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<section class="sphx-glr-example-title" id="transformations-tutorial">
<span id="sphx-glr-tutorials-advanced-transforms-tutorial-py"></span><h1>Transformations Tutorial<a class="headerlink" href="#transformations-tutorial" title="Permalink to this heading">#</a></h1>
<p>Like any graphics packages, Matplotlib is built on top of a transformation
framework to easily move between coordinate systems, the userland <em>data</em>
coordinate system, the <em>axes</em> coordinate system, the <em>figure</em> coordinate
system, and the <em>display</em> coordinate system. In 95% of your plotting, you
won't need to think about this, as it happens under the hood, but as you push
the limits of custom figure generation, it helps to have an understanding of
these objects so you can reuse the existing transformations Matplotlib makes
available to you, or create your own (see <a class="reference internal" href="../../api/transformations.html#module-matplotlib.transforms" title="matplotlib.transforms"><code class="xref py py-mod docutils literal notranslate"><span class="pre">matplotlib.transforms</span></code></a>). The
table below summarizes some useful coordinate systems, a description of each
system, and the transformation object for going from each coordinate system to
the <em>display</em> coordinates. In the "Transformation Object" column, <code class="docutils literal notranslate"><span class="pre">ax</span></code> is a
<a class="reference internal" href="../../api/axes_api.html#matplotlib.axes.Axes" title="matplotlib.axes.Axes"><code class="xref py py-class docutils literal notranslate"><span class="pre">Axes</span></code></a> instance, <code class="docutils literal notranslate"><span class="pre">fig</span></code> is a
<a class="reference internal" href="../../api/figure_api.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure"><code class="xref py py-class docutils literal notranslate"><span class="pre">Figure</span></code></a> instance, and <code class="docutils literal notranslate"><span class="pre">subfigure</span></code> is a
<a class="reference internal" href="../../api/figure_api.html#matplotlib.figure.SubFigure" title="matplotlib.figure.SubFigure"><code class="xref py py-class docutils literal notranslate"><span class="pre">SubFigure</span></code></a> instance.</p>
<table class="table">
<thead>
<tr class="row-odd"><th class="head"><p>Coordinate
system</p></th>
<th class="head"><p>Description</p></th>
<th class="head"><p>Transformation object
from system to display</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>"data"</p></td>
<td><p>The coordinate system of the data
in the Axes.</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">ax.transData</span></code></p></td>
</tr>
<tr class="row-odd"><td><p>"axes"</p></td>
<td><p>The coordinate system of the
<a class="reference internal" href="../../api/axes_api.html#matplotlib.axes.Axes" title="matplotlib.axes.Axes"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Axes</span></code></a>; (0, 0)
is bottom left of the axes, and
(1, 1) is top right of the axes.</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">ax.transAxes</span></code></p></td>
</tr>
<tr class="row-even"><td><p>"subfigure"</p></td>
<td><p>The coordinate system of the
<a class="reference internal" href="../../api/figure_api.html#matplotlib.figure.SubFigure" title="matplotlib.figure.SubFigure"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SubFigure</span></code></a>; (0, 0) is bottom left
of the subfigure, and (1, 1) is top
right of the subfigure. If a
figure has no subfigures, this is
the same as <code class="docutils literal notranslate"><span class="pre">transFigure</span></code>.</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">subfigure.transSubfigure</span></code></p></td>
</tr>
<tr class="row-odd"><td><p>"figure"</p></td>
<td><p>The coordinate system of the
<a class="reference internal" href="../../api/figure_api.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Figure</span></code></a>; (0, 0) is bottom left
of the figure, and (1, 1) is top
right of the figure.</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">fig.transFigure</span></code></p></td>
</tr>
<tr class="row-even"><td><p>"figure-inches"</p></td>
<td><p>The coordinate system of the
<a class="reference internal" href="../../api/figure_api.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Figure</span></code></a> in inches; (0, 0) is
bottom left of the figure, and
(width, height) is the top right
of the figure in inches.</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">fig.dpi_scale_trans</span></code></p></td>
</tr>
<tr class="row-odd"><td><p>"xaxis",
"yaxis"</p></td>
<td><p>Blended coordinate systems, using
data coordinates on one direction
and axes coordinates on the other.</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">ax.get_xaxis_transform()</span></code>,
<code class="docutils literal notranslate"><span class="pre">ax.get_yaxis_transform()</span></code></p></td>
</tr>
<tr class="row-even"><td><p>"display"</p></td>
<td><p>The native coordinate system of the
output ; (0, 0) is the bottom left
of the window, and (width, height)
is top right of the output in
"display units".</p>
<p>The exact interpretation of the
units depends on the back end. For
example it is pixels for Agg and
points for svg/pdf.</p>
</td>
<td><p><a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>, or
<a class="reference internal" href="../../api/transformations.html#matplotlib.transforms.IdentityTransform" title="matplotlib.transforms.IdentityTransform"><code class="xref py py-class docutils literal notranslate"><span class="pre">IdentityTransform()</span></code></a></p></td>
</tr>
</tbody>
</table>
<p>The <a class="reference internal" href="../../api/transformations.html#matplotlib.transforms.Transform" title="matplotlib.transforms.Transform"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Transform</span></code></a> objects are naive to the source and
destination coordinate systems, however the objects referred to in the table
above are constructed to take inputs in their coordinate system, and transform
the input to the <em>display</em> coordinate system. That is why the <em>display</em>
coordinate system has <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a> for the "Transformation Object" column -- it
already is in <em>display</em> coordinates. The naming and destination conventions
are an aid to keeping track of the available "standard" coordinate systems and
transforms.</p>
<p>The transformations also know how to invert themselves (via
<a class="reference internal" href="../../api/transformations.html#matplotlib.transforms.Transform.inverted" title="matplotlib.transforms.Transform.inverted"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Transform.inverted</span></code></a>) to generate a transform from output coordinate system
back to the input coordinate system. For example, <code class="docutils literal notranslate"><span class="pre">ax.transData</span></code> converts
values in data coordinates to display coordinates and
<code class="docutils literal notranslate"><span class="pre">ax.transData.inversed()</span></code> is a <a class="reference internal" href="../../api/transformations.html#matplotlib.transforms.Transform" title="matplotlib.transforms.Transform"><code class="xref py py-class docutils literal notranslate"><span class="pre">matplotlib.transforms.Transform</span></code></a> that
goes from display coordinates to data coordinates. This is particularly useful
when processing events from the user interface, which typically occur in
display space, and you want to know where the mouse click or key-press occurred
in your <em>data</em> coordinate system.</p>
<p>Note that specifying the position of Artists in <em>display</em> coordinates may
change their relative location if the <code class="docutils literal notranslate"><span class="pre">dpi</span></code> or size of the figure changes.
