コード例 #1
0
ファイル: line.py プロジェクト: bukzor/sage
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
コード例 #2
0
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
コード例 #3
0
ファイル: point.py プロジェクト: sagemath/sagetrac-mirror
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
コード例 #4
0
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
コード例 #5
0
ファイル: point.py プロジェクト: biasse/sage
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
コード例 #6
0
ファイル: polygon.py プロジェクト: CETHop/sage
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
コード例 #7
0
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
コード例 #8
0
ファイル: point.py プロジェクト: bukzor/sage
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
コード例 #9
0
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 
コード例 #10
0
ファイル: point.py プロジェクト: CETHop/sage
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
コード例 #11
0
ファイル: point.py プロジェクト: chiragsinghal283/sage
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
コード例 #12
0
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