def my_hyperbolic_triangle(a, b, c, **options):
"""
Return a hyperbolic triangle in the complex hyperbolic plane with points
(a, b, c). Type ``?hyperbolic_triangle`` to see all options.
INPUT:
- ``a, b, c`` - complex numbers in the upper half complex plane
OPTIONS:
- ``alpha`` - default: 1
- ``fill`` - default: False
- ``thickness`` - default: 1
- ``rgbcolor`` - default: 'blue'
- ``linestyle`` - default: 'solid'
EXAMPLES:
Show a hyperbolic triangle with coordinates 0, `1/2+i\sqrt{3}/2` and
`-1/2+i\sqrt{3}/2`::
sage: hyperbolic_triangle(0, -1/2+I*sqrt(3)/2, 1/2+I*sqrt(3)/2)
A hyperbolic triangle with coordinates 0, 1 and 2+i::
sage: hyperbolic_triangle(0, 1, 2+i, fill=true, rgbcolor='red')
"""
from sage.plot.all import Graphics
g = Graphics()
g._set_extra_kwds(g._extract_kwds_for_show(options))
model = options['model']
npts = options.get('npts',10)
sides = options.pop('sides',[1,2,3]) ## Which of the sides we will draw.
verbose = options.get('verbose',0)
options.pop('model',None); options.pop('method',None)
if model=="D":
#g.add_primitive(HyperbolicTriangleDisc(a, b, c, **options))
#print "options=",options
options['sides']=sides
H = HyperbolicTriangleDisc(a, b, c, **options)
g += H()
else:
options.pop('npts',None)
if sides == [1,2,3]:
if verbose>0:
print "adding HyperbolicTriangle({0}, {1}, {2},options={3})".format(a,b,c,options)
options.pop('verbose',0)
g.add_primitive(HyperbolicTriangle(a, b, c, options))
else:
options['sides']=sides
if verbose>0:
print "adding MyHyperbolicTriangle({0}, {1}, {2},options={3})".format(a,b,c,options)
g.add_primitive(MyHyperbolicTriangle(a, b, c, options))
g.set_aspect_ratio(1)
return g
def ellipse(center, r1, r2, angle=0, **options):
"""
Return an ellipse centered at a point center = ``(x,y)`` with radii =
``r1,r2`` and angle ``angle``. Type ``ellipse.options`` to see all
options.
INPUT:
- ``center`` - 2-tuple of real numbers - coordinates of the center
- ``r1``, ``r2`` - positive real numbers - the radii of the ellipse
- ``angle`` - real number (default: 0) - the angle between the first axis
and the horizontal
OPTIONS:
- ``alpha`` - default: 1 - transparency
- ``fill`` - default: False - whether to fill the ellipse or not
- ``thickness`` - default: 1 - thickness of the line
- ``linestyle`` - default: ``'solid'`` - The style of the line, which is one
of ``'dashed'``, ``'dotted'``, ``'solid'``, ``'dashdot'``, or ``'--'``,
``':'``, ``'-'``, ``'-.'``, respectively.
- ``edgecolor`` - default: 'black' - color of the contour
- ``facecolor`` - default: 'red' - color of the filling
- ``rgbcolor`` - 2D or 3D plotting. This option overrides
``edgecolor`` and ``facecolor`` for 2D plotting.
EXAMPLES:
An ellipse centered at (0,0) with major and minor axes of lengths 2 and 1.
Note that the default color is blue::
sage: ellipse((0,0),2,1)
More complicated examples with tilted axes and drawing options::
sage: ellipse((0,0),3,1,pi/6,fill=True,alpha=0.3,linestyle="dashed")
sage: ellipse((0,0),3,1,pi/6,fill=True,alpha=0.3,linestyle="--")
::
sage: ellipse((0,0),3,1,pi/6,fill=True,edgecolor='black',facecolor='red')
We see that ``rgbcolor`` overrides these other options, as this plot
is green::
sage: ellipse((0,0),3,1,pi/6,fill=True,edgecolor='black',facecolor='red',rgbcolor='green')
The default aspect ratio for ellipses is 1.0::
sage: ellipse((0,0),2,1).aspect_ratio()
1.0
One cannot yet plot ellipses in 3D::
sage: ellipse((0,0,0),2,1)
Traceback (most recent call last):
...