This can cause confusion when printing or changing screen resolution, because
the object can change location and size. Therefore it is most common for
artists placed in an Axes or figure to have their transform set to something
<em>other</em> than the <a class="reference internal" href="../../api/transformations.html#matplotlib.transforms.IdentityTransform" title="matplotlib.transforms.IdentityTransform"><code class="xref py py-obj docutils literal notranslate"><span class="pre">IdentityTransform()</span></code></a>; the default when an artist
is added to an Axes using <a class="reference internal" href="../../api/_as_gen/matplotlib.axes.Axes.add_artist.html#matplotlib.axes.Axes.add_artist" title="matplotlib.axes.Axes.add_artist"><code class="xref py py-obj docutils literal notranslate"><span class="pre">add_artist</span></code></a> is for the transform to be
<code class="docutils literal notranslate"><span class="pre">ax.transData</span></code> so that you can work and think in <em>data</em> coordinates and let
Matplotlib take care of the transformation to <em>display</em>.</p>
<section id="data-coordinates">
<span id="data-coords"></span><h2>Data coordinates<a class="headerlink" href="#data-coordinates" title="Permalink to this heading">#</a></h2>
<p>Let's start with the most commonly used coordinate, the <em>data</em> coordinate
system. Whenever you add data to the axes, Matplotlib updates the datalimits,
most commonly updated with the <a class="reference internal" href="../../api/_as_gen/matplotlib.axes.Axes.set_xlim.html#matplotlib.axes.Axes.set_xlim" title="matplotlib.axes.Axes.set_xlim"><code class="xref py py-meth docutils literal notranslate"><span class="pre">set_xlim()</span></code></a> and
<a class="reference internal" href="../../api/_as_gen/matplotlib.axes.Axes.set_ylim.html#matplotlib.axes.Axes.set_ylim" title="matplotlib.axes.Axes.set_ylim"><code class="xref py py-meth docutils literal notranslate"><span class="pre">set_ylim()</span></code></a> methods. For example, in the figure
below, the data limits stretch from 0 to 10 on the x-axis, and -1 to 1 on the
y-axis.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">matplotlib.patches</span> <span class="k">as</span> <span class="nn">mpatches</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mf">0.005</span><span class="p">)</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ufunc.html#numpy.ufunc" title="numpy.ufunc" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">exp</span></a><span class="p">(</span><span class="o">-</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a><span class="o">/</span><span class="mf">2.</span><span class="p">)</span> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ufunc.html#numpy.ufunc" title="numpy.ufunc" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">sin</span></a><span class="p">(</span><span class="mi">2</span><span class="o">*</span><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">pi</span></a><span class="o">*</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a><span class="p">)</span>
<a href="../../api/figure_api.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fig</span></a><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <a href="../../api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">()</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.plot.html#matplotlib.axes.Axes.plot" title="matplotlib.axes.Axes.plot" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.set_xlim.html#matplotlib.axes.Axes.set_xlim" title="matplotlib.axes.Axes.set_xlim" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span></a><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.set_ylim.html#matplotlib.axes.Axes.set_ylim" title="matplotlib.axes.Axes.set_ylim" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span></a><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_transforms_tutorial_001.png" srcset="../../_images/sphx_glr_transforms_tutorial_001.png, ../../_images/sphx_glr_transforms_tutorial_001_2_0x.png 2.0x" alt="transforms tutorial" class = "sphx-glr-single-img"/><p>You can use the <code class="docutils literal notranslate"><span class="pre">ax.transData</span></code> instance to transform from your
<em>data</em> to your <em>display</em> coordinate system, either a single point or a
sequence of points as shown below:</p>
<div class="highlight-ipython notranslate"><div class="highlight"><pre><span></span><span class="gp">In [14]: </span><span class="nb">type</span><span class="p">(</span><a href="../../api/transformations.html#matplotlib.transforms.CompositeGenericTransform" title="matplotlib.transforms.CompositeGenericTransform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span><span class="o">.</span><span class="n">transData</span></a><span class="p">)</span>
<span class="gh">Out[14]: </span><span class="go"><class 'matplotlib.transforms.CompositeGenericTransform'></span>
<span class="gp">In [15]: </span><a href="../../api/transformations.html#matplotlib.transforms.Transform.transform" title="matplotlib.transforms.Transform.transform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">transData</span><span class="o">.</span><span class="n">transform</span></a><span class="p">((</span><span class="mi">5</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
<span class="gh">Out[15]: </span><span class="go">array([ 335.175, 247. ])</span>
<span class="gp">In [16]: </span><a href="../../api/transformations.html#matplotlib.transforms.Transform.transform" title="matplotlib.transforms.Transform.transform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">transData</span><span class="o">.</span><span class="n">transform</span></a><span class="p">([(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)])</span>
<span class="gh">Out[16]:</span>
<span class="go">array([[ 335.175, 247. ],</span>
<span class="go"> [ 132.435, 642.2 ]])</span>
</pre></div>
</div>
<p>You can use the <a class="reference internal" href="../../api/transformations.html#matplotlib.transforms.Transform.inverted" title="matplotlib.transforms.Transform.inverted"><code class="xref py py-meth docutils literal notranslate"><span class="pre">inverted()</span></code></a>
method to create a transform which will take you from <em>display</em> to <em>data</em>
coordinates:</p>
<div class="highlight-ipython notranslate"><div class="highlight"><pre><span></span><span class="gp">In [41]: </span><span class="n">inv</span> <span class="o">=</span> <a href="../../api/transformations.html#matplotlib.transforms.CompositeGenericTransform" title="matplotlib.transforms.CompositeGenericTransform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span><span class="o">.</span><span class="n">transData</span></a><span class="o">.</span><span class="n">inverted</span><span class="p">()</span>
<span class="gp">In [42]: </span><span class="nb">type</span><span class="p">(</span><span class="n">inv</span><span class="p">)</span>
<span class="gh">Out[42]: </span><span class="go"><class 'matplotlib.transforms.CompositeGenericTransform'></span>
<span class="gp">In [43]: </span><span class="n">inv</span><span class="o">.</span><span class="n">transform</span><span class="p">((</span><span class="mf">335.175</span><span class="p">,</span> <span class="mf">247.</span><span class="p">))</span>
<span class="gh">Out[43]: </span><span class="go">array([ 5., 0.])</span>
</pre></div>
</div>
<p>If your are typing along with this tutorial, the exact values of the
<em>display</em> coordinates may differ if you have a different window size or
dpi setting. Likewise, in the figure below, the display labeled
points are probably not the same as in the ipython session because the
documentation figure size defaults are different.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mf">0.005</span><span class="p">)</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ufunc.html#numpy.ufunc" title="numpy.ufunc" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">exp</span></a><span class="p">(</span><span class="o">-</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a><span class="o">/</span><span class="mf">2.</span><span class="p">)</span> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ufunc.html#numpy.ufunc" title="numpy.ufunc" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">sin</span></a><span class="p">(</span><span class="mi">2</span><span class="o">*</span><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">pi</span></a><span class="o">*</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a><span class="p">)</span>
