def limit_arrow(tailpoint=None, headpoint=None, path=None, **options):
from sage.plot.all import Graphics
g = Graphics()
g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
if headpoint is not None and tailpoint is not None:
xtail, ytail = tailpoint
xhead, yhead = headpoint
g.add_primitive(LimitArrow(xtail, ytail, xhead, yhead, options=options))
elif path is not None:
g.add_primitive(CurveArrow(path, options=options))
elif tailpoint is None and headpoint is None:
return g
else:
raise TypeError('Arrow requires either both headpoint and tailpoint or a path parameter.')
if options['legend_label']:
g.legend(True)
g._legend_colors = [options['legend_color']]
return g
def point2d(points, **options):
r"""
A point of size ``size`` defined by point = `(x, y)`.
INPUT:
- ``points`` -- either a single point (as a tuple), a list of
points, a single complex number, or a list of complex numbers
- ``alpha`` -- how transparent the point is
- ``faceted`` -- if ``True``, color the edge of the point (only for 2D plots)
- ``hue`` -- the color given as a hue
- ``legend_color`` -- the color of the legend text
- ``legend_label`` -- the label for this item in the legend
- ``marker`` -- the marker symbol for 2D plots only (see documentation of
:func:`plot` for details)
- ``markeredgecolor`` -- the color of the marker edge (only for 2D plots)
- ``rgbcolor`` -- the color as an RGB tuple
- ``size`` -- how big the point is (i.e., area in points^2=(1/72 inch)^2)
- ``zorder`` -- the layer level in which to draw
EXAMPLES:
A purple point from a single tuple of coordinates::
sage: point((0.5, 0.5), rgbcolor=hue(0.75))
Graphics object consisting of 1 graphics primitive
Points with customized markers and edge colors::
sage: r = [(random(), random()) for _ in range(10)]
sage: point(r, marker='d', markeredgecolor='red', size=20)
Graphics object consisting of 1 graphics primitive
Passing an empty list returns an empty plot::
sage: point([])
Graphics object consisting of 0 graphics primitives
sage: import numpy; point(numpy.array([]))
Graphics object consisting of 0 graphics primitives
If you need a 2D point to live in 3-space later, this is possible::
sage: A = point((1, 1))
sage: a = A[0]; a
Point set defined by 1 point(s)
sage: b = a.plot3d(z=3)
This is also true with multiple points::
sage: P = point([(0, 0), (1, 1)])
sage: p = P[0]
sage: q = p.plot3d(z=[2,3])
Here are some random larger red points, given as a list of tuples::
sage: point(((0.5, 0.5), (1, 2), (0.5, 0.9), (-1, -1)), rgbcolor=hue(1), size=30)
Graphics object consisting of 1 graphics primitive
And an example with a legend::
sage: point((0, 0), rgbcolor='black', pointsize=40, legend_label='origin')
Graphics object consisting of 1 graphics primitive
The legend can be colored::
sage: P = points([(0, 0), (1, 0)], pointsize=40, legend_label='origin', legend_color='red')
sage: P + plot(x^2, (x, 0, 1), legend_label='plot', legend_color='green')
Graphics object consisting of 2 graphics primitives
Extra options will get passed on to show(), as long as they are valid::
sage: point([(cos(theta), sin(theta)) for theta in srange(0, 2*pi, pi/8)], frame=True)
Graphics object consisting of 1 graphics primitive
sage: point([(cos(theta), sin(theta)) for theta in srange(0, 2*pi, pi/8)]).show(frame=True) # These are equivalent
For plotting data, we can use a logarithmic scale, as long as we are sure
not to include any nonpositive points in the logarithmic direction::
sage: point([(1, 2),(2, 4),(3, 4),(4, 8),(4.5, 32)], scale='semilogy', base=2)
Graphics object consisting of 1 graphics primitive
Since Sage Version 4.4 (:trac:`8599`), the size of a 2d point can be
given by the argument ``size`` instead of ``pointsize``. The argument
``pointsize`` is still supported::
sage: point((3, 4), size=100)
Graphics object consisting of 1 graphics primitive
::
sage: point((3, 4), pointsize=100)
Graphics object consisting of 1 graphics primitive
We can plot a single complex number::
sage: point(1 + I, pointsize=100)
Graphics object consisting of 1 graphics primitive
sage: point(sqrt(2) + I, pointsize=100)
Graphics object consisting of 1 graphics primitive
We can also plot a list of complex numbers::
sage: point([I, 1 + I, 2 + 2*I], pointsize=100)
Graphics object consisting of 1 graphics primitive
TESTS::
sage: point2d(iter([]))
Graphics object consisting of 0 graphics primitives
"""
from sage.plot.plot import xydata_from_point_list
from sage.plot.all import Graphics
from sage.structure.element import Expression
# points could be a single number
if isinstance(points, numbers.Complex):
points = [(points.real(), points.imag())]
elif isinstance(points, numbers.Real):
points = [points]
elif isinstance(points, Expression):
points = [points]
elif not isinstance(points, (list, tuple)): # or an iterator
points = list(points)
l = len(points)
if l == 0:
return Graphics()
elif l == 2: # special case for a single 2D point
if all(
isinstance(z, numbers.Real) or (
isinstance(z, Expression) and not complex(z).imag)
for z in points):
points = [points]
elif l == 3: # special case for a single 3D point
if all(
isinstance(z, numbers.Real) or (
isinstance(z, Expression) and not complex(z).imag)
for z in points):
raise TypeError('not a 2D point')
xdata, ydata = xydata_from_point_list(points)
g = Graphics()
g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
g.add_primitive(Point(xdata, ydata, options))
if options['legend_label']:
g.legend(True)
g._legend_colors = [options['legend_color']]
return g
def polygon2d(points, **options):
r"""
Returns a 2-dimensional polygon defined by ``points``.
Type ``polygon2d.options`` for a dictionary of the default
options for polygons. You can change this to change the
defaults for all future polygons. Use ``polygon2d.reset()``
to reset to the default options.
EXAMPLES:
We create a purple-ish polygon::
sage: polygon2d([[1,2], [5,6], [5,0]], rgbcolor=(1,0,1))
Graphics object consisting of 1 graphics primitive
.. PLOT::
sphinx_plot(polygon2d([[1,2], [5,6], [5,0]], rgbcolor=(1,0,1)))
By default, polygons are filled in, but we can make them
without a fill as well::
sage: polygon2d([[1,2], [5,6], [5,0]], fill=False)
Graphics object consisting of 1 graphics primitive
.. PLOT::
sphinx_plot(polygon2d([[1,2], [5,6], [5,0]], fill=False))
In either case, the thickness of the border can be controlled::
sage: polygon2d([[1,2], [5,6], [5,0]], fill=False, thickness=4, color='orange')
Graphics object consisting of 1 graphics primitive
.. PLOT::
P = polygon2d([[1,2], [5,6], [5,0]], fill=False, thickness=4, color='orange')
sphinx_plot(P)
For filled polygons, one can use different colors for the border
and the interior as follows::
sage: L = [[0,0]]+[[i/100, 1.1+cos(i/20)] for i in range(100)]+[[1,0]]
sage: polygon2d(L, color="limegreen", edgecolor="black", axes=False)
Graphics object consisting of 1 graphics primitive
.. PLOT::
L = [[0,0]]+[[i*0.01, 1.1+cos(i*0.05)] for i in range(100)]+[[1,0]]
P = polygon2d(L, color="limegreen", edgecolor="black", axes=False)
sphinx_plot(P)
Some modern art -- a random polygon, with legend::
sage: v = [(randrange(-5,5), randrange(-5,5)) for _ in range(10)]
sage: polygon2d(v, legend_label='some form')
Graphics object consisting of 1 graphics primitive
.. PLOT::
v = [(randrange(-5,5), randrange(-5,5)) for _ in range(10)]
P = polygon2d(v, legend_label='some form')
sphinx_plot(P)
A purple hexagon::
sage: L = [[cos(pi*i/3),sin(pi*i/3)] for i in range(6)]
sage: polygon2d(L, rgbcolor=(1,0,1))
Graphics object consisting of 1 graphics primitive
.. PLOT::
L = [[cos(pi*i/3.0),sin(pi*i/3.0)] for i in range(6)]
P = polygon2d(L, rgbcolor=(1,0,1))
sphinx_plot(P)
A green deltoid::
sage: L = [[-1+cos(pi*i/100)*(1+cos(pi*i/100)),2*sin(pi*i/100)*(1-cos(pi*i/100))] for i in range(200)]
sage: polygon2d(L, rgbcolor=(1/8,3/4,1/2))
Graphics object consisting of 1 graphics primitive
.. PLOT::
L = [[-1+cos(pi*i*0.01)*(1+cos(pi*i*0.01)),2*sin(pi*i*0.01)*(1-cos(pi*i*0.01))] for i in range(200)]
P = polygon2d(L, rgbcolor=(0.125,0.75,0.5))
sphinx_plot(P)
A blue hypotrochoid::
sage: L = [[6*cos(pi*i/100)+5*cos((6/2)*pi*i/100),6*sin(pi*i/100)-5*sin((6/2)*pi*i/100)] for i in range(200)]
sage: polygon2d(L, rgbcolor=(1/8,1/4,1/2))
Graphics object consisting of 1 graphics primitive
.. PLOT::
L = [[6*cos(pi*i*0.01)+5*cos(3*pi*i*0.01),6*sin(pi*i*0.01)-5*sin(3*pi*i*0.01)] for i in range(200)]
