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polar.py

import math

import numpy as npy

import matplotlib
rcParams = matplotlib.rcParams
from matplotlib.artist import kwdocd
from matplotlib.axes import Axes
from matplotlib import cbook
from matplotlib.patches import Circle
from matplotlib.path import Path
from matplotlib.ticker import Formatter, Locator
from matplotlib.transforms import Affine2D, Affine2DBase, Bbox, \
    BboxTransformTo, IdentityTransform, Transform, TransformWrapper

00016 class PolarAxes(Axes):
    """
    A polar graph projection, where the input dimensions are theta, r.

    Theta starts pointing east and goes anti-clockwise.
    """
    name = 'polar'

00024     class PolarTransform(Transform):
        """
        The base polar transform.  This handles projection theta and r into
        Cartesian coordinate space, but does not perform the ultimate affine
        transformation into the correct position.
        """
        input_dims = 2
        output_dims = 2
        is_separable = False

00034         def __init__(self, resolution):
            """
            Create a new polar transform.  Resolution is the number of steps
            to interpolate between each input line segment to approximate its
            path in curved polar space.
            """
            Transform.__init__(self)
            self._resolution = resolution

        def transform(self, tr):
            xy   = npy.zeros(tr.shape, npy.float_)
            t    = tr[:, 0:1]
            r    = tr[:, 1:2]
            x    = xy[:, 0:1]
            y    = xy[:, 1:2]
            x[:] = r * npy.cos(t)
            y[:] = r * npy.sin(t)
            return xy
        transform.__doc__ = Transform.transform.__doc__

        transform_non_affine = transform
        transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__

        def transform_path(self, path):
            vertices = path.vertices
            if len(vertices) == 2 and vertices[0, 0] == vertices[1, 0]:
                return Path(self.transform(vertices), path.codes)
            ipath = path.interpolated(self._resolution)
            return Path(self.transform(ipath.vertices), ipath.codes)
        transform_path.__doc__ = Transform.transform_path.__doc__

        transform_path_non_affine = transform_path
        transform_path_non_affine.__doc__ = Transform.transform_path_non_affine.__doc__

        def inverted(self):
            return PolarAxes.InvertedPolarTransform(self._resolution)
        inverted.__doc__ = Transform.inverted.__doc__

00072     class PolarAffine(Affine2DBase):
        """
        The affine part of the polar projection.  Scales the output so
        that maximum radius rests on the edge of the axes circle.
        """
00077         def __init__(self, scale_transform, limits):
            """
            limits is the view limit of the data.  The only part of
            its bounds that is used is ymax (for the radius maximum).
            """
            Affine2DBase.__init__(self)
            self._scale_transform = scale_transform
            self._limits = limits
            self.set_children(scale_transform, limits)
            self._mtx = None

        def get_matrix(self):
            if self._invalid:
                limits_scaled = self._limits.transformed(self._scale_transform)
                ymax = limits_scaled.ymax
                affine = Affine2D() \
                    .scale(0.5 / ymax) \
                    .translate(0.5, 0.5)
                self._mtx = affine.get_matrix()
                self._inverted = None
                self._invalid = 0
            return self._mtx
        get_matrix.__doc__ = Affine2DBase.get_matrix.__doc__

00101     class InvertedPolarTransform(Transform):
        """
        The inverse of the polar transform, mapping Cartesian
        coordinate space back to t and r.
        """
        input_dims = 2
        output_dims = 2
        is_separable = False

        def __init__(self, resolution):
            Transform.__init__(self)
            self._resolution = resolution

        def transform(self, xy):
            x = xy[:, 0:1]
            y = xy[:, 1:]
            r = npy.sqrt(x*x + y*y)
            theta = npy.arccos(x / r)
            theta = npy.where(y < 0, 2 * npy.pi - theta, theta)
            return npy.concatenate((theta, r), 1)
        transform.__doc__ = Transform.transform.__doc__

        def inverted(self):
            return PolarAxes.PolarTransform(self._resolution)
        inverted.__doc__ = Transform.inverted.__doc__

00127     class ThetaFormatter(Formatter):
        """
        Used to format the theta tick labels.  Converts the native
        unit of radians into degrees and adds a degree symbol.
        """
        def __call__(self, x, pos=None):
            # \u00b0 : degree symbol
            return u"%d\u00b0" % ((x / npy.pi) * 180.0)

00136     class RadialLocator(Locator):
        """
        Used to locate radius ticks.