<a href="../../api/figure_api.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fig</span></a><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <a href="../../api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">()</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.plot.html#matplotlib.axes.Axes.plot" title="matplotlib.axes.Axes.plot" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.set_xlim.html#matplotlib.axes.Axes.set_xlim" title="matplotlib.axes.Axes.set_xlim" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span></a><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.set_ylim.html#matplotlib.axes.Axes.set_ylim" title="matplotlib.axes.Axes.set_ylim" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span></a><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">xdata</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ydata</span></a> <span class="o">=</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">0</span>
<span class="c1"># This computing the transform now, if anything</span>
<span class="c1"># (figure size, dpi, axes placement, data limits, scales..)</span>
<span class="c1"># changes re-calling transform will get a different value.</span>
<a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">xdisplay</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">ydisplay</span></a> <span class="o">=</span> <a href="../../api/transformations.html#matplotlib.transforms.Transform.transform" title="matplotlib.transforms.Transform.transform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">transData</span><span class="o">.</span><span class="n">transform</span></a><span class="p">((</span><a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">xdata</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ydata</span></a><span class="p">))</span>
<a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">bbox</span></a> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="n">boxstyle</span><span class="o">=</span><span class="s2">"round"</span><span class="p">,</span> <span class="n">fc</span><span class="o">=</span><span class="s2">"0.8"</span><span class="p">)</span>
<a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">arrowprops</span></a> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span>
<span class="n">arrowstyle</span><span class="o">=</span><span class="s2">"->"</span><span class="p">,</span>
<span class="n">connectionstyle</span><span class="o">=</span><span class="s2">"angle,angleA=0,angleB=90,rad=10"</span><span class="p">)</span>
<a href="../../api/transformations.html#matplotlib.transforms.ScaledTranslation" title="matplotlib.transforms.ScaledTranslation" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">offset</span></a> <span class="o">=</span> <span class="mi">72</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.annotate.html#matplotlib.axes.Axes.annotate" title="matplotlib.axes.Axes.annotate" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">annotate</span></a><span class="p">(</span><span class="s1">'data = (</span><span class="si">%.1f</span><span class="s1">, </span><span class="si">%.1f</span><span class="s1">)'</span> <span class="o">%</span> <span class="p">(</span><a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">xdata</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ydata</span></a><span class="p">),</span>
<span class="p">(</span><a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">xdata</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ydata</span></a><span class="p">),</span> <span class="n">xytext</span><span class="o">=</span><span class="p">(</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><a href="../../api/transformations.html#matplotlib.transforms.ScaledTranslation" title="matplotlib.transforms.ScaledTranslation" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">offset</span></a><span class="p">,</span> <a href="../../api/transformations.html#matplotlib.transforms.ScaledTranslation" title="matplotlib.transforms.ScaledTranslation" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">offset</span></a><span class="p">),</span> <span class="n">textcoords</span><span class="o">=</span><span class="s1">'offset points'</span><span class="p">,</span>
<a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">bbox</span></a><span class="o">=</span><a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">bbox</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">arrowprops</span></a><span class="o">=</span><a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">arrowprops</span></a><span class="p">)</span>
<a href="../../api/text_api.html#matplotlib.text.Annotation" title="matplotlib.text.Annotation" class="sphx-glr-backref-module-matplotlib-text sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">disp</span></a> <span class="o">=</span> <a href="../../api/_as_gen/matplotlib.axes.Axes.annotate.html#matplotlib.axes.Axes.annotate" title="matplotlib.axes.Axes.annotate" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">annotate</span></a><span class="p">(</span><span class="s1">'display = (</span><span class="si">%.1f</span><span class="s1">, </span><span class="si">%.1f</span><span class="s1">)'</span> <span class="o">%</span> <span class="p">(</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">xdisplay</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">ydisplay</span></a><span class="p">),</span>
<span class="p">(</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">xdisplay</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">ydisplay</span></a><span class="p">),</span> <span class="n">xytext</span><span class="o">=</span><span class="p">(</span><span class="mf">0.5</span><span class="o">*</span><a href="../../api/transformations.html#matplotlib.transforms.ScaledTranslation" title="matplotlib.transforms.ScaledTranslation" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">offset</span></a><span class="p">,</span> <span class="o">-</span><a href="../../api/transformations.html#matplotlib.transforms.ScaledTranslation" title="matplotlib.transforms.ScaledTranslation" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">offset</span></a><span class="p">),</span>
<span class="n">xycoords</span><span class="o">=</span><span class="s1">'figure pixels'</span><span class="p">,</span>
<span class="n">textcoords</span><span class="o">=</span><span class="s1">'offset points'</span><span class="p">,</span>
<a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">bbox</span></a><span class="o">=</span><a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">bbox</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">arrowprops</span></a><span class="o">=</span><a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">arrowprops</span></a><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_transforms_tutorial_002.png" srcset="../../_images/sphx_glr_transforms_tutorial_002.png, ../../_images/sphx_glr_transforms_tutorial_002_2_0x.png 2.0x" alt="transforms tutorial" class = "sphx-glr-single-img"/><div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>If you run the source code in the example above in a GUI backend,
you may also find that the two arrows for the <em>data</em> and <em>display</em>
annotations do not point to exactly the same point. This is because
the display point was computed before the figure was displayed, and
the GUI backend may slightly resize the figure when it is created.
The effect is more pronounced if you resize the figure yourself.
This is one good reason why you rarely want to work in <em>display</em>
space, but you can connect to the <code class="docutils literal notranslate"><span class="pre">'on_draw'</span></code>
<a class="reference internal" href="../../api/backend_bases_api.html#matplotlib.backend_bases.Event" title="matplotlib.backend_bases.Event"><code class="xref py py-class docutils literal notranslate"><span class="pre">Event</span></code></a> to update <em>figure</em>
coordinates on figure draws; see <a class="reference internal" href="../../users/explain/event_handling.html#event-handling-tutorial"><span class="std std-ref">Event handling and picking</span></a>.</p>
</div>
<p>When you change the x or y limits of your axes, the data limits are
updated so the transformation yields a new display point. Note that
when we just change the ylim, only the y-display coordinate is
altered, and when we change the xlim too, both are altered. More on
this later when we talk about the
<a class="reference internal" href="../../api/transformations.html#matplotlib.transforms.Bbox" title="matplotlib.transforms.Bbox"><code class="xref py py-class docutils literal notranslate"><span class="pre">Bbox</span></code></a>.</p>
<div class="highlight-ipython notranslate"><div class="highlight"><pre><span></span><span class="gp">In [54]: </span><a href="../../api/transformations.html#matplotlib.transforms.Transform.transform" title="matplotlib.transforms.Transform.transform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">transData</span><span class="o">.</span><span class="n">transform</span></a><span class="p">((</span><span class="mi">5</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