P = polygon2d(L, rgbcolor=(0.125,0.25,0.5))
sphinx_plot(P)
Another one::
sage: n = 4; h = 5; b = 2
sage: L = [[n*cos(pi*i/100)+h*cos((n/b)*pi*i/100),n*sin(pi*i/100)-h*sin((n/b)*pi*i/100)] for i in range(200)]
sage: polygon2d(L, rgbcolor=(1/8,1/4,3/4))
Graphics object consisting of 1 graphics primitive
.. PLOT::
n = 4.0; h = 5.0; b = 2.0
L = [[n*cos(pi*i*0.01)+h*cos((n/b)*pi*i*0.01),n*sin(pi*i*0.01)-h*sin((n/b)*pi*i*0.01)] for i in range(200)]
P = polygon2d(L, rgbcolor=(0.125,0.25,0.75))
sphinx_plot(P)
A purple epicycloid::
sage: m = 9; b = 1
sage: L = [[m*cos(pi*i/100)+b*cos((m/b)*pi*i/100),m*sin(pi*i/100)-b*sin((m/b)*pi*i/100)] for i in range(200)]
sage: polygon2d(L, rgbcolor=(7/8,1/4,3/4))
Graphics object consisting of 1 graphics primitive
.. PLOT::
m = 9.0; b = 1
L = [[m*cos(pi*i*0.01)+b*cos((m/b)*pi*i*0.01),m*sin(pi*i*0.01)-b*sin((m/b)*pi*i*0.01)] for i in range(200)]
P = polygon2d(L, rgbcolor=(0.875,0.25,0.75))
sphinx_plot(P)
A brown astroid::
sage: L = [[cos(pi*i/100)^3,sin(pi*i/100)^3] for i in range(200)]
sage: polygon2d(L, rgbcolor=(3/4,1/4,1/4))
Graphics object consisting of 1 graphics primitive
.. PLOT::
L = [[cos(pi*i*0.01)**3,sin(pi*i*0.01)**3] for i in range(200)]
P = polygon2d(L, rgbcolor=(0.75,0.25,0.25))
sphinx_plot(P)
And, my favorite, a greenish blob::
sage: L = [[cos(pi*i/100)*(1+cos(pi*i/50)), sin(pi*i/100)*(1+sin(pi*i/50))] for i in range(200)]
sage: polygon2d(L, rgbcolor=(1/8,3/4,1/2))
Graphics object consisting of 1 graphics primitive
.. PLOT::
L = [[cos(pi*i*0.01)*(1+cos(pi*i*0.02)), sin(pi*i*0.01)*(1+sin(pi*i*0.02))] for i in range(200)]
P = polygon2d(L, rgbcolor=(0.125,0.75,0.5))
sphinx_plot(P)
This one is for my wife::
sage: L = [[sin(pi*i/100)+sin(pi*i/50),-(1+cos(pi*i/100)+cos(pi*i/50))] for i in range(-100,100)]
sage: polygon2d(L, rgbcolor=(1,1/4,1/2))
Graphics object consisting of 1 graphics primitive
.. PLOT::
L = [[sin(pi*i*0.01)+sin(pi*i*0.02),-(1+cos(pi*i*0.01)+cos(pi*i*0.02))] for i in range(-100,100)]
P = polygon2d(L, rgbcolor=(1,0.25,0.5))
sphinx_plot(P)
One can do the same one with a colored legend label::
sage: polygon2d(L, color='red', legend_label='For you!', legend_color='red')
Graphics object consisting of 1 graphics primitive
.. PLOT::
L = [[sin(pi*i*0.01)+sin(pi*i*0.02),-(1+cos(pi*i*0.01)+cos(pi*i*0.02))] for i in range(-100,100)]
P = polygon2d(L, color='red', legend_label='For you!', legend_color='red')
sphinx_plot(P)
Polygons have a default aspect ratio of 1.0::
sage: polygon2d([[1,2], [5,6], [5,0]]).aspect_ratio()
1.0
AUTHORS:
- David Joyner (2006-04-14): the long list of examples above.
"""
from sage.plot.plot import xydata_from_point_list
from sage.plot.all import Graphics
if options["thickness"] is None: # If the user did not specify thickness
if options["fill"] and options["edgecolor"] is None:
# If the user chose fill
options["thickness"] = 0
else:
options["thickness"] = 1
xdata, ydata = xydata_from_point_list(points)
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(Polygon(xdata, ydata, options))
if options['legend_label']:
g.legend(True)
g._legend_colors = [options['legend_color']]
return g
def disk(point, radius, angle, **options):
r"""
A disk (that is, a sector or wedge of a circle) with center
at a point = `(x,y)` (or `(x,y,z)` and parallel to the
`xy`-plane) with radius = `r` spanning (in radians)
angle=`(rad1, rad2)`.
Type ``disk.options`` to see all options.
EXAMPLES:
Make some dangerous disks::
sage: bl = disk((0.0,0.0), 1, (pi, 3*pi/2), color='yellow')
sage: tr = disk((0.0,0.0), 1, (0, pi/2), color='yellow')
sage: tl = disk((0.0,0.0), 1, (pi/2, pi), color='black')
sage: br = disk((0.0,0.0), 1, (3*pi/2, 2*pi), color='black')
sage: P = tl+tr+bl+br
sage: P.show(xmin=-2,xmax=2,ymin=-2,ymax=2)
The default aspect ratio is 1.0::
sage: disk((0.0,0.0), 1, (pi, 3*pi/2)).aspect_ratio()
1.0
Another example of a disk::
sage: bl = disk((0.0,0.0), 1, (pi, 3*pi/2), rgbcolor=(1,1,0))
sage: bl.show(figsize=[5,5])
Note that since ``thickness`` defaults to zero, it is best to change
that option when using ``fill=False``::
sage: disk((2,3), 1, (pi/4,pi/3), hue=.8, alpha=.3, fill=False, thickness=2)
The previous two examples also illustrate using ``hue`` and ``rgbcolor``
as ways of specifying the color of the graphic.
We can also use this command to plot three-dimensional disks parallel
to the `xy`-plane::
sage: d = disk((1,1,3), 1, (pi,3*pi/2), rgbcolor=(1,0,0))
sage: d
sage: type(d)
<type 'sage.plot.plot3d.index_face_set.IndexFaceSet'>
Extra options will get passed on to ``show()``, as long as they are valid::
sage: disk((0, 0), 5, (0, pi/2), xmin=0, xmax=5, ymin=0, ymax=5, figsize=(2,2), rgbcolor=(1, 0, 1))
sage: disk((0, 0), 5, (0, pi/2), rgbcolor=(1, 0, 1)).show(xmin=0, xmax=5, ymin=0, ymax=5, figsize=(2,2)) # These are equivalent
TESTS:
Testing that legend labels work right::
sage: disk((2,4), 3, (pi/8, pi/4), hue=1, legend_label='disk', legend_color='blue')
We cannot currently plot disks in more than three dimensions::
sage: d = disk((1,1,1,1), 1, (0,pi))
Traceback (most recent call last):
...
ValueError: The center point of a plotted disk should have two or three coordinates.
"""
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(Disk(point, radius, angle, options))
if options['legend_label']:
g.legend(True)
g._legend_colors = [options['legend_color']]
if len(point)==2:
return g
elif len(point)==3:
return g[0].plot3d(z=point[2])
else:
raise ValueError, 'The center point of a plotted disk should have two or three coordinates.'
def point2d(points, **options):
r"""
A point of size ``size`` defined by point = `(x,y)`.
INPUT:
- ``points`` - either a single point (as a tuple), a list of
points, a single complex number, or a list of complex numbers.
Type ``point2d.options`` to see all options.
EXAMPLES:
A purple point from a single tuple or coordinates::
sage: point((0.5, 0.5), rgbcolor=hue(0.75))
Passing an empty list returns an empty plot::
sage: point([])
sage: import numpy; point(numpy.array([]))
If you need a 2D point to live in 3-space later,
this is possible::
sage: A=point((1,1))
sage: a=A[0];a
Point set defined by 1 point(s)
sage: b=a.plot3d(z=3)
This is also true with multiple points::
sage: P=point([(0,0), (1,1)])
sage: p=P[0]
sage: q=p.plot3d(z=[2,3])
Here are some random larger red points, given as a list of tuples::
sage: point(((0.5, 0.5), (1, 2), (0.5, 0.9), (-1, -1)), rgbcolor=hue(1), size=30)
And an example with a legend::
sage: point((0,0), rgbcolor='black', pointsize=40, legend_label='origin')
The legend can be colored::
sage: P = points([(0,0),(1,0)], pointsize=40, legend_label='origin', legend_color='red')
sage: P + plot(x^2,(x,0,1), legend_label='plot', legend_color='green')
Extra options will get passed on to show(), as long as they are valid::
sage: point([(cos(theta), sin(theta)) for theta in srange(0, 2*pi, pi/8)], frame=True)
sage: point([(cos(theta), sin(theta)) for theta in srange(0, 2*pi, pi/8)]).show(frame=True) # These are equivalent
For plotting data, we can use a logarithmic scale, as long as we are sure
not to include any nonpositive points in the logarithmic direction::
sage: point([(1,2),(2,4),(3,4),(4,8),(4.5,32)],scale='semilogy',base=2)
Since Sage Version 4.4 (ticket #8599), the size of a 2d point can be
given by the argument ``size`` instead of ``pointsize``. The argument
``pointsize`` is still supported::
sage: point((3,4), size=100)
::
sage: point((3,4), pointsize=100)
We can plot a single complex number::
sage: point(CC(1+I), pointsize=100)
We can also plot a list of complex numbers::
sage: point([CC(I), CC(I+1), CC(2+2*I)], pointsize=100)
"""
from sage.plot.plot import xydata_from_point_list
from sage.plot.all import Graphics
from sage.rings.all import CC, CDF
if points in CC or points in CDF:
pass
else:
try:
if not points:
return Graphics()
except ValueError: # numpy raises a ValueError if not empty
pass
xdata, ydata = xydata_from_point_list(points)
g = Graphics()
g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
g.add_primitive(Point(xdata, ydata, options))
if options['legend_label']:
g.legend(True)
g._legend_colors = [options['legend_color']]
return g
def circle(center, radius, **options):
"""
Return a circle at a point center = `(x,y)` (or `(x,y,z)` and
parallel to the `xy`-plane) with radius = `r`. Type
``circle.options`` to see all options.
