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Merge pull request #22702 from tacaswell/doc_tweak_transform_tutorial
Doc tweak transform tutorial
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‎tutorials/advanced/transforms_tutorial.py

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Transformations Tutorial
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========================
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Like any graphics packages, Matplotlib is built on top of a
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transformation framework to easily move between coordinate systems,
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the userland *data* coordinate system, the *axes* coordinate system,
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the *figure* coordinate system, and the *display* coordinate system.
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In 95% of your plotting, you won't need to think about this, as it
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happens under the hood, but as you push the limits of custom figure
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generation, it helps to have an understanding of these objects so you
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can reuse the existing transformations Matplotlib makes available to
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you, or create your own (see :mod:`matplotlib.transforms`). The table
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below summarizes the some useful coordinate systems, the transformation
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object you should use to work in that coordinate system, and the
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description of that system. In the ``Transformation Object`` column,
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``ax`` is a :class:`~matplotlib.axes.Axes` instance, and ``fig`` is a
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:class:`~matplotlib.figure.Figure` instance.
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+----------------+-----------------------------+-----------------------------------+
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|Coordinates |Transformation object |Description |
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+================+=============================+===================================+
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|"data" |``ax.transData`` |The coordinate system for the data,|
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| | |controlled by xlim and ylim. |
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+----------------+-----------------------------+-----------------------------------+
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|"axes" |``ax.transAxes`` |The coordinate system of the |
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| | |`~matplotlib.axes.Axes`; (0, 0) |
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| | |is bottom left of the axes, and |
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| | |(1, 1) is top right of the axes. |
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+----------------+-----------------------------+-----------------------------------+
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|"subfigure" |``subfigure.transSubfigure`` |The coordinate system of the |
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| | |`.SubFigure`; (0, 0) is bottom left|
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| | |of the subfigure, and (1, 1) is top|
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| | |right of the subfigure. If a |
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| | |figure has no subfigures, this is |
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| | |the same as ``transFigure``. |
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+----------------+-----------------------------+-----------------------------------+
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|"figure" |``fig.transFigure`` |The coordinate system of the |
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| | |`.Figure`; (0, 0) is bottom left |
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| | |of the figure, and (1, 1) is top |
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| | |right of the figure. |
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+----------------+-----------------------------+-----------------------------------+
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|"figure-inches" |``fig.dpi_scale_trans`` |The coordinate system of the |
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| | |`.Figure` in inches; (0, 0) is |
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| | |bottom left of the figure, and |
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| | |(width, height) is the top right |
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| | |of the figure in inches. |
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+----------------+-----------------------------+-----------------------------------+
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|"display" |``None``, or |The pixel coordinate system of the |
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| |``IdentityTransform()`` |display window; (0, 0) is bottom |
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| | |left of the window, and (width, |
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| | |height) is top right of the |
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| | |display window in pixels. |
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+----------------+-----------------------------+-----------------------------------+
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|"xaxis", |``ax.get_xaxis_transform()``,|Blended coordinate systems; use |
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|"yaxis" |``ax.get_yaxis_transform()`` |data coordinates on one of the axis|
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| | |and axes coordinates on the other. |
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+----------------+-----------------------------+-----------------------------------+
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All of the transformation objects in the table above take inputs in
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their coordinate system, and transform the input to the *display*
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coordinate system. That is why the *display* coordinate system has
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``None`` for the ``Transformation Object`` column -- it already is in
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*display* coordinates. The transformations also know how to invert
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themselves, to go from *display* back to the native coordinate system.
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This is particularly useful when processing events from the user
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interface, which typically occur in display space, and you want to
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know where the mouse click or key-press occurred in your *data*
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coordinate system.
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Note that specifying objects in *display* coordinates will change their
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location if the ``dpi`` of the figure changes. This can cause confusion when
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printing or changing screen resolution, because the object can change location
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and size. Therefore it is most common
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for artists placed in an Axes or figure to have their transform set to
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something *other* than the `~.transforms.IdentityTransform()`; the default when
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an artist is placed on an Axes using `~.axes.Axes.add_artist` is for the
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transform to be ``ax.transData``.
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Like any graphics packages, Matplotlib is built on top of a transformation
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framework to easily move between coordinate systems, the userland *data*
8+
coordinate system, the *axes* coordinate system, the *figure* coordinate
9+
system, and the *display* coordinate system. In 95% of your plotting, you
10+
won't need to think about this, as it happens under the hood, but as you push
11+
the limits of custom figure generation, it helps to have an understanding of
12+
these objects so you can reuse the existing transformations Matplotlib makes
13+
available to you, or create your own (see :mod:`matplotlib.transforms`). The
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table below summarizes some useful coordinate systems, a description of each
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system, and the transformation object for going from each coordinate system to
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the *display* coordinates. In the "Transformation Object" column, ``ax`` is a
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:class:`~matplotlib.axes.Axes` instance, ``fig`` is a
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:class:`~matplotlib.figure.Figure` instance, and ``subfigure`` is a
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:class:`~matplotlib.figure.SubFigure` instance.