<span class="gh">Out[54]: </span><span class="go">array([ 335.175, 247. ])</span>
<span class="gp">In [55]: </span><a href="../../api/_as_gen/matplotlib.axes.Axes.set_ylim.html#matplotlib.axes.Axes.set_ylim" title="matplotlib.axes.Axes.set_ylim" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span></a><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gh">Out[55]: </span><span class="go">(-1, 2)</span>
<span class="gp">In [56]: </span><a href="../../api/transformations.html#matplotlib.transforms.Transform.transform" title="matplotlib.transforms.Transform.transform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">transData</span><span class="o">.</span><span class="n">transform</span></a><span class="p">((</span><span class="mi">5</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
<span class="gh">Out[56]: </span><span class="go">array([ 335.175 , 181.13333333])</span>
<span class="gp">In [57]: </span><a href="../../api/_as_gen/matplotlib.axes.Axes.set_xlim.html#matplotlib.axes.Axes.set_xlim" title="matplotlib.axes.Axes.set_xlim" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span></a><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">20</span><span class="p">)</span>
<span class="gh">Out[57]: </span><span class="go">(10, 20)</span>
<span class="gp">In [58]: </span><a href="../../api/transformations.html#matplotlib.transforms.Transform.transform" title="matplotlib.transforms.Transform.transform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">transData</span><span class="o">.</span><span class="n">transform</span></a><span class="p">((</span><span class="mi">5</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
<span class="gh">Out[58]: </span><span class="go">array([-171.675 , 181.13333333])</span>
</pre></div>
</div>
</section>
<section id="axes-coordinates">
<span id="axes-coords"></span><h2>Axes coordinates<a class="headerlink" href="#axes-coordinates" title="Permalink to this heading">#</a></h2>
<p>After the <em>data</em> coordinate system, <em>axes</em> is probably the second most
useful coordinate system. Here the point (0, 0) is the bottom left of
your axes or subplot, (0.5, 0.5) is the center, and (1.0, 1.0) is the
top right. You can also refer to points outside the range, so (-0.1,
1.1) is to the left and above your axes. This coordinate system is
extremely useful when placing text in your axes, because you often
want a text bubble in a fixed, location, e.g., the upper left of the axes
pane, and have that location remain fixed when you pan or zoom. Here
is a simple example that creates four panels and labels them 'A', 'B',
'C', 'D' as you often see in journals.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><a href="../../api/figure_api.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fig</span></a> <span class="o">=</span> <a href="../../api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
<span class="k">for</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">i</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#str" title="builtins.str" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">label</span></a> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">((</span><span class="s1">'A'</span><span class="p">,</span> <span class="s1">'B'</span><span class="p">,</span> <span class="s1">'C'</span><span class="p">,</span> <span class="s1">'D'</span><span class="p">)):</span>
<span class="n">ax</span> <span class="o">=</span> <a href="../../api/figure_api.html#matplotlib.figure.Figure.add_subplot" title="matplotlib.figure.Figure.add_subplot" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-method"><span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span></a><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">i</span></a><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.text.html#matplotlib.axes.Axes.text" title="matplotlib.axes.Axes.text" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">text</span></a><span class="p">(</span><span class="mf">0.05</span><span class="p">,</span> <span class="mf">0.95</span><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#str" title="builtins.str" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">label</span></a><span class="p">,</span> <span class="n">transform</span><span class="o">=</span><a href="../../api/transformations.html#matplotlib.transforms.BboxTransformTo" title="matplotlib.transforms.BboxTransformTo" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span><span class="o">.</span><span class="n">transAxes</span></a><span class="p">,</span>
<span class="n">fontsize</span><span class="o">=</span><span class="mi">16</span><span class="p">,</span> <span class="n">fontweight</span><span class="o">=</span><span class="s1">'bold'</span><span class="p">,</span> <span class="n">va</span><span class="o">=</span><span class="s1">'top'</span><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_transforms_tutorial_003.png" srcset="../../_images/sphx_glr_transforms_tutorial_003.png, ../../_images/sphx_glr_transforms_tutorial_003_2_0x.png 2.0x" alt="transforms tutorial" class = "sphx-glr-single-img"/><p>You can also make lines or patches in the <em>axes</em> coordinate system, but
this is less useful in my experience than using <code class="docutils literal notranslate"><span class="pre">ax.transAxes</span></code> for
placing text. Nonetheless, here is a silly example which plots some
random dots in data space, and overlays a semi-transparent
<a class="reference internal" href="../../api/_as_gen/matplotlib.patches.Circle.html#matplotlib.patches.Circle" title="matplotlib.patches.Circle"><code class="xref py py-class docutils literal notranslate"><span class="pre">Circle</span></code></a> centered in the middle of the axes
with a radius one quarter of the axes -- if your axes does not
preserve aspect ratio (see <a class="reference internal" href="../../api/_as_gen/matplotlib.axes.Axes.set_aspect.html#matplotlib.axes.Axes.set_aspect" title="matplotlib.axes.Axes.set_aspect"><code class="xref py py-meth docutils literal notranslate"><span class="pre">set_aspect()</span></code></a>),
this will look like an ellipse. Use the pan/zoom tool to move around,
or manually change the data xlim and ylim, and you will see the data
move, but the circle will remain fixed because it is not in <em>data</em>
coordinates and will always remain at the center of the axes.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><a href="../../api/figure_api.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fig</span></a><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <a href="../../api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">()</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a> <span class="o">=</span> <span class="mi">10</span><span class="o">*</span><a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.rand.html#numpy.random.rand" title="numpy.random.rand" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span></a><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.plot.html#matplotlib.axes.Axes.plot" title="matplotlib.axes.Axes.plot" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a><span class="p">,</span> <span class="s1">'go'</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span> <span class="c1"># plot some data in data coordinates</span>
<a href="../../api/_as_gen/matplotlib.patches.Circle.html#matplotlib.patches.Circle" title="matplotlib.patches.Circle" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">circ</span></a> <span class="o">=</span> <a href="../../api/_as_gen/matplotlib.patches.Circle.html#matplotlib.patches.Circle" title="matplotlib.patches.Circle" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class"><span class="n">mpatches</span><span class="o">.</span><span class="n">Circle</span></a><span class="p">((</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">),</span> <span class="mf">0.25</span><span class="p">,</span> <span class="n">transform</span><span class="o">=</span><a href="../../api/transformations.html#matplotlib.transforms.BboxTransformTo" title="matplotlib.transforms.BboxTransformTo" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span><span class="o">.</span><span class="n">transAxes</span></a><span class="p">,</span>
<span class="n">facecolor</span><span class="o">=</span><span class="s1">'blue'</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.75</span><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.add_patch.html#matplotlib.axes.Axes.add_patch" title="matplotlib.axes.Axes.add_patch" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">add_patch</span></a><span class="p">(</span><a href="../../api/_as_gen/matplotlib.patches.Circle.html#matplotlib.patches.Circle" title="matplotlib.patches.Circle" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">circ</span></a><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_transforms_tutorial_004.png" srcset="../../_images/sphx_glr_transforms_tutorial_004.png, ../../_images/sphx_glr_transforms_tutorial_004_2_0x.png 2.0x" alt="transforms tutorial" class = "sphx-glr-single-img"/></section>