OPTIONS:
- ``alpha`` - default: 1
- ``fill`` - default: False
- ``thickness`` - default: 1
- ``linestyle`` - default: ``'solid'`` (2D plotting only) The style of the
line, which is one of ``'dashed'``, ``'dotted'``, ``'solid'``, ``'dashdot'``,
or ``'--'``, ``':'``, ``'-'``, ``'-.'``, respectively.
- ``edgecolor`` - default: 'blue' (2D plotting only)
- ``facecolor`` - default: 'blue' (2D plotting only, useful only
if ``fill=True``)
- ``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:
The default color is blue, the default linestyle is solid, but this is easy to change::
sage: c = circle((1,1), 1)
sage: c
::
sage: c = circle((1,1), 1, rgbcolor=(1,0,0), linestyle='-.')
sage: c
We can also use this command to plot three-dimensional circles parallel
to the `xy`-plane::
sage: c = circle((1,1,3), 1, rgbcolor=(1,0,0))
sage: c
sage: type(c)
<class 'sage.plot.plot3d.base.TransformGroup'>
To correct the aspect ratio of certain graphics, it is necessary
to show with a ``figsize`` of square dimensions::
sage: c.show(figsize=[5,5],xmin=-1,xmax=3,ymin=-1,ymax=3)
Here we make a more complicated plot, with many circles of different colors::
sage: g = Graphics()
sage: step=6; ocur=1/5; paths=16;
sage: PI = math.pi # numerical for speed -- fine for graphics
sage: for r in range(1,paths+1):
... for x,y in [((r+ocur)*math.cos(n), (r+ocur)*math.sin(n)) for n in srange(0, 2*PI+PI/step, PI/step)]:
... g += circle((x,y), ocur, rgbcolor=hue(r/paths))
... rnext = (r+1)^2
... ocur = (rnext-r)-ocur
...
sage: g.show(xmin=-(paths+1)^2, xmax=(paths+1)^2, ymin=-(paths+1)^2, ymax=(paths+1)^2, figsize=[6,6])
Note that the ``rgbcolor`` option overrides the other coloring options.
This produces red fill in a blue circle::
sage: circle((2,3), 1, fill=True, edgecolor='blue')
This produces an all-green filled circle::
sage: circle((2,3), 1, fill=True, edgecolor='blue', rgbcolor='green')
The option ``hue`` overrides *all* other options, so be careful with its use.
This produces a purplish filled circle::
sage: circle((2,3), 1, fill=True, edgecolor='blue', rgbcolor='green', hue=.8)
And circles with legends::
sage: circle((4,5), 1, rgbcolor='yellow', fill=True, legend_label='the sun').show(xmin=0, ymin=0)
::
sage: circle((4,5), 1, legend_label='the sun', legend_color='yellow').show(xmin=0, ymin=0)
Extra options will get passed on to show(), as long as they are valid::
sage: circle((0, 0), 2, figsize=[10,10]) # That circle is huge!
::
sage: circle((0, 0), 2).show(figsize=[10,10]) # These are equivalent
TESTS:
We cannot currently plot circles in more than three dimensions::
sage: circle((1,1,1,1), 1, rgbcolor=(1,0,0))
Traceback (most recent call last):
...
ValueError: The center of a plotted circle should have two or three coordinates.
The default aspect ratio for a circle is 1.0::
sage: P = circle((1,1), 1)
sage: P.aspect_ratio()
1.0
"""
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'
g = Graphics()
g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
g.add_primitive(Circle(center[0], center[1], radius, options))
if options['legend_label']:
g.legend(True)
g._legend_colors = [options['legend_color']]
if len(center) == 2:
return g
elif len(center) == 3:
return g[0].plot3d(z=center[2])
else:
raise ValueError, 'The center of a plotted circle should have two or three coordinates.'
def line2d(points, **options):
r"""
Create the line through the given list of points.
INPUT:
- ``points`` - either a single point (as a tuple), a list of
points, a single complex number, or a list of complex numbers.
Type ``line2d.options`` for a dictionary of the default options for
lines. You can change this to change the defaults for all future
lines. Use ``line2d.reset()`` to reset to the default options.
INPUT:
- ``alpha`` -- How transparent the line is
- ``thickness`` -- How thick the line is
- ``rgbcolor`` -- The color as an RGB tuple
- ``hue`` -- The color given as a hue
- ``legend_color`` -- The color of the text in the legend
- ``legend_label`` -- the label for this item in the legend
Any MATPLOTLIB line option may also be passed in. E.g.,
- ``linestyle`` - (default: "-") The style of the line, which is one of
- ``"-"`` or ``"solid"``
- ``"--"`` or ``"dashed"``
- ``"-."`` or ``"dash dot"``
- ``":"`` or ``"dotted"``
- ``"None"`` or ``" "`` or ``""`` (nothing)
The linestyle can also be prefixed with a drawing style (e.g., ``"steps--"``)
- ``"default"`` (connect the points with straight lines)
- ``"steps"`` or ``"steps-pre"`` (step function; horizontal
line is to the left of point)
- ``"steps-mid"`` (step function; points are in the middle of
horizontal lines)
- ``"steps-post"`` (step function; horizontal line is to the
right of point)
- ``marker`` - The style of the markers, which is one of
- ``"None"`` or ``" "`` or ``""`` (nothing) -- default
- ``","`` (pixel), ``"."`` (point)
- ``"_"`` (horizontal line), ``"|"`` (vertical line)
- ``"o"`` (circle), ``"p"`` (pentagon), ``"s"`` (square), ``"x"`` (x), ``"+"`` (plus), ``"*"`` (star)
- ``"D"`` (diamond), ``"d"`` (thin diamond)
- ``"H"`` (hexagon), ``"h"`` (alternative hexagon)
- ``"<"`` (triangle left), ``">"`` (triangle right), ``"^"`` (triangle up), ``"v"`` (triangle down)
- ``"1"`` (tri down), ``"2"`` (tri up), ``"3"`` (tri left), ``"4"`` (tri right)
- ``0`` (tick left), ``1`` (tick right), ``2`` (tick up), ``3`` (tick down)
- ``4`` (caret left), ``5`` (caret right), ``6`` (caret up), ``7`` (caret down)
- ``"$...$"`` (math TeX string)
- ``markersize`` -- the size of the marker in points
- ``markeredgecolor`` -- the color of the marker edge
- ``markerfacecolor`` -- the color of the marker face
- ``markeredgewidth`` -- the size of the marker edge in points
EXAMPLES:
A line with no points or one point::
sage: line([]) #returns an empty plot
Graphics object consisting of 0 graphics primitives
sage: import numpy; line(numpy.array([]))
Graphics object consisting of 0 graphics primitives
sage: line([(1,1)])
Graphics object consisting of 1 graphics primitive
A line with numpy arrays::
sage: line(numpy.array([[1,2], [3,4]]))
Graphics object consisting of 1 graphics primitive
A line with a legend::
sage: line([(0,0),(1,1)], legend_label='line')
Graphics object consisting of 1 graphics primitive
Lines with different colors in the legend text::
sage: p1 = line([(0,0),(1,1)], legend_label='line')
sage: p2 = line([(1,1),(2,4)], legend_label='squared', legend_color='red')
sage: p1 + p2
Graphics object consisting of 2 graphics primitives
Extra options will get passed on to show(), as long as they are valid::
sage: line([(0,1), (3,4)], figsize=[10, 2])
Graphics object consisting of 1 graphics primitive
sage: line([(0,1), (3,4)]).show(figsize=[10, 2]) # These are equivalent
We can also use a logarithmic scale if the data will support it::
sage: line([(1,2),(2,4),(3,4),(4,8),(4.5,32)],scale='loglog',base=2)
Graphics object consisting of 1 graphics primitive
Many more examples below!
