This page is rather personal notes of the author and summarizes the things learned about Matplotlib during the mpltern implementation.

Aims of mpltern

Compared with other Python-based implementations for ternary plots, mpltern focuses on providing a similar user experience to Matplotlib. Practically, this aim is hopefully accomplished by:

  • Implementation of TernaryAxes inheriting Axes of Matplotlib.
    • Components of Axes like Axis and Tick are also overridden as TernaryAxis and TernaryTick, respectively.

  • Parameters in rcParams of Matplotlib rather than hard-coded defaults. This also enables us to use seaborn styles with mpltern.

  • Employments of new transform classes useful for ternary plots. This particularly makes mpltern work nicely not only in non-interactive modes but also in interactive modes.



The first arguments x and y are actually positional arguments, and therefore their order cannot be exchanged. Following this behavior, also in mpltern, the order of t, l, r cannot be exchanged.

ax.plot can run even without any positional arguments. In this case, a list of no length ([]) is returned. (see the implementation of matplotlib.axes._base._process_plot_var_args.__call__).


The AxesSubplot class is dynamically created by matplotlib.axes._subplots.subplot_class_factory.

In mpltern, TernaryAxes is defined without the suffix Subplot, similarly to Axes in Matplotlib, but if it is created e.g. via fig.add_subplot it becomes TernaryAxesSubplot.

Registration of a New Projection

In Matplotlib, to use Axes3D one has to import mpl_toolkits.mplot3d.Axes3D, as described in the Matplotlib mplot3d tutorial. In mpltern, however, it is decided NOT to follow this way due to the increase of the typing effort. Instead, TernaryAxes is available by just importing mpltern. While in most cases mpltern tries to follow the ways of Matplotlib, this is one of the exceptions.



In Matplotlib, 'default' actually does not restore the default positions of ticks. This may be due to the compatibility with Matplotlib 1.x. In mpltern, 'default' is equivalent to 'tick1'.


When, for example, we have a large y-axis values, Matplotlib shows the values as the differences from the reference value, which is shown at one end. The offsetText indicates the text showing this reference value.

Remove round-off

Before Matplotlib 3.1.0, _get_pixel_distance_along_axis was used in Axis classes. In TernaryAxis, this method had to be overridden. In Matplotlib 3.1.0, this becomes not necessary thanks to the simplification and the improvement of consistency (#12158 in Matplotlib).


  • To be overridden
    • update_label_position
      • The positions of ticks are updated via _update_ticks.

The default verticalaligment of axis labels in Matplotlib are:

  • XAxis.label
    • 'bottom': 'top'

    • 'top': 'baseline'

  • YAxis.label
    • 'left': 'bottom'

    • 'right': 'top'

The above gives different spaces between tick labels and the axis labels for the x and the y axes when tick labels come below the axis label. In mpltern, bottom is used by default when the tick labels come below the axis label. This is because baseline and top apparently give different spaces to their tick labels if the label text has a descent.



In Matplotlib, ticks are defined as a list of Tick instances. Each Tick corresponds to a value of the corresponding coordinate. A Tick has three Line2D instances to show a tick marker for each side and a grid and has two Text instances to show tick labels on both sides.

A tick is shown by a marker. By default, the tick-maker in Matplotlib is already scaled as

  • 1.0 if self._tickdir in ['in', 'out']

  • 0.5 if self._tickdir in ['inout']

and is already rotated by 90 degrees for the XTick.

To make a tilted tick marker, mpltern rotates and scales the default one in the TernaryTick._tilt_marker method. When tilting the tick-marker, we must also re-apply the above rotation and the scaling to it.

RadialTick in PolarAxes

When a circular sector is drawn, the horizontal and the vertical alignments of tick labels cannot be modified from outside.

TernaryTick in mpltern

  • To be overridden:
    • _get_tick1line, _get_tick2line, _get_gridline
      • transform of the line must be overridden by the one suitable for the corresponding ternary axis.

    • update_position
      • Tick-angles are modified in this method with calling the _tilt_marker method inside.


In fig.colorbar in Matplotlib, the position of the colorbar does not care y-ticks on the right. The keywords fraction and pad determine the position of the colorbar, which we specify by hand. Following to this behavior, mpltern does NOT automatically position the colorbar but requests users to do by hand.

Interactive Modes

The buttons in the interactive mode call the following methods:

  • Home: _set_view

  • Pan/Zoom: drag_pan

  • Zoom-to-rectangle: _set_view_from_bbox

If you want to scale the axes for ternary plots according to the change of (xmin, ymin, xmax, ymax), these methods should be overridden to call the rescaling method for the axes of ternary plots (_set_ternary_lim_from_xlim_and_ylim).

If you want to prohibit e.g. Zoom-to-rectanble, you need to override e.g. can_zoom to return False. (PolarAxes in Matplotlib does this.)


The versioning is automatically done using To make mpltern.__version__ available, versionfile_build must be specified in setup.cfg. Details are found in


This summarizes the things learned about Sphinx and Read the Docs during the documentation of mpltern 0.3.1+.

How to redirect to Read the Docs

The website is now redirected to following the way in

How the table of contents displays

In Sphinx version 2.0+, the TOC taken from “contents” by default. Read the Docs, in contrast, the home page, which is “index” by default, is supposed to have toctree, from which the TOC is created. What I wanted to do is to set “index” as the home page without showing the TOC explicitly. This can be actually achieved by following




  • Crosshairs

  • Reduce the usages of private methods in Matplotlib


  • annotate (Adequate manipulations for xycoords and textcoords are required, which is tough for my current time schedule.)

  • Isoproportion lines

  • errorbar (Implementation of error bars along ternary axes? The error bars in ternary plots for different axes may be correlated with each other.)

  • More general (hexagonal) plotting of a part of the triangle

  • Parallelogram plots

  • Piper diagram

  • Triangular and hexagonal binning with values (like ggtern)

  • Tie lines

  • Log scale

  • Scatter Hist (ternary-plot version of Matplotlib)