<section id="blended-transformations">
<span id="id1"></span><h2>Blended transformations<a class="headerlink" href="#blended-transformations" title="Permalink to this heading">#</a></h2>
<p>Drawing in <em>blended</em> coordinate spaces which mix <em>axes</em> with <em>data</em>
coordinates is extremely useful, for example to create a horizontal
span which highlights some region of the y-data but spans across the
x-axis regardless of the data limits, pan or zoom level, etc. In fact
these blended lines and spans are so useful, we have built in
functions to make them easy to plot (see
<a class="reference internal" href="../../api/_as_gen/matplotlib.axes.Axes.axhline.html#matplotlib.axes.Axes.axhline" title="matplotlib.axes.Axes.axhline"><code class="xref py py-meth docutils literal notranslate"><span class="pre">axhline()</span></code></a>,
<a class="reference internal" href="../../api/_as_gen/matplotlib.axes.Axes.axvline.html#matplotlib.axes.Axes.axvline" title="matplotlib.axes.Axes.axvline"><code class="xref py py-meth docutils literal notranslate"><span class="pre">axvline()</span></code></a>,
<a class="reference internal" href="../../api/_as_gen/matplotlib.axes.Axes.axhspan.html#matplotlib.axes.Axes.axhspan" title="matplotlib.axes.Axes.axhspan"><code class="xref py py-meth docutils literal notranslate"><span class="pre">axhspan()</span></code></a>,
<a class="reference internal" href="../../api/_as_gen/matplotlib.axes.Axes.axvspan.html#matplotlib.axes.Axes.axvspan" title="matplotlib.axes.Axes.axvspan"><code class="xref py py-meth docutils literal notranslate"><span class="pre">axvspan()</span></code></a>) but for didactic purposes we
will implement the horizontal span here using a blended
transformation. This trick only works for separable transformations,
like you see in normal Cartesian coordinate systems, but not on
inseparable transformations like the
<a class="reference internal" href="../../api/projections_api.html#matplotlib.projections.polar.PolarAxes.PolarTransform" title="matplotlib.projections.polar.PolarAxes.PolarTransform"><code class="xref py py-class docutils literal notranslate"><span class="pre">PolarTransform</span></code></a>.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.transforms</span> <span class="k">as</span> <span class="nn">transforms</span>
<a href="../../api/figure_api.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fig</span></a><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <a href="../../api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">()</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.randn.html#numpy.random.randn" title="numpy.random.randn" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span></a><span class="p">(</span><span class="mi">1000</span><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.hist.html#matplotlib.axes.Axes.hist" title="matplotlib.axes.Axes.hist" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">hist</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a><span class="p">,</span> <span class="mi">30</span><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.set_title.html#matplotlib.axes.Axes.set_title" title="matplotlib.axes.Axes.set_title" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">set_title</span></a><span class="p">(</span><span class="sa">r</span><span class="s1">'$\sigma=1 \/ \dots \/ \sigma=2$'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">16</span><span class="p">)</span>
<span class="c1"># the x coords of this transformation are data, and the y coord are axes</span>
<a href="../../api/transformations.html#matplotlib.transforms.CompositeGenericTransform" title="matplotlib.transforms.CompositeGenericTransform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">trans</span></a> <span class="o">=</span> <a href="../../api/transformations.html#matplotlib.transforms.blended_transform_factory" title="matplotlib.transforms.blended_transform_factory" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-function"><span class="n">transforms</span><span class="o">.</span><span class="n">blended_transform_factory</span></a><span class="p">(</span>
<a href="../../api/transformations.html#matplotlib.transforms.CompositeGenericTransform" title="matplotlib.transforms.CompositeGenericTransform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span><span class="o">.</span><span class="n">transData</span></a><span class="p">,</span> <a href="../../api/transformations.html#matplotlib.transforms.BboxTransformTo" title="matplotlib.transforms.BboxTransformTo" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span><span class="o">.</span><span class="n">transAxes</span></a><span class="p">)</span>
<span class="c1"># highlight the 1..2 stddev region with a span.</span>
<span class="c1"># We want x to be in data coordinates and y to span from 0..1 in axes coords.</span>
<a href="../../api/_as_gen/matplotlib.patches.Rectangle.html#matplotlib.patches.Rectangle" title="matplotlib.patches.Rectangle" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">rect</span></a> <span class="o">=</span> <a href="../../api/_as_gen/matplotlib.patches.Rectangle.html#matplotlib.patches.Rectangle" title="matplotlib.patches.Rectangle" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class"><span class="n">mpatches</span><span class="o">.</span><span class="n">Rectangle</span></a><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="n">width</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">height</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">transform</span><span class="o">=</span><a href="../../api/transformations.html#matplotlib.transforms.CompositeGenericTransform" title="matplotlib.transforms.CompositeGenericTransform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">trans</span></a><span class="p">,</span>
<span class="n">color</span><span class="o">=</span><span class="s1">'yellow'</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.add_patch.html#matplotlib.axes.Axes.add_patch" title="matplotlib.axes.Axes.add_patch" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">add_patch</span></a><span class="p">(</span><a href="../../api/_as_gen/matplotlib.patches.Rectangle.html#matplotlib.patches.Rectangle" title="matplotlib.patches.Rectangle" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">rect</span></a><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_transforms_tutorial_005.png" srcset="../../_images/sphx_glr_transforms_tutorial_005.png, ../../_images/sphx_glr_transforms_tutorial_005_2_0x.png 2.0x" alt="$\sigma=1 \/ \dots \/ \sigma=2$" class = "sphx-glr-single-img"/><div class="admonition note">
<p class="admonition-title">Note</p>
<p>The blended transformations where x is in <em>data</em> coords and y in <em>axes</em>
coordinates is so useful that we have helper methods to return the
versions Matplotlib uses internally for drawing ticks, ticklabels, etc.
The methods are <a class="reference internal" href="../../api/_as_gen/matplotlib.axes.Axes.get_xaxis_transform.html#matplotlib.axes.Axes.get_xaxis_transform" title="matplotlib.axes.Axes.get_xaxis_transform"><code class="xref py py-meth docutils literal notranslate"><span class="pre">matplotlib.axes.Axes.get_xaxis_transform()</span></code></a> and
<a class="reference internal" href="../../api/_as_gen/matplotlib.axes.Axes.get_yaxis_transform.html#matplotlib.axes.Axes.get_yaxis_transform" title="matplotlib.axes.Axes.get_yaxis_transform"><code class="xref py py-meth docutils literal notranslate"><span class="pre">matplotlib.axes.Axes.get_yaxis_transform()</span></code></a>. So in the example
above, the call to
<a class="reference internal" href="../../api/transformations.html#matplotlib.transforms.blended_transform_factory" title="matplotlib.transforms.blended_transform_factory"><code class="xref py py-meth docutils literal notranslate"><span class="pre">blended_transform_factory()</span></code></a> can be
replaced by <code class="docutils literal notranslate"><span class="pre">get_xaxis_transform</span></code>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><a href="../../api/transformations.html#matplotlib.transforms.CompositeGenericTransform" title="matplotlib.transforms.CompositeGenericTransform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">trans</span></a> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">get_xaxis_transform</span><span class="p">()</span>
</pre></div>
</div>
</div>
</section>
<section id="plotting-in-physical-coordinates">
<span id="transforms-fig-scale-dpi"></span><h2>Plotting in physical coordinates<a class="headerlink" href="#plotting-in-physical-coordinates" title="Permalink to this heading">#</a></h2>
<p>Sometimes we want an object to be a certain physical size on the plot.
