def bar_chart(datalist, **options):
"""
A bar chart of (currently) one list of numerical data.
Support for more data lists in progress.
EXAMPLES:
A bar_chart with blue bars::
sage: bar_chart([1,2,3,4])
A bar_chart with thinner bars::
sage: bar_chart([x^2 for x in range(1,20)], width=0.2)
A bar_chart with negative values and red bars::
sage: bar_chart([-3,5,-6,11], rgbcolor=(1,0,0))
A bar chart with a legend (it's possible, not necessarily useful)::
sage: bar_chart([-1,1,-1,1], legend_label='wave')
Extra options will get passed on to show(), as long as they are valid::
sage: bar_chart([-2,8,-7,3], rgbcolor=(1,0,0), axes=False)
sage: bar_chart([-2,8,-7,3], rgbcolor=(1,0,0)).show(axes=False) # These are equivalent
"""
dl = len(datalist)
#if dl > 1:
# print "WARNING, currently only 1 data set allowed"
# datalist = datalist[0]
if dl == 3:
datalist = datalist+[0]
#bardata = []
#cnt = 1
#for pnts in datalist:
#ind = [i+cnt/dl for i in range(len(pnts))]
#bardata.append([ind, pnts, xrange, yrange])
#cnt += 1
g = Graphics()
g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
#TODO: improve below for multiple data sets!
#cnt = 1
#for ind, pnts, xrange, yrange in bardata:
#options={'rgbcolor':hue(cnt/dl),'width':0.5/dl}
# g._bar_chart(ind, pnts, xrange, yrange, options=options)
# cnt += 1
#else:
ind = range(len(datalist))
g.add_primitive(BarChart(ind, datalist, options=options))
if options['legend_label']:
g.legend(True)
return g
def bar_chart(datalist, **options):
"""
A bar chart of (currently) one list of numerical data.
Support for more data lists in progress.
EXAMPLES:
A bar_chart with blue bars::
sage: bar_chart([1,2,3,4])
A bar_chart with thinner bars::
sage: bar_chart([x^2 for x in range(1,20)], width=0.2)
A bar_chart with negative values and red bars::
sage: bar_chart([-3,5,-6,11], rgbcolor=(1,0,0))
A bar chart with a legend (it's possible, not necessarily useful)::
sage: bar_chart([-1,1,-1,1], legend_label='wave')
Extra options will get passed on to show(), as long as they are valid::
sage: bar_chart([-2,8,-7,3], rgbcolor=(1,0,0), axes=False)
sage: bar_chart([-2,8,-7,3], rgbcolor=(1,0,0)).show(axes=False) # These are equivalent
"""
dl = len(datalist)
#if dl > 1:
# print "WARNING, currently only 1 data set allowed"
# datalist = datalist[0]
if dl == 3:
datalist = datalist + [0]
#bardata = []
#cnt = 1
#for pnts in datalist:
#ind = [i+cnt/dl for i in range(len(pnts))]
#bardata.append([ind, pnts, xrange, yrange])
#cnt += 1
g = Graphics()
g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
#TODO: improve below for multiple data sets!
#cnt = 1
#for ind, pnts, xrange, yrange in bardata:
#options={'rgbcolor':hue(cnt/dl),'width':0.5/dl}
# g._bar_chart(ind, pnts, xrange, yrange, options=options)
# cnt += 1
#else:
ind = range(len(datalist))
g.add_primitive(BarChart(ind, datalist, options=options))
if options['legend_label']:
g.legend(True)
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:
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.plot import Graphics
g = Graphics()
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)
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 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.
- ``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
- ``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)
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')
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.plot 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)
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
- ``rgbcolor`` - default: (0,0,0)
- ``linestyle`` - default: 'solid' (2D plotting only)
- ``edgecolor`` - default: 'black' (2D plotting only)
- ``facecolor`` - default: 'red' (2D plotting only, useful only
if fill=True)
- ``legend_label`` -- the label for this item in the legend
EXAMPLES::
sage: c = circle((1,1), 1, rgbcolor=(1,0,0))
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 a circle with a legend::
sage: circle((4,5), 1, rgbcolor='yellow', fill=True, legend_label='the sun').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.plot import Graphics
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)
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 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
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, 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 ``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, 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 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.
- ``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
- ``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)
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')
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.plot 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)
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