        Ensures that all ticks are strictly positive.  For all other
        tasks, it delegates to the base Locator (which may be
        different depending on the scale of the r-axis.
        """
        def __init__(self, base):
            self.base = base

        def __call__(self):
            ticks = self.base()
            return [x for x in ticks if x > 0]

        def autoscale(self):
            return self.base.autoscale()

        def pan(self, numsteps):
            return self.base.pan(numsteps)

        def zoom(self, direction):
            return self.base.zoom(direction)

        def refresh(self):
            return self.base.refresh()

    RESOLUTION = 75

00165     def __init__(self, *args, **kwargs):
        """
        Create a new Polar Axes for a polar plot.
        """

        self._rpad = 0.05
        Axes.__init__(self, *args, **kwargs)
        self.set_aspect('equal', adjustable='box', anchor='C')
        self.cla()
    __init__.__doc__ = Axes.__init__.__doc__

    def cla(self):
        Axes.cla(self)

        self.title.set_y(1.05)

        self.xaxis.set_major_formatter(self.ThetaFormatter())
        angles = npy.arange(0.0, 360.0, 45.0)
        self.set_thetagrids(angles)
        self.yaxis.set_major_locator(self.RadialLocator(self.yaxis.get_major_locator()))

        self.grid(rcParams['polaraxes.grid'])
        self.xaxis.set_ticks_position('none')
        self.yaxis.set_ticks_position('none')

    def _set_lim_and_transforms(self):
        self.transAxes = BboxTransformTo(self.bbox)

        # Transforms the x and y axis separately by a scale factor
        # It is assumed that this part will have non-linear components
        self.transScale = TransformWrapper(IdentityTransform())

        # A (possibly non-linear) projection on the (already scaled) data
        self.transProjection = self.PolarTransform(self.RESOLUTION)

        # An affine transformation on the data, generally to limit the
        # range of the axes
        self.transProjectionAffine = self.PolarAffine(self.transScale, self.viewLim)

        # The complete data transformation stack -- from data all the
        # way to display coordinates
        self.transData = self.transScale + self.transProjection + \
            (self.transProjectionAffine + self.transAxes)

        # This is the transform for theta-axis ticks.  It is
        # equivalent to transData, except it always puts r == 1.0 at
        # the edge of the axis circle.
        self._xaxis_transform = (
            self.transProjection +
            self.PolarAffine(IdentityTransform(), Bbox.unit()) +
            self.transAxes)
        # The theta labels are moved from radius == 0.0 to radius == 1.1
        self._theta_label1_position = Affine2D().translate(0.0, 1.1)
        self._xaxis_text1_transform = (
            self._theta_label1_position +
            self._xaxis_transform)
        self._theta_label2_position = Affine2D().translate(0.0, 1.0 / 1.1)
        self._xaxis_text2_transform = (
            self._theta_label2_position +
            self._xaxis_transform)

        # This is the transform for r-axis ticks.  It scales the theta
        # axis so the gridlines from 0.0 to 1.0, now go from 0.0 to
        # 2pi.
        self._yaxis_transform = (
            Affine2D().scale(npy.pi * 2.0, 1.0) +
            self.transData)
        # The r-axis labels are put at an angle and padded in the r-direction
        self._r_label1_position = Affine2D().translate(22.5, self._rpad)
        self._yaxis_text1_transform = (
            self._r_label1_position +
            Affine2D().scale(1.0 / 360.0, 1.0) +
            self._yaxis_transform
            )
        self._r_label2_position = Affine2D().translate(22.5, self._rpad)
        self._yaxis_text2_transform = (
            self._r_label2_position +
            Affine2D().scale(1.0 / 360.0, 1.0) +
            self._yaxis_transform
            )