Here we draw the same circle as above, but in physical coordinates. If done
interactively, you can see that changing the size of the figure does
not change the offset of the circle from the lower-left corner,
does not change its size, and the circle remains a circle regardless of
the aspect ratio of the axes.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><a href="../../api/figure_api.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fig</span></a><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <a href="../../api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a> <span class="o">=</span> <span class="mi">10</span><span class="o">*</span><a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.rand.html#numpy.random.rand" title="numpy.random.rand" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span></a><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.plot.html#matplotlib.axes.Axes.plot" title="matplotlib.axes.Axes.plot" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a><span class="o">*</span><span class="mf">10.</span><span class="p">,</span> <span class="s1">'go'</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span> <span class="c1"># plot some data in data coordinates</span>
<span class="c1"># add a circle in fixed-coordinates</span>
<a href="../../api/_as_gen/matplotlib.patches.Circle.html#matplotlib.patches.Circle" title="matplotlib.patches.Circle" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">circ</span></a> <span class="o">=</span> <a href="../../api/_as_gen/matplotlib.patches.Circle.html#matplotlib.patches.Circle" title="matplotlib.patches.Circle" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class"><span class="n">mpatches</span><span class="o">.</span><span class="n">Circle</span></a><span class="p">((</span><span class="mf">2.5</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="mf">1.0</span><span class="p">,</span> <span class="n">transform</span><span class="o">=</span><a href="../../api/transformations.html#matplotlib.transforms.Affine2D" title="matplotlib.transforms.Affine2D" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fig</span><span class="o">.</span><span class="n">dpi_scale_trans</span></a><span class="p">,</span>
<span class="n">facecolor</span><span class="o">=</span><span class="s1">'blue'</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.75</span><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.add_patch.html#matplotlib.axes.Axes.add_patch" title="matplotlib.axes.Axes.add_patch" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">add_patch</span></a><span class="p">(</span><a href="../../api/_as_gen/matplotlib.patches.Circle.html#matplotlib.patches.Circle" title="matplotlib.patches.Circle" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">circ</span></a><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_transforms_tutorial_006.png" srcset="../../_images/sphx_glr_transforms_tutorial_006.png, ../../_images/sphx_glr_transforms_tutorial_006_2_0x.png 2.0x" alt="transforms tutorial" class = "sphx-glr-single-img"/><p>If we change the figure size, the circle does not change its absolute
position and is cropped.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><a href="../../api/figure_api.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fig</span></a><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <a href="../../api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">7</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a> <span class="o">=</span> <span class="mi">10</span><span class="o">*</span><a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.rand.html#numpy.random.rand" title="numpy.random.rand" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span></a><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.plot.html#matplotlib.axes.Axes.plot" title="matplotlib.axes.Axes.plot" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a><span class="o">*</span><span class="mf">10.</span><span class="p">,</span> <span class="s1">'go'</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span> <span class="c1"># plot some data in data coordinates</span>
<span class="c1"># add a circle in fixed-coordinates</span>
<a href="../../api/_as_gen/matplotlib.patches.Circle.html#matplotlib.patches.Circle" title="matplotlib.patches.Circle" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">circ</span></a> <span class="o">=</span> <a href="../../api/_as_gen/matplotlib.patches.Circle.html#matplotlib.patches.Circle" title="matplotlib.patches.Circle" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class"><span class="n">mpatches</span><span class="o">.</span><span class="n">Circle</span></a><span class="p">((</span><span class="mf">2.5</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="mf">1.0</span><span class="p">,</span> <span class="n">transform</span><span class="o">=</span><a href="../../api/transformations.html#matplotlib.transforms.Affine2D" title="matplotlib.transforms.Affine2D" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fig</span><span class="o">.</span><span class="n">dpi_scale_trans</span></a><span class="p">,</span>
<span class="n">facecolor</span><span class="o">=</span><span class="s1">'blue'</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.75</span><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.add_patch.html#matplotlib.axes.Axes.add_patch" title="matplotlib.axes.Axes.add_patch" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">add_patch</span></a><span class="p">(</span><a href="../../api/_as_gen/matplotlib.patches.Circle.html#matplotlib.patches.Circle" title="matplotlib.patches.Circle" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">circ</span></a><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_transforms_tutorial_007.png" srcset="../../_images/sphx_glr_transforms_tutorial_007.png, ../../_images/sphx_glr_transforms_tutorial_007_2_0x.png 2.0x" alt="transforms tutorial" class = "sphx-glr-single-img"/><p>Another use is putting a patch with a set physical dimension around a
data point on the axes. Here we add together two transforms. The
first sets the scaling of how large the ellipse should be and the second
sets its position. The ellipse is then placed at the origin, and then
we use the helper transform <a class="reference internal" href="../../api/transformations.html#matplotlib.transforms.ScaledTranslation" title="matplotlib.transforms.ScaledTranslation"><code class="xref py py-class docutils literal notranslate"><span class="pre">ScaledTranslation</span></code></a>
to move it
to the right place in the <code class="docutils literal notranslate"><span class="pre">ax.transData</span></code> coordinate system.
This helper is instantiated with:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><a href="../../api/transformations.html#matplotlib.transforms.CompositeGenericTransform" title="matplotlib.transforms.CompositeGenericTransform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">trans</span></a> <span class="o">=</span> <span class="n">ScaledTranslation</span><span class="p">(</span><span class="n">xt</span><span class="p">,</span> <span class="n">yt</span><span class="p">,</span> <span class="n">scale_trans</span><span class="p">)</span>
</pre></div>
</div>
<p>where <em>xt</em> and <em>yt</em> are the translation offsets, and <em>scale_trans</em> is
a transformation which scales <em>xt</em> and <em>yt</em> at transformation time
before applying the offsets.</p>
<p>Note the use of the plus operator on the transforms below.
This code says: first apply the scale transformation <code class="docutils literal notranslate"><span class="pre">fig.dpi_scale_trans</span></code>
to make the ellipse the proper size, but still centered at (0, 0),
and then translate the data to <code class="docutils literal notranslate"><span class="pre">xdata[0]</span></code> and <code class="docutils literal notranslate"><span class="pre">ydata[0]</span></code> in data space.</p>
<p>In interactive use, the ellipse stays the same size even if the
axes limits are changed via zoom.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><a href="../../api/figure_api.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fig</span></a><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <a href="../../api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">()</span>
<a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">xdata</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ydata</span></a> <span class="o">=</span> <span class="p">(</span><span class="mf">0.2</span><span class="p">,</span> <span class="mf">0.7</span><span class="p">),</span> <span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.plot.html#matplotlib.axes.Axes.plot" title="matplotlib.axes.Axes.plot" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">xdata</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ydata</span></a><span class="p">,</span> <span class="s2">"o"</span><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.set_xlim.html#matplotlib.axes.Axes.set_xlim" title="matplotlib.axes.Axes.set_xlim" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span></a><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
<a href="../../api/transformations.html#matplotlib.transforms.CompositeGenericTransform" title="matplotlib.transforms.CompositeGenericTransform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">trans</span></a> <span class="o">=</span> <span class="p">(</span><a href="../../api/transformations.html#matplotlib.transforms.Affine2D" title="matplotlib.transforms.Affine2D" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fig</span><span class="o">.</span><span class="n">dpi_scale_trans</span></a> <span class="o">+</span>
<a href="../../api/transformations.html#matplotlib.transforms.ScaledTranslation" title="matplotlib.transforms.ScaledTranslation" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class"><span class="n">transforms</span><span class="o">.</span><span class="n">ScaledTranslation</span></a><span class="p">(</span><a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">xdata</span></a><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ydata</span></a><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <a href="../../api/transformations.html#matplotlib.transforms.CompositeGenericTransform" title="matplotlib.transforms.CompositeGenericTransform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span><span class="o">.</span><span class="n">transData</span></a><span class="p">))</span>
<span class="c1"># plot an ellipse around the point that is 150 x 130 points in diameter...</span>
<a href="../../api/_as_gen/matplotlib.patches.Ellipse.html#matplotlib.patches.Ellipse" title="matplotlib.patches.Ellipse" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">circle</span></a> <span class="o">=</span> <a href="../../api/_as_gen/matplotlib.patches.Ellipse.html#matplotlib.patches.Ellipse" title="matplotlib.patches.Ellipse" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class"><span class="n">mpatches</span><span class="o">.</span><span class="n">Ellipse</span></a><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="mi">150</span><span class="o">/</span><span class="mi">72</span><span class="p">,</span> <span class="mi">130</span><span class="o">/</span><span class="mi">72</span><span class="p">,</span> <span class="n">angle</span><span class="o">=</span><span class="mi">40</span><span class="p">,</span>
<span class="n">fill</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">transform</span><span class="o">=</span><a href="../../api/transformations.html#matplotlib.transforms.CompositeGenericTransform" title="matplotlib.transforms.CompositeGenericTransform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">trans</span></a><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.add_patch.html#matplotlib.axes.Axes.add_patch" title="matplotlib.axes.Axes.add_patch" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">add_patch</span></a><span class="p">(</span><a href="../../api/_as_gen/matplotlib.patches.Ellipse.html#matplotlib.patches.Ellipse" title="matplotlib.patches.Ellipse" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">circle</span></a><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_transforms_tutorial_008.png" srcset="../../_images/sphx_glr_transforms_tutorial_008.png, ../../_images/sphx_glr_transforms_tutorial_008_2_0x.png 2.0x" alt="transforms tutorial" class = "sphx-glr-single-img"/><div class="admonition note">
<p class="admonition-title">Note</p>
<p>The order of transformation matters. Here the ellipse
is given the right dimensions in display space <em>first</em> and then moved
in data space to the correct spot.