A blue conchoid of Nicomedes::
sage: L = [[1+5*cos(pi/2+pi*i/100), tan(pi/2+pi*i/100)*(1+5*cos(pi/2+pi*i/100))] for i in range(1,100)]
sage: line(L, rgbcolor=(1/4,1/8,3/4))
Graphics object consisting of 1 graphics primitive
A line with 2 complex points::
sage: i = CC.0
sage: line([1+i, 2+3*i])
Graphics object consisting of 1 graphics primitive
A blue hypotrochoid (3 leaves)::
sage: n = 4; h = 3; b = 2
sage: L = [[n*cos(pi*i/100)+h*cos((n/b)*pi*i/100),n*sin(pi*i/100)-h*sin((n/b)*pi*i/100)] for i in range(200)]
sage: line(L, rgbcolor=(1/4,1/4,3/4))
Graphics object consisting of 1 graphics primitive
A blue hypotrochoid (4 leaves)::
sage: n = 6; h = 5; b = 2
sage: L = [[n*cos(pi*i/100)+h*cos((n/b)*pi*i/100),n*sin(pi*i/100)-h*sin((n/b)*pi*i/100)] for i in range(200)]
sage: line(L, rgbcolor=(1/4,1/4,3/4))
Graphics object consisting of 1 graphics primitive
A red limacon of Pascal::
sage: L = [[sin(pi*i/100)+sin(pi*i/50),-(1+cos(pi*i/100)+cos(pi*i/50))] for i in range(-100,101)]
sage: line(L, rgbcolor=(1,1/4,1/2))
Graphics object consisting of 1 graphics primitive
A light green trisectrix of Maclaurin::
sage: L = [[2*(1-4*cos(-pi/2+pi*i/100)^2),10*tan(-pi/2+pi*i/100)*(1-4*cos(-pi/2+pi*i/100)^2)] for i in range(1,100)]
sage: line(L, rgbcolor=(1/4,1,1/8))
Graphics object consisting of 1 graphics primitive
A green lemniscate of Bernoulli::
sage: cosines = [cos(-pi/2+pi*i/100) for i in range(201)]
sage: v = [(1/c, tan(-pi/2+pi*i/100)) for i,c in enumerate(cosines) if c != 0]
sage: L = [(a/(a^2+b^2), b/(a^2+b^2)) for a,b in v]
sage: line(L, rgbcolor=(1/4,3/4,1/8))
Graphics object consisting of 1 graphics primitive
A red plot of the Jacobi elliptic function `\text{sn}(x,2)`, `-3 < x < 3`::
sage: L = [(i/100.0, real_part(jacobi('sn', i/100.0, 2.0))) for i in
....: range(-300, 300, 30)]
sage: line(L, rgbcolor=(3/4, 1/4, 1/8))
Graphics object consisting of 1 graphics primitive
A red plot of `J`-Bessel function `J_2(x)`, `0 < x < 10`::
sage: L = [(i/10.0, bessel_J(2,i/10.0)) for i in range(100)]
sage: line(L, rgbcolor=(3/4,1/4,5/8))
Graphics object consisting of 1 graphics primitive
A purple plot of the Riemann zeta function `\zeta(1/2 + it)`, `0 < t < 30`::
sage: i = CDF.gen()
sage: v = [zeta(0.5 + n/10 * i) for n in range(300)]
sage: L = [(z.real(), z.imag()) for z in v]
sage: line(L, rgbcolor=(3/4,1/2,5/8))
Graphics object consisting of 1 graphics primitive
A purple plot of the Hasse-Weil `L`-function `L(E, 1 + it)`, `-1 < t < 10`::
sage: E = EllipticCurve('37a')
sage: vals = E.lseries().values_along_line(1-I, 1+10*I, 100) # critical line
sage: L = [(z[1].real(), z[1].imag()) for z in vals]
sage: line(L, rgbcolor=(3/4,1/2,5/8))
Graphics object consisting of 1 graphics primitive
A red, blue, and green "cool cat"::
sage: G = plot(-cos(x), -2, 2, thickness=5, rgbcolor=(0.5,1,0.5))
sage: P = polygon([[1,2], [5,6], [5,0]], rgbcolor=(1,0,0))
sage: Q = polygon([(-x,y) for x,y in P[0]], rgbcolor=(0,0,1))
sage: G + P + Q # show the plot
Graphics object consisting of 3 graphics primitives
TESTS:
Check that :trac:`13690` is fixed. The legend label should have circles
as markers.::
sage: line(enumerate(range(2)), marker='o', legend_label='circle')
Graphics object consisting of 1 graphics primitive
"""
from sage.plot.all import Graphics
from sage.plot.plot import xydata_from_point_list
from sage.rings.all import CC, CDF
if points in CC or points in CDF:
pass
else:
try:
if not points:
return Graphics()
except ValueError: # numpy raises a ValueError if not empty
pass
xdata, ydata = xydata_from_point_list(points)
g = Graphics()
g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
g.add_primitive(Line(xdata, ydata, options))
if options['legend_label']:
g.legend(True)
g._legend_colors = [options['legend_color']]
return g
def point2d(points, **options):
r"""
A point of size ``size`` defined by point = `(x,y)`.
INPUT:
- ``points`` - either a single point (as a tuple), a list of
points, a single complex number, or a list of complex numbers.
- ``alpha`` -- How transparent the point is.
- ``faceted`` -- If True color the edge of the point. (only for 2D plots)
- ``hue`` -- The color given as a hue.
- ``legend_color`` -- The color of the legend text
- ``legend_label`` -- The label for this item in the legend.
- ``marker`` -- the marker symbol for 2D plots only (see documentation of
:func:`plot` for details)
- ``markeredgecolor`` -- the color of the marker edge (only for 2D plots)
- ``rgbcolor`` -- The color as an RGB tuple.
- ``size`` -- How big the point is (i.e., area in points^2=(1/72 inch)^2).
- ``zorder`` -- The layer level in which to draw
EXAMPLES:
A purple point from a single tuple or coordinates::
sage: point((0.5, 0.5), rgbcolor=hue(0.75))
Graphics object consisting of 1 graphics primitive
Points with customized markers and edge colors::
sage: r = [(random(), random()) for _ in range(10)]
sage: point(r, marker='d', markeredgecolor='red', size=20)
Graphics object consisting of 1 graphics primitive
Passing an empty list returns an empty plot::
sage: point([])
Graphics object consisting of 0 graphics primitives
sage: import numpy; point(numpy.array([]))
Graphics object consisting of 0 graphics primitives
If you need a 2D point to live in 3-space later, this is possible::
sage: A=point((1,1))
sage: a=A[0];a
Point set defined by 1 point(s)
sage: b=a.plot3d(z=3)
This is also true with multiple points::
sage: P=point([(0,0), (1,1)])
sage: p=P[0]
sage: q=p.plot3d(z=[2,3])
Here are some random larger red points, given as a list of tuples::
sage: point(((0.5, 0.5), (1, 2), (0.5, 0.9), (-1, -1)), rgbcolor=hue(1), size=30)
Graphics object consisting of 1 graphics primitive
And an example with a legend::
sage: point((0,0), rgbcolor='black', pointsize=40, legend_label='origin')
Graphics object consisting of 1 graphics primitive
The legend can be colored::
sage: P = points([(0,0),(1,0)], pointsize=40, legend_label='origin', legend_color='red')
sage: P + plot(x^2,(x,0,1), legend_label='plot', legend_color='green')
Graphics object consisting of 2 graphics primitives
Extra options will get passed on to show(), as long as they are valid::
sage: point([(cos(theta), sin(theta)) for theta in srange(0, 2*pi, pi/8)], frame=True)
Graphics object consisting of 1 graphics primitive
sage: point([(cos(theta), sin(theta)) for theta in srange(0, 2*pi, pi/8)]).show(frame=True) # These are equivalent
For plotting data, we can use a logarithmic scale, as long as we are sure
not to include any nonpositive points in the logarithmic direction::
sage: point([(1,2),(2,4),(3,4),(4,8),(4.5,32)],scale='semilogy',base=2)
Graphics object consisting of 1 graphics primitive
Since Sage Version 4.4 (:trac:`8599`), the size of a 2d point can be
given by the argument ``size`` instead of ``pointsize``. The argument
``pointsize`` is still supported::
sage: point((3,4), size=100)
Graphics object consisting of 1 graphics primitive
::
sage: point((3,4), pointsize=100)
Graphics object consisting of 1 graphics primitive
We can plot a single complex number::
sage: point(CC(1+I), pointsize=100)
Graphics object consisting of 1 graphics primitive
We can also plot a list of complex numbers::
sage: point([CC(I), CC(I+1), CC(2+2*I)], pointsize=100)
Graphics object consisting of 1 graphics primitive
"""
from sage.plot.plot import xydata_from_point_list
from sage.plot.all import Graphics
from sage.rings.all import CC, CDF
if points in CC or points in CDF:
pass
else:
try:
if not points:
return Graphics()
except ValueError: # numpy raises a ValueError if not empty
pass
xdata, ydata = xydata_from_point_list(points)
g = Graphics()
g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
g.add_primitive(Point(xdata, ydata, options))
if options['legend_label']:
g.legend(True)
g._legend_colors = [options['legend_color']]
return g
def arrow2d(tailpoint=None, headpoint=None, path=None, **options):
"""
If tailpoint and headpoint are provided, returns an arrow from (xmin, ymin)
to (xmax, ymax). If tailpoint or headpoint is None and path is not None,
returns an arrow along the path. (See further info on paths in bezier_path).
INPUT:
- ``tailpoint`` - the starting point of the arrow
- ``headpoint`` - where the arrow is pointing to
- ``path`` - the list of points and control points (see bezier_path for detail) that
the arrow will follow from source to destination
- ``head`` - 0, 1 or 2, whether to draw the head at the start (0), end (1) or both (2)
of the path (using 0 will swap headpoint and tailpoint). This is ignored
in 3D plotting.