NotImplementedError: plotting ellipse in 3D is not implemented
"""
from sage.plot.all import Graphics
g = Graphics()
# Reset aspect_ratio to 'automatic' in case scale is 'semilog[xy]'.
# Otherwise matplotlib complains.
scale = options.get('scale', None)
if isinstance(scale, (list, tuple)):
scale = scale[0]
if scale == 'semilogy' or scale == 'semilogx':
options['aspect_ratio'] = 'automatic'
g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
g.add_primitive(Ellipse(center[0], center[1], r1, r2, angle, options))
if options['legend_label']:
g.legend(True)
if len(center) == 2:
return g
elif len(center) == 3:
raise NotImplementedError, "plotting ellipse in 3D is not implemented"
def arc(center, r1, r2=None, angle=0.0, sector=(0.0,2*pi), **options):
r"""
An arc (that is a portion of a circle or an ellipse)
Type ``arc.options`` to see all options.
INPUT:
- ``center`` - 2-tuple of real numbers - position of the center.
- ``r1``, ``r2`` - positive real numbers - radii of the ellipse. If only ``r1``
is set, then the two radii are supposed to be equal and this function returns
an arc of of circle.
- ``angle`` - real number - angle between the horizontal and the axis that
corresponds to ``r1``.
- ``sector`` - 2-tuple (default: (0,2*pi))- angles sector in which the arc will
be drawn.
OPTIONS:
- ``alpha`` - float (default: 1) - transparency
- ``thickness`` - float (default: 1) - thickness of the arc
- ``color``, ``rgbcolor`` - string or 2-tuple (default: 'blue') - the color
of the arc
- ``linestyle`` - string (default: ``'solid'``) - The style of the line,
which is one of ``'dashed'``, ``'dotted'``, ``'solid'``, ``'dashdot'``,
or ``'--'``, ``':'``, ``'-'``, ``'-.'``, respectively.
EXAMPLES:
Plot an arc of circle centered at (0,0) with radius 1 in the sector
`(\pi/4,3*\pi/4)`::
sage: arc((0,0), 1, sector=(pi/4,3*pi/4))
Graphics object consisting of 1 graphics primitive
Plot an arc of an ellipse between the angles 0 and `\pi/2`::
sage: arc((2,3), 2, 1, sector=(0,pi/2))
Graphics object consisting of 1 graphics primitive
Plot an arc of a rotated ellipse between the angles 0 and `\pi/2`::
sage: arc((2,3), 2, 1, angle=pi/5, sector=(0,pi/2))
Graphics object consisting of 1 graphics primitive
Plot an arc of an ellipse in red with a dashed linestyle::
sage: arc((0,0), 2, 1, 0, (0,pi/2), linestyle="dashed", color="red")
Graphics object consisting of 1 graphics primitive
sage: arc((0,0), 2, 1, 0, (0,pi/2), linestyle="--", color="red")
Graphics object consisting of 1 graphics primitive
The default aspect ratio for arcs is 1.0::
sage: arc((0,0), 1, sector=(pi/4,3*pi/4)).aspect_ratio()
1.0
It is not possible to draw arcs in 3D::
sage: A = arc((0,0,0), 1)
Traceback (most recent call last):
...
NotImplementedError
"""
from sage.plot.all import Graphics
# Reset aspect_ratio to 'automatic' in case scale is 'semilog[xy]'.
# Otherwise matplotlib complains.
scale = options.get('scale', None)
if isinstance(scale, (list, tuple)):
scale = scale[0]
if scale == 'semilogy' or scale == 'semilogx':
options['aspect_ratio'] = 'automatic'
if len(center)==2:
if r2 is None: r2 = r1
g = Graphics()
g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
if len(sector) != 2:
raise ValueError("the sector must consist of two angles")
g.add_primitive(Arc(
center[0],center[1],
r1,r2,
angle,
sector[0],sector[1],
options))
return g
elif len(center)==3:
raise NotImplementedError
def my_hyperbolic_triangle(a, b, c, **options):
"""
Return a hyperbolic triangle in the complex hyperbolic plane with points
(a, b, c). Type ``?hyperbolic_triangle`` to see all options.
