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Axislines

Axislines includes a derived Axes implementation. The biggest difference is that the artists responsible to draw axis line, ticks, ticklabel and axis labels are separated out from the mpl’s Axis class, which are much more than artists in the original mpl. This change was strongly motivated to support curvlinear grid. Here are a few things that axes_grid.axislines.Axes is different from original Axes from mpl.

  • Axis elements (axis line(spine), ticks, ticklabel and axis labels) are drawn by a AxisArtist instance. Unlike Axis, left, right, top and bottom axis are drawn by separate artists. And each of them may have different tick location and different tick labels.
  • gridlines are drawn by a Gridlines instance. The change was motivated that in curvelinear coordinate, a gridline may not cross axislines (i.e., no associated ticks). In the original Axes class, gridlines are tied to ticks.
  • ticklines can be rotated if necessary (i.e, along the gridlines)

In summary, all these changes was to support

  • a curvelinear grid.
  • a floating axis

[source code, hires.png, pdf]

../../../_images/demo_floating_axis1.png

axes_grid.axislines.Axes defines a axis attribute, which is a dictionary of AxisArtist instances. By default, the dictionary has 4 AxisArtist instances, responsible for drawing of left, right, bottom and top axis.

xaxis and yaxis attributes are still available, however they are set to not visible. As separate artists are used for rendering axis, some axis-related method in mpl may have no effect. In addition to AxisArtist instances, the axes_grid.axislines.Axes will have gridlines attribute (Gridlines), which obviously draws grid lines.

In both AxisArtist and Gridlines, the calculation of tick and grid location is delegated to an instance of GridHelper class. axes_grid.axislines.Axes class uses GridHelperRectlinear as a grid helper. The GridHelperRectlinear class is a wrapper around the xaxis and yaxis of mpl’s original Axes, and it was meant to work as the way how mpl’s original axes works. For example, tick location changes using set_ticks method and etc. should work as expected. But change in artist properties (e.g., color) will not work in general, although some effort has been made so that some often-change attributes (color, etc.) are respected.

AxisArtist

AxisArtist can be considered as a container artist with following attributes which will draw ticks, labels, etc.

  • line
  • major_ticks, major_ticklabels
  • minor_ticks, minor_ticklabels
  • offsetText
  • label

line

Derived from Line2d class. Responsible for drawing a spinal(?) line.

major_ticks, minor_ticks

Derived from Line2d class. Note that ticks are markers.

major_ticklabels, minor_ticklabels

Derived from Text. Note that it is not a list of Text artist, but a single artist (similar to a collection).

axislabel

Derived from Text.

Default AxisArtists

By default, following for axis artists are defined.:

ax.axis["left"], ax.axis["bottom"], ax.axis["right"], ax.axis["top"]

The ticklabels and axislabel of the top and the right axis are set to not visible.

HowTo

  1. Changing tick locations and label.

Same as the original mpl’s axes.:

ax.set_xticks([1,2,3])
  1. Changing axis properties like color, etc.

Change the properties of appropriate artists. For example, to change the color of the ticklabels:

ax.axis["left"].major_ticklabels.set_color("r")

GridHelper

To actually define a curvelinear coordinate, you have to use your own grid helper. A generalised version of grid helper class is supplied and this class should be suffice in most of cases. A user may provide two functions which defines a transformation (and its inverse pair) from the curved coordinate to (rectlinear) image coordinate. Note that while ticks and grids are drawn for curved coordinate, the data transform of the axes itself (ax.transData) is still rectlinear (image) coordinate.

from  mpl_toolkits.axes_grid.grid_helper_curvelinear \
     import GridHelperCurveLinear
from mpl_toolkits.axes_grid.axislines import Subplot

# from curved coordinate to rectlinear coordinate.
def tr(x, y):
    x, y = np.asarray(x), np.asarray(y)
    return x, y-x

# from rectlinear coordinate to curved coordinate.
def inv_tr(x,y):
    x, y = np.asarray(x), np.asarray(y)
    return x, y+x


grid_helper = GridHelperCurveLinear((tr, inv_tr))

ax1 = Subplot(fig, 1, 1, 1, grid_helper=grid_helper)

fig.add_subplot(ax1)

You may use matplotlib’s Transform instance instead (but a inverse transformation must be defined). Often, coordinate range in a curved coordinate system may have a limited range, or may have cycles. In those cases, a more customized version of grid helper is required.

import  mpl_toolkits.axes_grid.angle_helper as angle_helper

# PolarAxes.PolarTransform takes radian. However, we want our coordinate
# system in degree
tr = Affine2D().scale(np.pi/180., 1.) + PolarAxes.PolarTransform()


# extreme finder :  find a range of coordinate.
# 20, 20 : number of sampling points along x, y direction
# The first coordinate (longitude, but theta in polar)
#   has a cycle of 360 degree.
# The second coordinate (latitude, but radius in polar)  has a minimum of 0
extreme_finder = angle_helper.ExtremeFinderCycle(20, 20,
                                                 lon_cycle = 360,
                                                 lat_cycle = None,
                                                 lon_minmax = None,
                                                 lat_minmax = (0, np.inf),
                                                 )

# Find a grid values appropriate for the coordinate (degree,
# minute, second). The argument is a approximate number of grids.
grid_locator1 = angle_helper.LocatorDMS(12)

# And also uses an appropriate formatter.  Note that,the
# acceptable Locator and Formatter class is a bit different than
# that of mpl's, and you cannot directly use mpl's Locator and
# Formatter here (but may be possible in the future).
tick_formatter1 = angle_helper.FormatterDMS()

grid_helper = GridHelperCurveLinear(tr,
                                    extreme_finder=extreme_finder,
                                    grid_locator1=grid_locator1,
                                    tick_formatter1=tick_formatter1
                                    )

Again, the transData of the axes is still a rectlinear coordinate (image coordinate). You may manually do conversion between two coordinates, or you may use Parasite Axes for convenience.:

ax1 = SubplotHost(fig, 1, 2, 2, grid_helper=grid_helper)

# A parasite axes with given transform
ax2 = ParasiteAxesAuxTrans(ax1, tr, "equal")
# note that ax2.transData == tr + ax1.transData
# Anthing you draw in ax2 will match the ticks and grids of ax1.
ax1.parasites.append(ax2)

[source code, hires.png, pdf]

../../../_images/demo_curvelinear_grid1.png

FloatingAxis

A floating axis is an axis one of whose data coordinate is fixed, i.e, its location is not fixed in Axes coordinate but changes as axes data limits changes. A floating axis can be created using new_floating_axis method. However, it is your responsibility that the resulting AxisArtist is properly added to the axes. A recommended way is to add it as an item of Axes’s axis attribute.:

# floating axis whose first (index starts from 0) coordinate
# (theta) is fixed at 60

ax1.axis["lat"] = axis = ax1.new_floating_axis(0, 60)
axis.label.set_text(r"$\theta = 60^{\circ}$")
axis.label.set_visible(True)

See the first example of this page.

Current Limitations and TODO’s

The code need more refinement. Here is a incomplete list of issues and TODO’s

  • No easy way to support a user customized tick location (for curvelinear grid). A new Locator class needs to be created.
  • FloatingAxis may have coordinate limits, e.g., a floating axis of x = 0, but y only spans from 0 to 1.
  • The location of axislabel of FloatingAxis needs to be optionally given as a coordinate value. ex, a floating axis of x=0 with label at y=1