- ``linestyle`` - (default: ``'solid'``) The style of the line, which is one of
``'dashed'``, ``'dotted'``, ``'solid'``, ``'dashdot'``, or ``'--'``, ``':'``,
``'-'``, ``'-.'``, respectively.
- ``width`` - (default: 2) the width of the arrow shaft, in points
- ``color`` - (default: (0,0,1)) the color of the arrow (as an RGB tuple or a string)
- ``hue`` - the color of the arrow (as a number)
- ``arrowsize`` - the size of the arrowhead
- ``arrowshorten`` - the length in points to shorten the arrow (ignored if using path
parameter)
- ``legend_label`` - the label for this item in the legend
- ``legend_color`` - the color for the legend label
- ``zorder`` - the layer level to draw the arrow-- note that this is ignored in 3D
plotting.
EXAMPLES:
A straight, blue arrow::
sage: arrow2d((1, 1), (3, 3))
Make a red arrow::
sage: arrow2d((-1, -1), (2, 3), color=(1,0,0))
sage: arrow2d((-1, -1), (2, 3), color='red')
You can change the width of an arrow::
sage: arrow2d((1, 1), (3, 3), width=5, arrowsize=15)
Use a dashed line instead of a solid one for the arrow::
sage: arrow2d((1, 1), (3, 3), linestyle='dashed')
sage: arrow2d((1, 1), (3, 3), linestyle='--')
A pretty circle of arrows::
sage: sum([arrow2d((0,0), (cos(x),sin(x)), hue=x/(2*pi)) for x in [0..2*pi,step=0.1]])
If we want to draw the arrow between objects, for example, the
boundaries of two lines, we can use the arrowshorten option
to make the arrow shorter by a certain number of points::
sage: line([(0,0),(1,0)],thickness=10)+line([(0,1),(1,1)], thickness=10)+arrow2d((0.5,0),(0.5,1), arrowshorten=10,rgbcolor=(1,0,0))
If BOTH headpoint and tailpoint are None, then an empty plot is returned::
sage: arrow2d(headpoint=None, tailpoint=None)
We can also draw an arrow with a legend::
sage: arrow((0,0), (0,2), legend_label='up', legend_color='purple')
Extra options will get passed on to show(), as long as they are valid::
sage: arrow2d((-2, 2), (7,1), frame=True)
sage: arrow2d((-2, 2), (7,1)).show(frame=True)
"""
from sage.plot.all import Graphics
g = Graphics()
g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
if headpoint is not None and tailpoint is not None:
xtail, ytail = tailpoint
xhead, yhead = headpoint
g.add_primitive(Arrow(xtail, ytail, xhead, yhead, options=options))
elif path is not None:
g.add_primitive(CurveArrow(path, options=options))
elif tailpoint is None and headpoint is None:
return g
else:
raise TypeError("Arrow requires either both headpoint and tailpoint or a path parameter.")
if options["legend_label"]:
g.legend(True)
g._legend_colors = [options["legend_color"]]
return g
def circle(center, radius, **options):
"""
Return a circle at a point center = `(x,y)` (or `(x,y,z)` and
parallel to the `xy`-plane) with radius = `r`. Type
``circle.options`` to see all options.
OPTIONS:
- ``alpha`` - default: 1
- ``fill`` - default: False
- ``thickness`` - default: 1
- ``linestyle`` - default: ``'solid'`` (2D plotting only) The style of the
line, which is one of ``'dashed'``, ``'dotted'``, ``'solid'``, ``'dashdot'``,
or ``'--'``, ``':'``, ``'-'``, ``'-.'``, respectively.
- ``edgecolor`` - default: 'blue' (2D plotting only)
- ``facecolor`` - default: 'blue' (2D plotting only, useful only
if ``fill=True``)
- ``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:
The default color is blue, the default linestyle is solid, but this is easy to change::
sage: c = circle((1,1), 1)
sage: c
Graphics object consisting of 1 graphics primitive
.. PLOT::
sphinx_plot(circle((1,1), 1))
::
sage: c = circle((1,1), 1, rgbcolor=(1,0,0), linestyle='-.')
sage: c
Graphics object consisting of 1 graphics primitive
.. PLOT::
c = circle((1,1), 1, rgbcolor=(1,0,0), linestyle='-.')
sphinx_plot(c)
We can also use this command to plot three-dimensional circles parallel
to the `xy`-plane::
sage: c = circle((1,1,3), 1, rgbcolor=(1,0,0))
sage: c
Graphics3d Object
sage: type(c)
<class 'sage.plot.plot3d.base.TransformGroup'>
.. PLOT::
c = circle((1,1,3), 1, rgbcolor=(1,0,0))
sphinx_plot(c)
To correct the aspect ratio of certain graphics, it is necessary
to show with a ``figsize`` of square dimensions::
sage: c.show(figsize=[5,5],xmin=-1,xmax=3,ymin=-1,ymax=3)
Here we make a more complicated plot, with many circles of different colors::
sage: g = Graphics()
sage: step=6; ocur=1/5; paths=16;
sage: PI = math.pi # numerical for speed -- fine for graphics
sage: for r in range(1,paths+1):
....: for x,y in [((r+ocur)*math.cos(n), (r+ocur)*math.sin(n)) for n in srange(0, 2*PI+PI/step, PI/step)]:
....: g += circle((x,y), ocur, rgbcolor=hue(r/paths))
....: rnext = (r+1)^2
....: ocur = (rnext-r)-ocur
sage: g.show(xmin=-(paths+1)^2, xmax=(paths+1)^2, ymin=-(paths+1)^2, ymax=(paths+1)^2, figsize=[6,6])
.. PLOT::
g = Graphics()
step=6; ocur=1/5; paths=16;
PI = math.pi # numerical for speed -- fine for graphics
for r in range(1,paths+1):
for x,y in [((r+ocur)*math.cos(n), (r+ocur)*math.sin(n)) for n in srange(0, 2*PI+PI/step, PI/step)]:
g += circle((x,y), ocur, rgbcolor=hue(r*1.0/paths))
rnext = (r+1)**2
ocur = (rnext-r)-ocur
g.set_axes_range(-(paths+1)**2,(paths+1)**2,-(paths+1)**2,(paths+1)**2)
sphinx_plot(g)
Note that the ``rgbcolor`` option overrides the other coloring options.
This produces red fill in a blue circle::
sage: circle((2,3), 1, fill=True, edgecolor='blue', facecolor='red')
Graphics object consisting of 1 graphics primitive
.. PLOT::
sphinx_plot(circle((2,3), 1, fill=True, edgecolor='blue', facecolor='red'))
This produces an all-green filled circle::
sage: circle((2,3), 1, fill=True, edgecolor='blue', rgbcolor='green')
Graphics object consisting of 1 graphics primitive
.. PLOT::
sphinx_plot(circle((2,3), 1, fill=True, edgecolor='blue', rgbcolor='green'))
The option ``hue`` overrides *all* other options, so be careful with its use.
This produces a purplish filled circle::
sage: circle((2,3), 1, fill=True, edgecolor='blue', rgbcolor='green', hue=.8)
Graphics object consisting of 1 graphics primitive
.. PLOT::
C = circle((2,3), 1, fill=True, edgecolor='blue', rgbcolor='green', hue=.8)
sphinx_plot(C)
And circles with legends::
sage: circle((4,5), 1, rgbcolor='yellow', fill=True, legend_label='the sun').show(xmin=0, ymin=0)
.. PLOT::
C = circle((4,5), 1, rgbcolor='yellow', fill=True, legend_label='the sun')
C.set_axes_range(xmin=0, ymin=0)
sphinx_plot(C)
::
sage: circle((4,5), 1, legend_label='the sun', legend_color='yellow').show(xmin=0, ymin=0)
.. PLOT::
C = circle((4,5), 1, legend_label='the sun', legend_color='yellow')
C.set_axes_range(xmin=0, ymin=0)
sphinx_plot(C)
Extra options will get passed on to show(), as long as they are valid::
sage: circle((0, 0), 2, figsize=[10,10]) # That circle is huge!
Graphics object consisting of 1 graphics primitive
::
sage: circle((0, 0), 2).show(figsize=[10,10]) # These are equivalent
TESTS:
We cannot currently plot circles in more than three dimensions::
sage: circle((1,1,1,1), 1, rgbcolor=(1,0,0))
Traceback (most recent call last):
...
ValueError: The center of a plotted circle should have two or three coordinates.
The default aspect ratio for a circle is 1.0::
sage: P = circle((1,1), 1)
sage: P.aspect_ratio()
1.0
"""
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'
g = Graphics()
g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
g.add_primitive(Circle(center[0], center[1], radius, options))
if options['legend_label']:
g.legend(True)
g._legend_colors = [options['legend_color']]
if len(center) == 2:
return g
elif len(center) == 3:
return g[0].plot3d(z=center[2])
else:
raise ValueError('The center of a plotted circle should have two or three coordinates.')
def polygon2d(points, **options):
r"""
Returns a 2-dimensional polygon defined by ``points``.
Type ``polygon2d.options`` for a dictionary of the default
options for polygons. You can change this to change the
defaults for all future polygons. Use ``polygon2d.reset()``
to reset to the default options.