INPUT:
- ``a, b, c`` - complex numbers in the upper half complex plane
OPTIONS:
- ``alpha`` - default: 1
- ``fill`` - default: False
- ``thickness`` - default: 1
- ``rgbcolor`` - default: 'blue'
- ``linestyle`` - default: 'solid'
EXAMPLES:
Show a hyperbolic triangle with coordinates 0, `1/2+i\sqrt{3}/2` and
`-1/2+i\sqrt{3}/2`::
sage: hyperbolic_triangle(0, -1/2+I*sqrt(3)/2, 1/2+I*sqrt(3)/2)
A hyperbolic triangle with coordinates 0, 1 and 2+i::
sage: hyperbolic_triangle(0, 1, 2+i, fill=true, rgbcolor='red')
"""
from sage.plot.all import Graphics
g = Graphics()
g._set_extra_kwds(g._extract_kwds_for_show(options))
model = options['model']
npts = options.get('npts', 10)
sides = options.pop('sides',
[1, 2, 3]) ## Which of the sides we will draw.
verbose = options.get('verbose', 0)
options.pop('model', None)
options.pop('method', None)
if model == "D":
#g.add_primitive(HyperbolicTriangleDisc(a, b, c, **options))
#print "options=",options
options['sides'] = sides
H = HyperbolicTriangleDisc(a, b, c, **options)
g += H()
else:
options.pop('npts', None)
if sides == [1, 2, 3]:
if verbose > 0:
print "adding HyperbolicTriangle({0}, {1}, {2},options={3})".format(
a, b, c, options)
options.pop('verbose', 0)
## check if We need my class or the original class
g.add_primitive(HyperbolicTriangle(a, b, c, options))
else:
options['sides'] = sides
if verbose > 0:
print "adding HyperbolicTriangle({0}, {1}, {2},options={3})".format(
a, b, c, options)
g.add_primitive(HyperbolicTriangle(a, b, c, options))
g.set_aspect_ratio(1)
return g
def ellipse(center, r1, r2, angle=0, **options):
"""
Return an ellipse centered at a point center = ``(x,y)`` with radii =
``r1,r2`` and angle ``angle``. Type ``ellipse.options`` to see all
options.
INPUT:
- ``center`` - 2-tuple of real numbers - coordinates of the center
- ``r1``, ``r2`` - positive real numbers - the radii of the ellipse
- ``angle`` - real number (default: 0) - the angle between the first axis
and the horizontal
OPTIONS:
- ``alpha`` - default: 1 - transparency
- ``fill`` - default: False - whether to fill the ellipse or not
- ``thickness`` - default: 1 - thickness of the line
- ``linestyle`` - default: ``'solid'`` - The style of the line, which is one
of ``'dashed'``, ``'dotted'``, ``'solid'``, ``'dashdot'``, or ``'--'``,
``':'``, ``'-'``, ``'-.'``, respectively.
- ``edgecolor`` - default: 'black' - color of the contour
- ``facecolor`` - default: 'red' - color of the filling
- ``rgbcolor`` - 2D or 3D plotting. This option overrides
``edgecolor`` and ``facecolor`` for 2D plotting.
- ``legend_label`` - the label for this item in the legend
- ``legend_color`` - the color for the legend label
EXAMPLES:
An ellipse centered at (0,0) with major and minor axes of lengths 2 and 1.
Note that the default color is blue::
sage: ellipse((0,0),2,1)
More complicated examples with tilted axes and drawing options::
sage: ellipse((0,0),3,1,pi/6,fill=True,alpha=0.3,linestyle="dashed")
sage: ellipse((0,0),3,1,pi/6,fill=True,alpha=0.3,linestyle="--")
::
sage: ellipse((0,0),3,1,pi/6,fill=True,edgecolor='black',facecolor='red')
We see that ``rgbcolor`` overrides these other options, as this plot
is green::
sage: ellipse((0,0),3,1,pi/6,fill=True,edgecolor='black',facecolor='red',rgbcolor='green')
The default aspect ratio for ellipses is 1.0::
sage: ellipse((0,0),2,1).aspect_ratio()
1.0
One cannot yet plot ellipses in 3D::
sage: ellipse((0,0,0),2,1)
Traceback (most recent call last):
...
NotImplementedError: plotting ellipse in 3D is not implemented
We can also give ellipses a legend::
sage: ellipse((0,0),2,1,legend_label="My ellipse", legend_color='green')
"""
from sage.plot.all import Graphics
g = Graphics()
# Reset aspect_ratio to 'automatic' in case scale is 'semilog[xy]'.
# Otherwise matplotlib complains.
scale = options.get('scale', None)
if isinstance(scale, (list, tuple)):
scale = scale[0]
if scale == 'semilogy' or scale == 'semilogx':
options['aspect_ratio'] = 'automatic'
g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
g.add_primitive(Ellipse(center[0],center[1],r1,r2,angle,options))
if options['legend_label']:
g.legend(True)
g._legend_colors = [options['legend_color']]
if len(center)==2:
return g
elif len(center)==3:
raise NotImplementedError("plotting ellipse in 3D is not implemented")