If we had done the <code class="docutils literal notranslate"><span class="pre">ScaledTranslation</span></code> first, then
<code class="docutils literal notranslate"><span class="pre">xdata[0]</span></code> and <code class="docutils literal notranslate"><span class="pre">ydata[0]</span></code> would
first be transformed to <em>display</em> coordinates (<code class="docutils literal notranslate"><span class="pre">[</span> <span class="pre">358.4</span>  <span class="pre">475.2]</span></code> on
a 200-dpi monitor) and then those coordinates
would be scaled by <code class="docutils literal notranslate"><span class="pre">fig.dpi_scale_trans</span></code> pushing the center of
the ellipse well off the screen (i.e. <code class="docutils literal notranslate"><span class="pre">[</span> <span class="pre">71680.</span>  <span class="pre">95040.]</span></code>).</p>
</div>
</section>
<section id="using-offset-transforms-to-create-a-shadow-effect">
<span id="offset-transforms-shadow"></span><h2>Using offset transforms to create a shadow effect<a class="headerlink" href="#using-offset-transforms-to-create-a-shadow-effect" title="Permalink to this heading">#</a></h2>
<p>Another use of <a class="reference internal" href="../../api/transformations.html#matplotlib.transforms.ScaledTranslation" title="matplotlib.transforms.ScaledTranslation"><code class="xref py py-class docutils literal notranslate"><span class="pre">ScaledTranslation</span></code></a> is to create
a new transformation that is
offset from another transformation, e.g., to place one object shifted a
bit relative to another object. Typically you want the shift to be in
some physical dimension, like points or inches rather than in <em>data</em>
coordinates, so that the shift effect is constant at different zoom
levels and dpi settings.</p>
<p>One use for an offset is to create a shadow effect, where you draw one
object identical to the first just to the right of it, and just below
it, adjusting the zorder to make sure the shadow is drawn first and
then the object it is shadowing above it.</p>
<p>Here we apply the transforms in the <em>opposite</em> order to the use of
<a class="reference internal" href="../../api/transformations.html#matplotlib.transforms.ScaledTranslation" title="matplotlib.transforms.ScaledTranslation"><code class="xref py py-class docutils literal notranslate"><span class="pre">ScaledTranslation</span></code></a> above. The plot is
first made in data coordinates (<code class="docutils literal notranslate"><span class="pre">ax.transData</span></code>) and then shifted by
<code class="docutils literal notranslate"><span class="pre">dx</span></code> and <code class="docutils literal notranslate"><span class="pre">dy</span></code> points using <code class="docutils literal notranslate"><span class="pre">fig.dpi_scale_trans</span></code>. (In typography,
a <a class="reference external" href="https://en.wikipedia.org/wiki/Point_%28typography%29">point</a> is
1/72 inches, and by specifying your offsets in points, your figure
will look the same regardless of the dpi resolution it is saved in.)</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><a href="../../api/figure_api.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fig</span></a><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <a href="../../api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">()</span>
<span class="c1"># make a simple sine wave</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="mf">0.01</span><span class="p">)</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ufunc.html#numpy.ufunc" title="numpy.ufunc" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">sin</span></a><span class="p">(</span><span class="mi">2</span><span class="o">*</span><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">pi</span></a><span class="o">*</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.lines.Line2D.html#matplotlib.lines.Line2D" title="matplotlib.lines.Line2D" class="sphx-glr-backref-module-matplotlib-lines sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">line</span></a><span class="p">,</span> <span class="o">=</span> <a href="../../api/_as_gen/matplotlib.axes.Axes.plot.html#matplotlib.axes.Axes.plot" title="matplotlib.axes.Axes.plot" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'blue'</span><span class="p">)</span>
<span class="c1"># shift the object over 2 points, and down 2 points</span>
<a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">dx</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">dy</span></a> <span class="o">=</span> <span class="mi">2</span><span class="o">/</span><span class="mf">72.</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="o">/</span><span class="mf">72.</span>
<a href="../../api/transformations.html#matplotlib.transforms.ScaledTranslation" title="matplotlib.transforms.ScaledTranslation" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">offset</span></a> <span class="o">=</span> <a href="../../api/transformations.html#matplotlib.transforms.ScaledTranslation" title="matplotlib.transforms.ScaledTranslation" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class"><span class="n">transforms</span><span class="o">.</span><span class="n">ScaledTranslation</span></a><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">dx</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">dy</span></a><span class="p">,</span> <a href="../../api/transformations.html#matplotlib.transforms.Affine2D" title="matplotlib.transforms.Affine2D" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fig</span><span class="o">.</span><span class="n">dpi_scale_trans</span></a><span class="p">)</span>
<a href="../../api/transformations.html#matplotlib.transforms.CompositeGenericTransform" title="matplotlib.transforms.CompositeGenericTransform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">shadow_transform</span></a> <span class="o">=</span> <a href="../../api/transformations.html#matplotlib.transforms.CompositeGenericTransform" title="matplotlib.transforms.CompositeGenericTransform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span><span class="o">.</span><span class="n">transData</span></a> <span class="o">+</span> <a href="../../api/transformations.html#matplotlib.transforms.ScaledTranslation" title="matplotlib.transforms.ScaledTranslation" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">offset</span></a>
<span class="c1"># now plot the same data with our offset transform;</span>
<span class="c1"># use the zorder to make sure we are below the line</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.plot.html#matplotlib.axes.Axes.plot" title="matplotlib.axes.Axes.plot" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'gray'</span><span class="p">,</span>
<span class="n">transform</span><span class="o">=</span><a href="../../api/transformations.html#matplotlib.transforms.CompositeGenericTransform" title="matplotlib.transforms.CompositeGenericTransform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">shadow_transform</span></a><span class="p">,</span>
<span class="n">zorder</span><span class="o">=</span><span class="mf">0.5</span><span class="o">*</span><a href="../../api/_as_gen/matplotlib.artist.Artist.get_zorder.html#matplotlib.artist.Artist.get_zorder" title="matplotlib.artist.Artist.get_zorder" class="sphx-glr-backref-module-matplotlib-artist sphx-glr-backref-type-py-method"><span class="n">line</span><span class="o">.</span><span class="n">get_zorder</span></a><span class="p">())</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.set_title.html#matplotlib.axes.Axes.set_title" title="matplotlib.axes.Axes.set_title" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">set_title</span></a><span class="p">(</span><span class="s1">'creating a shadow effect with an offset transform'</span><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_transforms_tutorial_009.png" srcset="../../_images/sphx_glr_transforms_tutorial_009.png, ../../_images/sphx_glr_transforms_tutorial_009_2_0x.png 2.0x" alt="creating a shadow effect with an offset transform" class = "sphx-glr-single-img"/><div class="admonition note">
<p class="admonition-title">Note</p>
<p>The dpi and inches offset is a
common-enough use case that we have a special helper function to
create it in <a class="reference internal" href="../../api/transformations.html#matplotlib.transforms.offset_copy" title="matplotlib.transforms.offset_copy"><code class="xref py py-func docutils literal notranslate"><span class="pre">matplotlib.transforms.offset_copy()</span></code></a>, which returns
