[(-0.25, j-1, i+0.75), (0, j-1, i+0.75), (0, j-1, i+1)]]))
elif -m==j:
b.append(bezier3d([[(0, j, i), (0, j, i+0.25), (0.25, j, i+0.25), (0.25, j-0.5, i+0.5)],
[(0.25, j-1, i+0.75), (0, j-1, i+0.75), (0, j-1, i+1)]]))
else:
b.append(bezier3d([[(0, j, i), (0, j, i+1)]]))
return sum(b)
def plot3d(self, color='rainbow'):
"""
Plots the braid in 3d.
The following option is available:
- ``color`` -- (default: ``'rainbow'``) the color of the
strands. Possible values are:
* ``'rainbow'``, uses :meth:`~sage.plot.colors.rainbow`
according to the number of strands.
* a valid color name for :meth:`~sage.plot.plot3d.bezier3d`.
Used for all strands.
* a list or a tuple of colors for each individual strand.
EXAMPLES::
sage: B = BraidGroup(4, 's')
sage: b = B([1, 2, 3, 1, 2, 1])
sage: b.plot3d()
sage: b.plot3d(color="red")
sage: b.plot3d(color=["red", "blue", "red", "blue"])
"""
from sage.plot.plot3d.shapes2 import bezier3d
from sage.plot.colors import rainbow
b = []
n = self.strands()
if isinstance(color, (list, tuple)):
if len(color) != n:
raise TypeError("color (=%s) must contain exactly %d colors" % (color, n))
col = list(color)
elif color == "rainbow":
col = rainbow(n)
else:
col = [color]*n
braid = self.Tietze()
for i, m in enumerate(braid):
for j in range(n):
if m==j+1:
b.append(bezier3d([[(0, j, i), (0, j, i+0.25), (0.25, j, i+0.25), (0.25, j+0.5, i+0.5)],
[(0.25, j+1, i+0.75), (0, j+1, i+0.75), (0, j+1, i+1)]], color=col[j]))
elif -m==j+1:
b.append(bezier3d([[(0, j, i), (0, j, i+0.25), (-0.25, j, i+0.25), (-0.25, j+0.5, i+0.5)],
[(-0.25, j+1, i+0.75), (0, j+1, i+0.75), (0, j+1, i+1)]], color=col[j]))
elif m==j:
b.append(bezier3d([[(0, j, i), (0, j, i+0.25), (-0.25, j, i+0.25), (-0.25, j-0.5, i+0.5)],
[(-0.25, j-1, i+0.75), (0, j-1, i+0.75), (0, j-1, i+1)]], color=col[j]))
col[j], col[j-1] = col[j-1], col[j]
elif -m==j:
b.append(bezier3d([[(0, j, i), (0, j, i+0.25), (0.25, j, i+0.25), (0.25, j-0.5, i+0.5)],
[(0.25, j-1, i+0.75), (0, j-1, i+0.75), (0, j-1, i+1)]], color=col[j]))
col[j], col[j-1] = col[j-1], col[j]
else:
b.append(bezier3d([[(0, j, i), (0, j, i+1)]], color=col[j]))
return sum(b)
def plot3d(self, z=0, **kwds):
"""
Returns a 3D plot (Jmol) of the Bezier path. Since a ``BezierPath``
primitive contains only `x,y` coordinates, the path will be drawn in
some plane (default is `z=0`). To create a Bezier path with nonzero
(and nonidentical) `z` coordinates in the path and control points, use
the function :func:`~sage.plot.plot3d.shapes2.bezier3d` instead of
:func:`bezier_path`.
EXAMPLES::
sage: b = bezier_path([[(0,0),(0,1),(1,0)]])
sage: A = b.plot3d()
sage: B = b.plot3d(z=2)
sage: A+B
::
sage: bezier3d([[(0,0,0),(1,0,0),(0,1,0),(0,1,1)]])
"""
from sage.plot.plot3d.shapes2 import bezier3d
options = self._plot3d_options()
options.update(kwds)
return bezier3d([[(x, y, 0) for x, y in self.path[i]]
for i in range(len(self.path))], **options)
def plot3d(self, z=0, **kwds):
"""
Returns a 3D plot (Jmol) of the Bezier path. Since a ``BezierPath``
primitive contains only `x,y` coordinates, the path will be drawn in
some plane (default is `z=0`). To create a Bezier path with nonzero
(and nonidentical) `z` coordinates in the path and control points, use
the function :func:`~sage.plot.plot3d.shapes2.bezier3d` instead of
:func:`bezier_path`.
EXAMPLES::
sage: b = bezier_path([[(0,0),(0,1),(1,0)]])
sage: A = b.plot3d()
sage: B = b.plot3d(z=2)
sage: A + B
Graphics3d Object
.. PLOT::
b = bezier_path([[(0,0),(0,1),(1,0)]])
A = b.plot3d()
B = b.plot3d(z=2)
sphinx_plot(A + B)
::
sage: bezier3d([[(0,0,0),(1,0,0),(0,1,0),(0,1,1)]])
Graphics3d Object
.. PLOT::
sphinx_plot(bezier3d([[(0,0,0),(1,0,0),(0,1,0),(0,1,1)]]))
"""
from sage.plot.plot3d.shapes2 import bezier3d
options = self._plot3d_options()
options.update(kwds)
return bezier3d([[(x,y,0) for x,y in self.path[i]] for i in range(len(self.path))], **options)