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+----------------+-----------------------------------+---------------------------------------------------+
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|Coordinate |Description |Transformation object |
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|system | |from system to display |
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+================+===================================+===================================================+
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|"data" |The coordinate system of the data |``ax.transData`` |
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| |in the Axes. | |
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+----------------+-----------------------------------+---------------------------------------------------+
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|"axes" |The coordinate system of the |``ax.transAxes`` |
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| |`~matplotlib.axes.Axes`; (0, 0) | |
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| |is bottom left of the axes, and | |
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| |(1, 1) is top right of the axes. | |
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+----------------+-----------------------------------+---------------------------------------------------+
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|"subfigure" |The coordinate system of the |``subfigure.transSubfigure`` |
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| |`.SubFigure`; (0, 0) is bottom left| |
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| |of the subfigure, and (1, 1) is top| |
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| |right of the subfigure. If a | |
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| |figure has no subfigures, this is | |
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| |the same as ``transFigure``. | |
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+----------------+-----------------------------------+---------------------------------------------------+
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|"figure" |The coordinate system of the |``fig.transFigure`` |
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| |`.Figure`; (0, 0) is bottom left | |
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| |of the figure, and (1, 1) is top | |
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| |right of the figure. | |
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+----------------+-----------------------------------+---------------------------------------------------+
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|"figure-inches" |The coordinate system of the |``fig.dpi_scale_trans`` |
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| |`.Figure` in inches; (0, 0) is | |
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| |bottom left of the figure, and | |
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| |(width, height) is the top right | |
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| |of the figure in inches. | |
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+----------------+-----------------------------------+---------------------------------------------------+
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|"xaxis", |Blended coordinate systems, using |``ax.get_xaxis_transform()``, |
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|"yaxis" |data coordinates on one direction |``ax.get_yaxis_transform()`` |
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| |and axes coordinates on the other. | |
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+----------------+-----------------------------------+---------------------------------------------------+
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|"display" |The native coordinate system of the|`None`, or |
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| |output ; (0, 0) is the bottom left |:class:`~matplotlib.transforms.IdentityTransform()`|
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| |of the window, and (width, height) | |
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| |is top right of the output in | |
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| |"display units". | |
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| | | |
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| |The exact interpertation of the | |
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| |units depends on the back end. For | |
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| |example it is pixels for Agg and | |
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| |points for svg/pdf. | |
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+----------------+-----------------------------------+---------------------------------------------------+
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The `~matplotlib.transforms.Transform` objects are naive to the source and
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destination coordinate systems, however the objects referred to in the table
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above are constructed to take inputs in their coordinate system, and transform
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the input to the *display* coordinate system. That is why the *display*
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coordinate system has `None` for the "Transformation Object" column -- it
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already is in *display* coordinates. The naming and destination conventions
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are an aid to keeping track of the available "standard" coordinate systems and
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transforms.
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The transformations also know how to invert themselves (via
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`.Transform.inverted`) to generate a transform from output coordinate system
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back to the input coordinate system. For example, ``ax.transData`` converts
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values in data coordinates to display coordinates and
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``ax.transData.inversed()`` is a :class:`matplotlib.transforms.Transform` that
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goes from display coordinates to data coordinates. This is particularly useful
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when processing events from the user interface, which typically occur in
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display space, and you want to know where the mouse click or key-press occurred
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in your *data* coordinate system.
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Note that specifying the position of Artists in *display* coordinates may
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change their relative location if the ``dpi`` or size of the figure changes.
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This can cause confusion when printing or changing screen resolution, because
94+
the object can change location and size. Therefore it is most common for
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artists placed in an Axes or figure to have their transform set to something
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*other* than the `~.transforms.IdentityTransform()`; the default when an artist
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is added to an Axes using `~.axes.Axes.add_artist` is for the transform to be
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``ax.transData`` so that you can work and think in *data* coordinates and let
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Matplotlib take care of the transformation to *display*.
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.. _data-coords:
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@@ -89,6 +109,7 @@
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:meth:`~matplotlib.axes.Axes.set_ylim` methods. For example, in the figure
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below, the data limits stretch from 0 to 10 on the x-axis, and -1 to 1 on the
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y-axis.
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"""
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import numpy as np

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