    def get_xaxis_transform(self):
        return self._xaxis_transform

    def get_xaxis_text1_transform(self, pad):
        return self._xaxis_text1_transform, 'center', 'center'

    def get_xaxis_text2_transform(self, pad):
        return self._xaxis_text2_transform, 'center', 'center'

    def get_yaxis_transform(self):
        return self._yaxis_transform

    def get_yaxis_text1_transform(self, pad):
        return self._yaxis_text1_transform, 'center', 'center'

    def get_yaxis_text2_transform(self, pad):
        return self._yaxis_text2_transform, 'center', 'center'

    def _gen_axes_patch(self):
        return Circle((0.5, 0.5), 0.5)

    def set_rmax(self, rmax):
        self.viewLim.y1 = rmax
        angle = self._r_label1_position.to_values()[4]
        self._r_label1_position.clear().translate(
            angle, rmax * self._rpad)
        self._r_label2_position.clear().translate(
            angle, -rmax * self._rpad)

    def get_rmax(self):
        return self.viewLim.ymax

    def set_yscale(self, *args, **kwargs):
        Axes.set_yscale(self, *args, **kwargs)
        self.yaxis.set_major_locator(
            self.RadialLocator(self.yaxis.get_major_locator()))

    set_rscale = Axes.set_yscale
    set_rticks = Axes.set_yticks

00286     def set_thetagrids(self, angles, labels=None, frac=None,
                       **kwargs):
        """
        Set the angles at which to place the theta grids (these
        gridlines are equal along the theta dimension).  angles is in
        degrees

        labels, if not None, is a len(angles) list of strings of the
        labels to use at each angle.

        if labels is None, the labels with be fmt%%angle

        frac is the fraction of the polar axes radius at which to
        place the label (1 is the edge).Eg 1.05 isd outside the axes
        and 0.95 is inside the axes

        Return value is a list of lines, labels where the lines are
        lines.Line2D instances and the labels are Text
        instances:

        kwargs are optional text properties for the labels
        %(Text)s
        ACCEPTS: sequence of floats
        """
        angles = npy.asarray(angles, npy.float_)
        self.set_xticks(angles * (npy.pi / 180.0))
        if labels is not None:
            self.set_xticklabels(labels)
        if frac is not None:
            self._theta_label1_position.clear().translate(0.0, frac)
            self._theta_label2_position.clear().translate(0.0, 1.0 / frac)
        for t in self.xaxis.get_ticklabels():
            t.update(kwargs)
        return self.xaxis.get_ticklines(), self.xaxis.get_ticklabels()
    set_thetagrids.__doc__ = cbook.dedent(set_thetagrids.__doc__) % kwdocd

00322     def set_rgrids(self, radii, labels=None, angle=None, rpad=None, **kwargs):
        """
        set the radial locations and labels of the r grids

        The labels will appear at radial distances radii at angle

        labels, if not None, is a len(radii) list of strings of the
        labels to use at each angle.

        if labels is None, the self.rformatter will be used

        rpad is a fraction of the max of radii which will pad each of
        the radial labels in the radial direction.

        Return value is a list of lines, labels where the lines are
        lines.Line2D instances and the labels are text.Text
        instances

        kwargs control the rgrid Text label properties:
        %(Text)s

        ACCEPTS: sequence of floats
        """
        radii = npy.asarray(radii)
        rmin = radii.min()
        if rmin <= 0:
            raise ValueError('radial grids must be strictly positive')

        self.set_yticks(radii)
        if labels is not None:
            self.set_yticklabels(labels)
        if angle is None:
            angle = self._r_label1_position.to_values()[4]
        if rpad is not None:
            self._rpad = rpad
        rmax = self.get_rmax()
        self._r_label1_position.clear().translate(angle, self._rpad * rmax)
        self._r_label2_position.clear().translate(angle, -self._rpad * rmax)
        for t in self.yaxis.get_ticklabels():
            t.update(kwargs)
        return self.yaxis.get_ticklines(), self.yaxis.get_ticklabels()

    set_rgrids.__doc__ = cbook.dedent(set_rgrids.__doc__) % kwdocd

    def set_xscale(self, scale, *args, **kwargs):
        if scale != 'linear':
            raise NotImplementedError("You can not set the xscale on a polar plot.")