EXAMPLES:
We create a purple-ish polygon::
sage: polygon2d([[1,2], [5,6], [5,0]], rgbcolor=(1,0,1))
By default, polygons are filled in, but we can make them
without a fill as well::
sage: polygon2d([[1,2], [5,6], [5,0]], fill=False)
In either case, the thickness of the border can be controlled::
sage: polygon2d([[1,2], [5,6], [5,0]], fill=False, thickness=4, color='orange')
Some modern art -- a random polygon, with legend::
sage: v = [(randrange(-5,5), randrange(-5,5)) for _ in range(10)]
sage: polygon2d(v, legend_label='some form')
A purple hexagon::
sage: L = [[cos(pi*i/3),sin(pi*i/3)] for i in range(6)]
sage: polygon2d(L, rgbcolor=(1,0,1))
A green deltoid::
sage: L = [[-1+cos(pi*i/100)*(1+cos(pi*i/100)),2*sin(pi*i/100)*(1-cos(pi*i/100))] for i in range(200)]
sage: polygon2d(L, rgbcolor=(1/8,3/4,1/2))
A blue hypotrochoid::
sage: L = [[6*cos(pi*i/100)+5*cos((6/2)*pi*i/100),6*sin(pi*i/100)-5*sin((6/2)*pi*i/100)] for i in range(200)]
sage: polygon2d(L, rgbcolor=(1/8,1/4,1/2))
Another one::
sage: n = 4; h = 5; b = 2
sage: L = [[n*cos(pi*i/100)+h*cos((n/b)*pi*i/100),n*sin(pi*i/100)-h*sin((n/b)*pi*i/100)] for i in range(200)]
sage: polygon2d(L, rgbcolor=(1/8,1/4,3/4))
A purple epicycloid::
sage: m = 9; b = 1
sage: L = [[m*cos(pi*i/100)+b*cos((m/b)*pi*i/100),m*sin(pi*i/100)-b*sin((m/b)*pi*i/100)] for i in range(200)]
sage: polygon2d(L, rgbcolor=(7/8,1/4,3/4))
A brown astroid::
sage: L = [[cos(pi*i/100)^3,sin(pi*i/100)^3] for i in range(200)]
sage: polygon2d(L, rgbcolor=(3/4,1/4,1/4))
And, my favorite, a greenish blob::
sage: L = [[cos(pi*i/100)*(1+cos(pi*i/50)), sin(pi*i/100)*(1+sin(pi*i/50))] for i in range(200)]
sage: polygon2d(L, rgbcolor=(1/8, 3/4, 1/2))
This one is for my wife::
sage: L = [[sin(pi*i/100)+sin(pi*i/50),-(1+cos(pi*i/100)+cos(pi*i/50))] for i in range(-100,100)]
sage: polygon2d(L, rgbcolor=(1,1/4,1/2))
One can do the same one with a colored legend label::
sage: polygon2d(L, color='red', legend_label='For you!', legend_color='red')
Polygons have a default aspect ratio of 1.0::
sage: polygon2d([[1,2], [5,6], [5,0]]).aspect_ratio()
1.0
AUTHORS:
- David Joyner (2006-04-14): the long list of examples above.
"""
from sage.plot.plot import xydata_from_point_list
from sage.plot.all import Graphics
if options["thickness"] is None: # If the user did not specify thickness
if options["fill"]: # If the user chose fill
options["thickness"] = 0
else:
options["thickness"] = 1
xdata, ydata = xydata_from_point_list(points)
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(Polygon(xdata, ydata, options))
if options['legend_label']:
g.legend(True)
g._legend_colors = [options['legend_color']]
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")
def point2d(points, **options):
r"""
A point of size ``size`` defined by point = `(x,y)`.
INPUT:
- ``points`` - either a single point (as a tuple), a list of
points, a single complex number, or a list of complex numbers.
- ``alpha`` -- How transparent the point is.
- ``faceted`` -- If True color the edge of the point. (only for 2D plots)
- ``hue`` -- The color given as a hue.
- ``legend_color`` -- The color of the legend text
- ``legend_label`` -- The label for this item in the legend.
- ``marker`` -- the marker symbol for 2D plots only (see documentation of
:func:`plot` for details)
- ``markeredgecolor`` -- the color of the marker edge (only for 2D plots)
- ``rgbcolor`` -- The color as an RGB tuple.
- ``size`` -- How big the point is (i.e., area in points^2=(1/72 inch)^2).
- ``zorder`` -- The layer level in which to draw
EXAMPLES:
A purple point from a single tuple or coordinates::
sage: point((0.5, 0.5), rgbcolor=hue(0.75))
Graphics object consisting of 1 graphics primitive
Points with customized markers and edge colors::
sage: r = [(random(), random()) for _ in range(10)]
sage: point(r, marker='d', markeredgecolor='red', size=20)
Graphics object consisting of 1 graphics primitive
Passing an empty list returns an empty plot::
sage: point([])
Graphics object consisting of 0 graphics primitives
sage: import numpy; point(numpy.array([]))
Graphics object consisting of 0 graphics primitives
If you need a 2D point to live in 3-space later, this is possible::
sage: A=point((1,1))
sage: a=A[0];a
Point set defined by 1 point(s)
sage: b=a.plot3d(z=3)
This is also true with multiple points::
sage: P=point([(0,0), (1,1)])
sage: p=P[0]
sage: q=p.plot3d(z=[2,3])
Here are some random larger red points, given as a list of tuples::
sage: point(((0.5, 0.5), (1, 2), (0.5, 0.9), (-1, -1)), rgbcolor=hue(1), size=30)
Graphics object consisting of 1 graphics primitive
And an example with a legend::
sage: point((0,0), rgbcolor='black', pointsize=40, legend_label='origin')
Graphics object consisting of 1 graphics primitive
The legend can be colored::
sage: P = points([(0,0),(1,0)], pointsize=40, legend_label='origin', legend_color='red')
sage: P + plot(x^2,(x,0,1), legend_label='plot', legend_color='green')
Graphics object consisting of 2 graphics primitives
Extra options will get passed on to show(), as long as they are valid::
sage: point([(cos(theta), sin(theta)) for theta in srange(0, 2*pi, pi/8)], frame=True)
Graphics object consisting of 1 graphics primitive
sage: point([(cos(theta), sin(theta)) for theta in srange(0, 2*pi, pi/8)]).show(frame=True) # These are equivalent
For plotting data, we can use a logarithmic scale, as long as we are sure
not to include any nonpositive points in the logarithmic direction::
sage: point([(1,2),(2,4),(3,4),(4,8),(4.5,32)],scale='semilogy',base=2)
Graphics object consisting of 1 graphics primitive
Since Sage Version 4.4 (:trac:`8599`), the size of a 2d point can be
given by the argument ``size`` instead of ``pointsize``. The argument
``pointsize`` is still supported::
sage: point((3,4), size=100)
Graphics object consisting of 1 graphics primitive
::
sage: point((3,4), pointsize=100)
Graphics object consisting of 1 graphics primitive
We can plot a single complex number::
sage: point(CC(1+I), pointsize=100)
Graphics object consisting of 1 graphics primitive
We can also plot a list of complex numbers::
sage: point([CC(I), CC(I+1), CC(2+2*I)], pointsize=100)
Graphics object consisting of 1 graphics primitive
"""
from sage.plot.plot import xydata_from_point_list
from sage.plot.all import Graphics
from sage.rings.all import CC, CDF
if points in CC or points in CDF:
pass
else:
try:
if not points:
return Graphics()
except ValueError: # numpy raises a ValueError if not empty
pass
xdata, ydata = xydata_from_point_list(points)
g = Graphics()
g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
g.add_primitive(Point(xdata, ydata, options))
if options['legend_label']:
g.legend(True)
g._legend_colors = [options['legend_color']]
return g
def point2d(points, **options):
r"""
A point of size ``size`` defined by point = `(x,y)`.
Point takes either a single tuple of coordinates or a list of tuples.
Type ``point2d.options`` to see all options.
EXAMPLES:
A purple point from a single tuple or coordinates::
sage: point((0.5, 0.5), rgbcolor=hue(0.75))
Passing an empty list returns an empty plot::
sage: point([])
If you need a 2D point to live in 3-space later,
this is possible::
sage: A=point((1,1))
sage: a=A[0];a
Point set defined by 1 point(s)
sage: b=a.plot3d(z=3)
This is also true with multiple points::
sage: P=point([(0,0), (1,1)])
sage: p=P[0]
sage: q=p.plot3d(z=[2,3])
Here are some random larger red points, given as a list of tuples::
sage: point(((0.5, 0.5), (1, 2), (0.5, 0.9), (-1, -1)), rgbcolor=hue(1), size=30)
And an example with a legend::
sage: point((0,0), rgbcolor='black', pointsize=40, legend_label='origin')
The legend can be colored::
sage: P = points([(0,0),(1,0)], pointsize=40, legend_label='origin', legend_color='red')
sage: P + plot(x^2,(x,0,1), legend_label='plot', legend_color='green')
Extra options will get passed on to show(), as long as they are valid::
sage: point([(cos(theta), sin(theta)) for theta in srange(0, 2*pi, pi/8)], frame=True)
sage: point([(cos(theta), sin(theta)) for theta in srange(0, 2*pi, pi/8)]).show(frame=True) # These are equivalent
For plotting data, we can use a logarithmic scale, as long as we are sure
not to include any nonpositive points in the logarithmic direction::
sage: point([(1,2),(2,4),(3,4),(4,8),(4.5,32)],scale='semilogy',base=2)
Since Sage Version 4.4 (ticket #8599), the size of a 2d point can be
given by the argument ``size`` instead of ``pointsize``. The argument
``pointsize`` is still supported::
sage: point((3,4), size=100)
::
sage: point((3,4), pointsize=100)
"""
from sage.plot.plot import xydata_from_point_list
from sage.plot.all import Graphics
if points == []:
return Graphics()
xdata, ydata = xydata_from_point_list(points)
g = Graphics()
g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
g.add_primitive(Point(xdata, ydata, options))
if options['legend_label']:
g.legend(True)
g._legend_colors = [options['legend_color']]
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)
Graphics object consisting of 1 graphics primitive
More complicated examples with tilted axes and drawing options::
sage: ellipse((0,0),3,1,pi/6,fill=True,alpha=0.3,linestyle="dashed")
Graphics object consisting of 1 graphics primitive
sage: ellipse((0,0),3,1,pi/6,fill=True,alpha=0.3,linestyle="--")
Graphics object consisting of 1 graphics primitive
::
sage: ellipse((0,0),3,1,pi/6,fill=True,edgecolor='black',facecolor='red')
Graphics object consisting of 1 graphics primitive
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')
Graphics object consisting of 1 graphics primitive
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')
Graphics object consisting of 1 graphics primitive
"""
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")
def line2d(points, **options):
r"""
Create the line through the given list of points.