a new transform with an added offset. So above we could have done:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><a href="../../api/transformations.html#matplotlib.transforms.CompositeGenericTransform" title="matplotlib.transforms.CompositeGenericTransform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">shadow_transform</span></a> <span class="o">=</span> <span class="n">transforms</span><span class="o">.</span><span class="n">offset_copy</span><span class="p">(</span><a href="../../api/transformations.html#matplotlib.transforms.CompositeGenericTransform" title="matplotlib.transforms.CompositeGenericTransform" class="sphx-glr-backref-module-matplotlib-transforms sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span><span class="o">.</span><span class="n">transData</span></a><span class="p">,</span>
<a href="../../api/figure_api.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fig</span></a><span class="o">=</span><a href="../../api/figure_api.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fig</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">dx</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">dy</span></a><span class="p">,</span> <span class="n">units</span><span class="o">=</span><span class="s1">'inches'</span><span class="p">)</span>
</pre></div>
</div>
</div>
</section>
<section id="the-transformation-pipeline">
<span id="transformation-pipeline"></span><h2>The transformation pipeline<a class="headerlink" href="#the-transformation-pipeline" title="Permalink to this heading">#</a></h2>
<p>The <code class="docutils literal notranslate"><span class="pre">ax.transData</span></code> transform we have been working with in this
tutorial is a composite of three different transformations that
comprise the transformation pipeline from <em>data</em> -> <em>display</em>
coordinates. Michael Droettboom implemented the transformations
framework, taking care to provide a clean API that segregated the
nonlinear projections and scales that happen in polar and logarithmic
plots, from the linear affine transformations that happen when you pan
and zoom. There is an efficiency here, because you can pan and zoom
in your axes which affects the affine transformation, but you may not
need to compute the potentially expensive nonlinear scales or
projections on simple navigation events. It is also possible to
multiply affine transformation matrices together, and then apply them
to coordinates in one step. This is not true of all possible
transformations.</p>
<p>Here is how the <code class="docutils literal notranslate"><span class="pre">ax.transData</span></code> instance is defined in the basic
separable axis <a class="reference internal" href="../../api/axes_api.html#matplotlib.axes.Axes" title="matplotlib.axes.Axes"><code class="xref py py-class docutils literal notranslate"><span class="pre">Axes</span></code></a> class:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="bp">self</span><span class="o">.</span><span class="n">transData</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">transScale</span> <span class="o">+</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">transLimits</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">transAxes</span><span class="p">)</span>
</pre></div>
</div>
<p>We've been introduced to the <code class="docutils literal notranslate"><span class="pre">transAxes</span></code> instance above in
<a class="reference internal" href="#axes-coords"><span class="std std-ref">Axes coordinates</span></a>, which maps the (0, 0), (1, 1) corners of the
axes or subplot bounding box to <em>display</em> space, so let's look at
these other two pieces.</p>
<p><code class="docutils literal notranslate"><span class="pre">self.transLimits</span></code> is the transformation that takes you from
<em>data</em> to <em>axes</em> coordinates; i.e., it maps your view xlim and ylim
to the unit space of the axes (and <code class="docutils literal notranslate"><span class="pre">transAxes</span></code> then takes that unit
space to display space). We can see this in action here</p>
<div class="highlight-ipython notranslate"><div class="highlight"><pre><span></span><span class="gp">In [80]: </span><span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">()</span>
<span class="gp">In [81]: </span><a href="../../api/_as_gen/matplotlib.axes.Axes.set_xlim.html#matplotlib.axes.Axes.set_xlim" title="matplotlib.axes.Axes.set_xlim" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span></a><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
<span class="gh">Out[81]: </span><span class="go">(0, 10)</span>
<span class="gp">In [82]: </span><a href="../../api/_as_gen/matplotlib.axes.Axes.set_ylim.html#matplotlib.axes.Axes.set_ylim" title="matplotlib.axes.Axes.set_ylim" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span></a><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="gh">Out[82]: </span><span class="go">(-1, 1)</span>
<span class="gp">In [84]: </span><span class="n">ax</span><span class="o">.</span><span class="n">transLimits</span><span class="o">.</span><span class="n">transform</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">))</span>
<span class="gh">Out[84]: </span><span class="go">array([ 0., 0.])</span>
<span class="gp">In [85]: </span><span class="n">ax</span><span class="o">.</span><span class="n">transLimits</span><span class="o">.</span><span class="n">transform</span><span class="p">((</span><span class="mi">10</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">))</span>
<span class="gh">Out[85]: </span><span class="go">array([ 1., 0.])</span>
<span class="gp">In [86]: </span><span class="n">ax</span><span class="o">.</span><span class="n">transLimits</span><span class="o">.</span><span class="n">transform</span><span class="p">((</span><span class="mi">10</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
<span class="gh">Out[86]: </span><span class="go">array([ 1., 1.])</span>
<span class="gp">In [87]: </span><span class="n">ax</span><span class="o">.</span><span class="n">transLimits</span><span class="o">.</span><span class="n">transform</span><span class="p">((</span><span class="mi">5</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
<span class="gh">Out[87]: </span><span class="go">array([ 0.5, 0.5])</span>
</pre></div>
</div>
<p>and we can use this same inverted transformation to go from the unit
<em>axes</em> coordinates back to <em>data</em> coordinates.</p>
<div class="highlight-ipython notranslate"><div class="highlight"><pre><span></span><span class="gp">In [90]: </span><span class="n">inv</span><span class="o">.</span><span class="n">transform</span><span class="p">((</span><span class="mf">0.25</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">))</span>
<span class="gh">Out[90]: </span><span class="go">array([ 2.5, -0.5])</span>
</pre></div>
</div>
<p>The final piece is the <code class="docutils literal notranslate"><span class="pre">self.transScale</span></code> attribute, which is
responsible for the optional non-linear scaling of the data, e.g., for
logarithmic axes. When an Axes is initially setup, this is just set to
the identity transform, since the basic Matplotlib axes has linear
scale, but when you call a logarithmic scaling function like
<a class="reference internal" href="../../api/_as_gen/matplotlib.axes.Axes.semilogx.html#matplotlib.axes.Axes.semilogx" title="matplotlib.axes.Axes.semilogx"><code class="xref py py-meth docutils literal notranslate"><span class="pre">semilogx()</span></code></a> or explicitly set the scale to
logarithmic with <a class="reference internal" href="../../api/_as_gen/matplotlib.axes.Axes.set_xscale.html#matplotlib.axes.Axes.set_xscale" title="matplotlib.axes.Axes.set_xscale"><code class="xref py py-meth docutils literal notranslate"><span class="pre">set_xscale()</span></code></a>, then the
<code class="docutils literal notranslate"><span class="pre">ax.transScale</span></code> attribute is set to handle the nonlinear projection.
The scales transforms are properties of the respective <code class="docutils literal notranslate"><span class="pre">xaxis</span></code> and
<code class="docutils literal notranslate"><span class="pre">yaxis</span></code> <a class="reference internal" href="../../api/axis_api.html#matplotlib.axis.Axis" title="matplotlib.axis.Axis"><code class="xref py py-class docutils literal notranslate"><span class="pre">Axis</span></code></a> instances. For example, when
you call <code class="docutils literal notranslate"><span class="pre">ax.set_xscale('log')</span></code>, the xaxis updates its scale to a
<a class="reference internal" href="../../api/scale_api.html#matplotlib.scale.LogScale" title="matplotlib.scale.LogScale"><code class="xref py py-class docutils literal notranslate"><span class="pre">matplotlib.scale.LogScale</span></code></a> instance.</p>
<p>For non-separable axes the PolarAxes, there is one more piece to
consider, the projection transformation. The <code class="docutils literal notranslate"><span class="pre">transData</span></code>