    def set_xlim(self, *args, **kargs):
        # The xlim is fixed, no matter what you do
        self.viewLim.intervalx = (0.0, npy.pi * 2.0)

    def format_coord(self, theta, r):
        'return a format string formatting the coordinate'
        theta /= math.pi
        # \u03b8: lower-case theta
        # \u03c0: lower-case pi
        # \u00b0: degree symbol
        return u'\u03b8=%0.3f\u03c0 (%0.3f\u00b0), r=%0.3f' % (theta, theta * 180.0, r)

00382     def get_data_ratio(self):
        '''
        Return the aspect ratio of the data itself.  For a polar plot,
        this should always be 1.0
        '''
        return 1.0

    ### Interactive panning

00391     def can_zoom(self):
        """
        Return True if this axes support the zoom box
        """
        return False

    def start_pan(self, x, y, button):
        angle = self._r_label1_position.to_values()[4] / 180.0 * npy.pi
        mode = ''
        if button == 1:
            epsilon = npy.pi / 45.0
            t, r = self.transData.inverted().transform_point((x, y))
            if t >= angle - epsilon and t <= angle + epsilon:
                mode = 'drag_r_labels'
        elif button == 3:
            mode = 'zoom'

        self._pan_start = cbook.Bunch(
            rmax          = self.get_rmax(),
            trans         = self.transData.frozen(),
            trans_inverse = self.transData.inverted().frozen(),
            r_label_angle = self._r_label1_position.to_values()[4],
            x             = x,
            y             = y,
            mode          = mode
            )

    def end_pan(self):
        del self._pan_start

    def drag_pan(self, button, key, x, y):
        p = self._pan_start

        if p.mode == 'drag_r_labels':
            startt, startr = p.trans_inverse.transform_point((p.x, p.y))
            t, r = p.trans_inverse.transform_point((x, y))

            # Deal with theta
            dt0 = t - startt
            dt1 = startt - t
            if abs(dt1) < abs(dt0):
                dt = abs(dt1) * sign(dt0) * -1.0
            else:
                dt = dt0 * -1.0
            dt = (dt / npy.pi) * 180.0

            rpad = self._r_label1_position.to_values()[5]
            self._r_label1_position.clear().translate(
                p.r_label_angle - dt, rpad)
            self._r_label2_position.clear().translate(
                p.r_label_angle - dt, -rpad)

        elif p.mode == 'zoom':
            startt, startr = p.trans_inverse.transform_point((p.x, p.y))
            t, r = p.trans_inverse.transform_point((x, y))

            dr = r - startr

            # Deal with r
            scale = r / startr
            self.set_rmax(p.rmax / scale)

# These are a couple of aborted attempts to project a polar plot using
# cubic bezier curves.

#         def transform_path(self, path):
#             twopi = 2.0 * npy.pi
#             halfpi = 0.5 * npy.pi

#             vertices = path.vertices
#             t0 = vertices[0:-1, 0]
#             t1 = vertices[1:  , 0]
#             td = npy.where(t1 > t0, t1 - t0, twopi - (t0 - t1))
#             maxtd = td.max()
#             interpolate = npy.ceil(maxtd / halfpi)
#             if interpolate > 1.0:
#                 vertices = self.interpolate(vertices, interpolate)