INPUT:
- ``points`` - either a single point (as a tuple), a list of
points, a single complex number, or a list of complex numbers.
Type ``line2d.options`` for a dictionary of the default options for
lines. You can change this to change the defaults for all future
lines. Use ``line2d.reset()`` to reset to the default options.
INPUT:
- ``alpha`` -- How transparent the line is
- ``thickness`` -- How thick the line is
- ``rgbcolor`` -- The color as an RGB tuple
- ``hue`` -- The color given as a hue
- ``legend_color`` -- The color of the text in the legend
- ``legend_label`` -- the label for this item in the legend
Any MATPLOTLIB line option may also be passed in. E.g.,
- ``linestyle`` - (default: "-") The style of the line, which is one of
- ``"-"`` or ``"solid"``
- ``"--"`` or ``"dashed"``
- ``"-."`` or ``"dash dot"``
- ``":"`` or ``"dotted"``
- ``"None"`` or ``" "`` or ``""`` (nothing)
The linestyle can also be prefixed with a drawing style (e.g., ``"steps--"``)
- ``"default"`` (connect the points with straight lines)
- ``"steps"`` or ``"steps-pre"`` (step function; horizontal
line is to the left of point)
- ``"steps-mid"`` (step function; points are in the middle of
horizontal lines)
- ``"steps-post"`` (step function; horizontal line is to the
right of point)
- ``marker`` - The style of the markers, which is one of
- ``"None"`` or ``" "`` or ``""`` (nothing) -- default
- ``","`` (pixel), ``"."`` (point)
- ``"_"`` (horizontal line), ``"|"`` (vertical line)
- ``"o"`` (circle), ``"p"`` (pentagon), ``"s"`` (square), ``"x"`` (x), ``"+"`` (plus), ``"*"`` (star)
- ``"D"`` (diamond), ``"d"`` (thin diamond)
- ``"H"`` (hexagon), ``"h"`` (alternative hexagon)
- ``"<"`` (triangle left), ``">"`` (triangle right), ``"^"`` (triangle up), ``"v"`` (triangle down)
- ``"1"`` (tri down), ``"2"`` (tri up), ``"3"`` (tri left), ``"4"`` (tri right)
- ``0`` (tick left), ``1`` (tick right), ``2`` (tick up), ``3`` (tick down)
- ``4`` (caret left), ``5`` (caret right), ``6`` (caret up), ``7`` (caret down)
- ``"$...$"`` (math TeX string)
- ``markersize`` -- the size of the marker in points
- ``markeredgecolor`` -- the color of the marker edge
- ``markerfacecolor`` -- the color of the marker face
- ``markeredgewidth`` -- the size of the marker edge in points
EXAMPLES:
A line with no points or one point::
sage: line([]) #returns an empty plot
Graphics object consisting of 0 graphics primitives
sage: import numpy; line(numpy.array([]))
Graphics object consisting of 0 graphics primitives
sage: line([(1,1)])
Graphics object consisting of 1 graphics primitive
A line with numpy arrays::
sage: line(numpy.array([[1,2], [3,4]]))
Graphics object consisting of 1 graphics primitive
A line with a legend::
sage: line([(0,0),(1,1)], legend_label='line')
Graphics object consisting of 1 graphics primitive
Lines with different colors in the legend text::
sage: p1 = line([(0,0),(1,1)], legend_label='line')
sage: p2 = line([(1,1),(2,4)], legend_label='squared', legend_color='red')
sage: p1 + p2
Graphics object consisting of 2 graphics primitives
Extra options will get passed on to show(), as long as they are valid::
sage: line([(0,1), (3,4)], figsize=[10, 2])
Graphics object consisting of 1 graphics primitive
sage: line([(0,1), (3,4)]).show(figsize=[10, 2]) # These are equivalent
We can also use a logarithmic scale if the data will support it::
sage: line([(1,2),(2,4),(3,4),(4,8),(4.5,32)],scale='loglog',base=2)
Graphics object consisting of 1 graphics primitive
Many more examples below!
A blue conchoid of Nicomedes::
sage: L = [[1+5*cos(pi/2+pi*i/100), tan(pi/2+pi*i/100)*(1+5*cos(pi/2+pi*i/100))] for i in range(1,100)]
sage: line(L, rgbcolor=(1/4,1/8,3/4))
Graphics object consisting of 1 graphics primitive
A line with 2 complex points::
sage: i = CC.0
sage: line([1+i, 2+3*i])
Graphics object consisting of 1 graphics primitive
A blue hypotrochoid (3 leaves)::
sage: n = 4; h = 3; b = 2
sage: L = [[n*cos(pi*i/100)+h*cos((n/b)*pi*i/100),n*sin(pi*i/100)-h*sin((n/b)*pi*i/100)] for i in range(200)]
sage: line(L, rgbcolor=(1/4,1/4,3/4))
Graphics object consisting of 1 graphics primitive
A blue hypotrochoid (4 leaves)::
sage: n = 6; h = 5; b = 2
sage: L = [[n*cos(pi*i/100)+h*cos((n/b)*pi*i/100),n*sin(pi*i/100)-h*sin((n/b)*pi*i/100)] for i in range(200)]
sage: line(L, rgbcolor=(1/4,1/4,3/4))
Graphics object consisting of 1 graphics primitive
A red limacon of Pascal::
sage: L = [[sin(pi*i/100)+sin(pi*i/50),-(1+cos(pi*i/100)+cos(pi*i/50))] for i in range(-100,101)]
sage: line(L, rgbcolor=(1,1/4,1/2))
Graphics object consisting of 1 graphics primitive
A light green trisectrix of Maclaurin::
sage: L = [[2*(1-4*cos(-pi/2+pi*i/100)^2),10*tan(-pi/2+pi*i/100)*(1-4*cos(-pi/2+pi*i/100)^2)] for i in range(1,100)]
sage: line(L, rgbcolor=(1/4,1,1/8))
Graphics object consisting of 1 graphics primitive
A green lemniscate of Bernoulli::
sage: cosines = [cos(-pi/2+pi*i/100) for i in range(201)]
sage: v = [(1/c, tan(-pi/2+pi*i/100)) for i,c in enumerate(cosines) if c != 0]
sage: L = [(a/(a^2+b^2), b/(a^2+b^2)) for a,b in v]
sage: line(L, rgbcolor=(1/4,3/4,1/8))
Graphics object consisting of 1 graphics primitive
A red plot of the Jacobi elliptic function `\text{sn}(x,2)`, `-3 < x < 3`::
sage: L = [(i/100.0, real_part(jacobi('sn', i/100.0, 2.0))) for i in
....: range(-300, 300, 30)]
sage: line(L, rgbcolor=(3/4, 1/4, 1/8))
Graphics object consisting of 1 graphics primitive
A red plot of `J`-Bessel function `J_2(x)`, `0 < x < 10`::
sage: L = [(i/10.0, bessel_J(2,i/10.0)) for i in range(100)]
sage: line(L, rgbcolor=(3/4,1/4,5/8))
Graphics object consisting of 1 graphics primitive
A purple plot of the Riemann zeta function `\zeta(1/2 + it)`, `0 < t < 30`::
sage: i = CDF.gen()
sage: v = [zeta(0.5 + n/10 * i) for n in range(300)]
sage: L = [(z.real(), z.imag()) for z in v]
sage: line(L, rgbcolor=(3/4,1/2,5/8))
Graphics object consisting of 1 graphics primitive
A purple plot of the Hasse-Weil `L`-function `L(E, 1 + it)`, `-1 < t < 10`::
sage: E = EllipticCurve('37a')
sage: vals = E.lseries().values_along_line(1-I, 1+10*I, 100) # critical line
sage: L = [(z[1].real(), z[1].imag()) for z in vals]
sage: line(L, rgbcolor=(3/4,1/2,5/8))
Graphics object consisting of 1 graphics primitive
A red, blue, and green "cool cat"::
sage: G = plot(-cos(x), -2, 2, thickness=5, rgbcolor=(0.5,1,0.5))
sage: P = polygon([[1,2], [5,6], [5,0]], rgbcolor=(1,0,0))
sage: Q = polygon([(-x,y) for x,y in P[0]], rgbcolor=(0,0,1))
sage: G + P + Q # show the plot
Graphics object consisting of 3 graphics primitives
TESTS:
Check that :trac:`13690` is fixed. The legend label should have circles
as markers.::
sage: line(enumerate(range(2)), marker='o', legend_label='circle')
Graphics object consisting of 1 graphics primitive
"""
from sage.plot.all import Graphics
from sage.plot.plot import xydata_from_point_list
from sage.rings.all import CC, CDF
if points in CC or points in CDF:
pass
else:
try:
if not points:
return Graphics()
except ValueError: # numpy raises a ValueError if not empty
pass
xdata, ydata = xydata_from_point_list(points)
g = Graphics()
g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
g.add_primitive(Line(xdata, ydata, options))
if options['legend_label']:
g.legend(True)
g._legend_colors = [options['legend_color']]
return g
def arrow2d(tailpoint=None, headpoint=None, path=None, **options):
"""
If ``tailpoint`` and ``headpoint`` are provided, returns an arrow from
(xtail, ytail) to (xhead, yhead). If ``tailpoint`` or ``headpoint`` is None and
``path`` is not None, returns an arrow along the path. (See further info on
paths in :class:`bezier_path`).
