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 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 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 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 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')
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)
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))
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 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 polygon2d(points, **options):
r"""
Returns a 2-dimensional polygon defined by ``points``.
Type ``polygon.options`` for a dictionary of the default
options for polygons. You can change this to change
the defaults for all future polygons. Use ``polygon.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))
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()
g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
g.add_primitive(Polygon(xdata, ydata, options))
if options['legend_label']:
g.legend(True)
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 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 line2d(points, **options):
r"""
Create the line through the given list of points.
Type \code{line2d.options} for a dictionary of the default options for
lines. You can change this to change the defaults for all future
lines. Use \code{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_label`` -- the label for this item in the legend
Any MATPLOTLIB line option may also be passed in. E.g.,
- ``linestyle`` - The style of the line, which is one of
- ``"-"`` (solid) -- default
- ``"--"`` (dashed)
- ``"-."`` (dash dot)
- ``":"`` (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 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))
A line with 2 complex points::
sage: i = CC.0
sage: line([1+i, 2+3*i])
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))
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))
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))
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))
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))
A red plot of the Jacobi elliptic function `\text{sn}(x,2)`, `-3 < x < 3`::
sage: L = [(i/100.0, jacobi('sn', i/100.0 ,2.0)) for i in range(-300,300,30)]
sage: line(L, rgbcolor=(3/4,1/4,1/8))
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))
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))
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))
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
A line with no points or one point::
sage: line([]) #returns an empty plot
sage: line([(1,1)])
A line with a legend::
sage: line([(0,0),(1,1)], legend_label='line')
Extra options will get passed on to show(), as long as they are valid::
sage: line([(0,1), (3,4)], figsize=[10, 2])
sage: line([(0,1), (3,4)]).show(figsize=[10, 2]) # These are equivalent
"""
from sage.plot.plot import Graphics, xydata_from_point_list
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(Line(xdata, ydata, options))
if options['legend_label']:
g.legend(True)
return g