#             vertices = self.transform(vertices)

#             result = npy.zeros((len(vertices) * 3 - 2, 2), npy.float_)
#             codes = mpath.Path.CURVE4 * npy.ones((len(vertices) * 3 - 2, ), mpath.Path.code_type)
#             result[0] = vertices[0]
#             codes[0] = mpath.Path.MOVETO

#             kappa = 4.0 * ((npy.sqrt(2.0) - 1.0) / 3.0)
#             kappa = 0.5

#             p0   = vertices[0:-1]
#             p1   = vertices[1:  ]

#             x0   = p0[:, 0:1]
#             y0   = p0[:, 1: ]
#             b0   = ((y0 - x0) - y0) / ((x0 + y0) - x0)
#             a0   = y0 - b0*x0

#             x1   = p1[:, 0:1]
#             y1   = p1[:, 1: ]
#             b1   = ((y1 - x1) - y1) / ((x1 + y1) - x1)
#             a1   = y1 - b1*x1

#             x = -(a0-a1) / (b0-b1)
#             y = a0 + b0*x

#             xk = (x - x0) * kappa + x0
#             yk = (y - y0) * kappa + y0

#             result[1::3, 0:1] = xk
#             result[1::3, 1: ] = yk

#             xk = (x - x1) * kappa + x1
#             yk = (y - y1) * kappa + y1

#             result[2::3, 0:1] = xk
#             result[2::3, 1: ] = yk

#             result[3::3] = p1

#             print vertices[-2:]
#             print result[-2:]

#             return mpath.Path(result, codes)

#             twopi = 2.0 * npy.pi
#             halfpi = 0.5 * npy.pi

#             vertices = path.vertices
#             t0 = vertices[0:-1, 0]
#             t1 = vertices[1:  , 0]
#             td = npy.where(t1 > t0, t1 - t0, twopi - (t0 - t1))
#             maxtd = td.max()
#             interpolate = npy.ceil(maxtd / halfpi)

#             print "interpolate", interpolate
#             if interpolate > 1.0:
#                 vertices = self.interpolate(vertices, interpolate)

#             result = npy.zeros((len(vertices) * 3 - 2, 2), npy.float_)
#             codes = mpath.Path.CURVE4 * npy.ones((len(vertices) * 3 - 2, ), mpath.Path.code_type)
#             result[0] = vertices[0]
#             codes[0] = mpath.Path.MOVETO

#             kappa = 4.0 * ((npy.sqrt(2.0) - 1.0) / 3.0)
#             tkappa = npy.arctan(kappa)
#             hyp_kappa = npy.sqrt(kappa*kappa + 1.0)

#             t0 = vertices[0:-1, 0]
#             t1 = vertices[1:  , 0]
#             r0 = vertices[0:-1, 1]
#             r1 = vertices[1:  , 1]

#             td = npy.where(t1 > t0, t1 - t0, twopi - (t0 - t1))
#             td_scaled = td / (npy.pi * 0.5)
#             rd = r1 - r0
#             r0kappa = r0 * kappa * td_scaled
#             r1kappa = r1 * kappa * td_scaled
#             ravg_kappa = ((r1 + r0) / 2.0) * kappa * td_scaled

#             result[1::3, 0] = t0 + (tkappa * td_scaled)
#             result[1::3, 1] = r0*hyp_kappa
#             # result[1::3, 1] = r0 / npy.cos(tkappa * td_scaled) # npy.sqrt(r0*r0 + ravg_kappa*ravg_kappa)

#             result[2::3, 0] = t1 - (tkappa * td_scaled)
#             result[2::3, 1] = r1*hyp_kappa
#             # result[2::3, 1] = r1 / npy.cos(tkappa * td_scaled) # npy.sqrt(r1*r1 + ravg_kappa*ravg_kappa)

#             result[3::3, 0] = t1
#             result[3::3, 1] = r1

#             print vertices[:6], result[:6], t0[:6], t1[:6], td[:6], td_scaled[:6], tkappa
#             result = self.transform(result)
#             return mpath.Path(result, codes)
#         transform_path_non_affine = transform_path



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