INPUT:
- ``tailpoint`` - the starting point of the arrow
- ``headpoint`` - where the arrow is pointing to
- ``path`` - the list of points and control points (see bezier_path for
detail) that the arrow will follow from source to destination
- ``head`` - 0, 1 or 2, whether to draw the head at the start (0), end (1)
or both (2) of the path (using 0 will swap headpoint and tailpoint).
This is ignored in 3D plotting.
- ``linestyle`` - (default: ``'solid'``) The style of the line, which is
one of ``'dashed'``, ``'dotted'``, ``'solid'``, ``'dashdot'``,
or ``'--'``, ``':'``, ``'-'``, ``'-.'``, respectively.
- ``width`` - (default: 2) the width of the arrow shaft, in points
- ``color`` - (default: (0,0,1)) the color of the arrow (as an RGB tuple or
a string)
- ``hue`` - the color of the arrow (as a number)
- ``arrowsize`` - the size of the arrowhead
- ``arrowshorten`` - the length in points to shorten the arrow (ignored if
using path parameter)
- ``legend_label`` - the label for this item in the legend
- ``legend_color`` - the color for the legend label
- ``zorder`` - the layer level to draw the arrow-- note that this is
ignored in 3D plotting.
EXAMPLES:
A straight, blue arrow::
sage: arrow2d((1,1), (3,3))
Graphics object consisting of 1 graphics primitive
.. PLOT::
sphinx_plot(arrow2d((1,1), (3,3)))
Make a red arrow::
sage: arrow2d((-1,-1), (2,3), color=(1,0,0))
Graphics object consisting of 1 graphics primitive
.. PLOT::
sphinx_plot(arrow2d((-1,-1), (2,3), color=(1,0,0)))
::
sage: arrow2d((-1,-1), (2,3), color='red')
Graphics object consisting of 1 graphics primitive
.. PLOT::
sphinx_plot(arrow2d((-1,-1), (2,3), color='red'))
You can change the width of an arrow::
sage: arrow2d((1,1), (3,3), width=5, arrowsize=15)
Graphics object consisting of 1 graphics primitive
.. PLOT::
P = arrow2d((1,1), (3,3), width=5, arrowsize=15)
sphinx_plot(P)
Use a dashed line instead of a solid one for the arrow::
sage: arrow2d((1,1), (3,3), linestyle='dashed')
Graphics object consisting of 1 graphics primitive
sage: arrow2d((1,1), (3,3), linestyle='--')
Graphics object consisting of 1 graphics primitive
.. PLOT::
P = arrow2d((1,1), (3,3), linestyle='--')
sphinx_plot(P)
A pretty circle of arrows::
sage: sum([arrow2d((0,0), (cos(x),sin(x)), hue=x/(2*pi)) for x in [0..2*pi,step=0.1]])
Graphics object consisting of 63 graphics primitives
.. PLOT::
P = sum([arrow2d((0,0), (cos(x*0.1),sin(x*0.1)), hue=x/(20*pi)) for x in range(floor(20*pi)+1)])
sphinx_plot(P)
If we want to draw the arrow between objects, for example, the
boundaries of two lines, we can use the ``arrowshorten`` option
to make the arrow shorter by a certain number of points::
sage: L1 = line([(0,0), (1,0)], thickness=10)
sage: L2 = line([(0,1), (1,1)], thickness=10)
sage: A = arrow2d((0.5,0), (0.5,1), arrowshorten=10, rgbcolor=(1,0,0))
sage: L1 + L2 + A
Graphics object consisting of 3 graphics primitives
.. PLOT::
L1 = line([(0,0), (1,0)],thickness=10)
L2 = line([(0,1), (1,1)], thickness=10)
A = arrow2d((0.5,0), (0.5,1), arrowshorten=10, rgbcolor=(1,0,0))
sphinx_plot(L1 + L2 + A)
If BOTH ``headpoint`` and ``tailpoint`` are None, then an empty plot is
returned::
sage: arrow2d(headpoint=None, tailpoint=None)
Graphics object consisting of 0 graphics primitives
We can also draw an arrow with a legend::
sage: arrow((0,0), (0,2), legend_label='up', legend_color='purple')
Graphics object consisting of 1 graphics primitive
.. PLOT::
P = arrow((0,0), (0,2), legend_label='up', legend_color='purple')
sphinx_plot(P)
Extra options will get passed on to :meth:`Graphics.show()`, as long as they are valid::
sage: arrow2d((-2,2), (7,1), frame=True)
Graphics object consisting of 1 graphics primitive
.. PLOT::
sphinx_plot(arrow2d((-2,2), (7,1), frame=True))
::
sage: arrow2d((-2,2), (7,1)).show(frame=True)
"""
from sage.plot.all import Graphics
g = Graphics()
g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
if headpoint is not None and tailpoint is not None:
xtail, ytail = tailpoint
xhead, yhead = headpoint
g.add_primitive(Arrow(xtail, ytail, xhead, yhead, options=options))
elif path is not None:
g.add_primitive(CurveArrow(path, options=options))
elif tailpoint is None and headpoint is None:
return g
else:
raise TypeError(
'Arrow requires either both headpoint and tailpoint or a path parameter.'
)
if options['legend_label']:
g.legend(True)
g._legend_colors = [options['legend_color']]
return g
def disk(point, radius, angle, **options):
r"""
A disk (that is, a sector or wedge of a circle) with center
at a point = `(x,y)` (or `(x,y,z)` and parallel to the
`xy`-plane) with radius = `r` spanning (in radians)
angle=`(rad1, rad2)`.
Type ``disk.options`` to see all options.
EXAMPLES:
Make some dangerous disks::
sage: bl = disk((0.0,0.0), 1, (pi, 3*pi/2), color='yellow')
sage: tr = disk((0.0,0.0), 1, (0, pi/2), color='yellow')
sage: tl = disk((0.0,0.0), 1, (pi/2, pi), color='black')
sage: br = disk((0.0,0.0), 1, (3*pi/2, 2*pi), color='black')
sage: P = tl+tr+bl+br
sage: P.show(xmin=-2,xmax=2,ymin=-2,ymax=2)
The default aspect ratio is 1.0::
sage: disk((0.0,0.0), 1, (pi, 3*pi/2)).aspect_ratio()
1.0
Another example of a disk::
sage: bl = disk((0.0,0.0), 1, (pi, 3*pi/2), rgbcolor=(1,1,0))
sage: bl.show(figsize=[5,5])
Note that since ``thickness`` defaults to zero, it is best to change
that option when using ``fill=False``::
sage: disk((2,3), 1, (pi/4,pi/3), hue=.8, alpha=.3, fill=False, thickness=2)
Graphics object consisting of 1 graphics primitive
The previous two examples also illustrate using ``hue`` and ``rgbcolor``
as ways of specifying the color of the graphic.
We can also use this command to plot three-dimensional disks parallel
to the `xy`-plane::
sage: d = disk((1,1,3), 1, (pi,3*pi/2), rgbcolor=(1,0,0))
sage: d
Graphics3d Object
sage: type(d)
<type 'sage.plot.plot3d.index_face_set.IndexFaceSet'>
Extra options will get passed on to ``show()``, as long as they are valid::
sage: disk((0, 0), 5, (0, pi/2), xmin=0, xmax=5, ymin=0, ymax=5, figsize=(2,2), rgbcolor=(1, 0, 1))
Graphics object consisting of 1 graphics primitive
sage: disk((0, 0), 5, (0, pi/2), rgbcolor=(1, 0, 1)).show(xmin=0, xmax=5, ymin=0, ymax=5, figsize=(2,2)) # These are equivalent
TESTS:
Testing that legend labels work right::
sage: disk((2,4), 3, (pi/8, pi/4), hue=1, legend_label='disk', legend_color='blue')
Graphics object consisting of 1 graphics primitive
We cannot currently plot disks in more than three dimensions::
sage: d = disk((1,1,1,1), 1, (0,pi))
Traceback (most recent call last):
...
ValueError: The center point of a plotted disk should have two or three coordinates.
"""
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(Disk(point, radius, angle, options))
if options['legend_label']:
g.legend(True)
g._legend_colors = [options['legend_color']]
if len(point)==2:
return g
elif len(point)==3:
return g[0].plot3d(z=point[2])
else:
raise ValueError('The center point of a plotted disk should have two or three coordinates.')
