forked from matplotlib/matplotlib
-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathtransforms_tutorial.py
More file actions
470 lines (427 loc) · 19.4 KB
/
transforms_tutorial.py
File metadata and controls
470 lines (427 loc) · 19.4 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
"""
========================
Transformations Tutorial
========================
Like any graphics packages, Matplotlib is built on top of a
transformation framework to easily move between coordinate systems,
the userland `data` coordinate system, the `axes` coordinate system,
the `figure` coordinate system, and the `display` 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 :mod:`matplotlib.transforms`). The table
below summarizes the some useful coordinate systems, the transformation
object you should use to work in that coordinate system, and the
description of that system. In the `Transformation Object` column,
``ax`` is a :class:`~matplotlib.axes.Axes` instance, and ``fig`` is a
:class:`~matplotlib.figure.Figure` instance.
+-----------+-----------------------------+-----------------------------------+
|Coordinates|Transformation object |Description |
+-----------+-----------------------------+-----------------------------------+
|"data" |``ax.transData`` |The coordinate system for the data,|
| | |controlled by xlim and ylim. |
+-----------+-----------------------------+-----------------------------------+
|"axes" |``ax.transAxes`` |The coordinate system of the |
| | |`~matplotlib.axes.Axes`; (0, 0) |
| | |is bottom left of the axes, and |
| | |(1, 1) is top right of the axes. |
+-----------+-----------------------------+-----------------------------------+
|"figure" |``fig.transFigure`` |The coordinate system of the |
| | |`.Figure`; (0, 0) is bottom left |
| | |of the figure, and (1, 1) is top |
| | |right of the figure. |
+-----------+-----------------------------+-----------------------------------+
|"display" |``None``, or |The pixel coordinate system of the |
| |``IdentityTransform()`` |display; (0, 0) is bottom left of |
| | |the display, and (width, height) is|
| | |top right of the display in pixels.|
+-----------+-----------------------------+-----------------------------------+
|"xaxis", |``ax.get_xaxis_transform()``,|Blended coordinate systems; use |
|"yaxis" |``ax.get_yaxis_transform()`` |data coordinates on one of the axis|
| | |and axes coordinates on the other. |
+-----------+-----------------------------+-----------------------------------+
All of the transformation objects in the table above take inputs in
their coordinate system, and transform the input to the `display`
coordinate system. That is why the `display` coordinate system has
`None` for the `Transformation Object` column -- it already is in
display coordinates. The transformations also know how to invert
themselves, to go from `display` back to the native coordinate system.
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 data
coordinate system.
.. _data-coords:
Data coordinates
================
Let's start with the most commonly used coordinate, the `data`
coordinate system. Whenever you add data to the axes, Matplotlib
updates the datalimits, most commonly updated with the
:meth:`~matplotlib.axes.Axes.set_xlim` and
:meth:`~matplotlib.axes.Axes.set_ylim` 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.
"""
import numpy as np
import matplotlib.pyplot as plt
x = np.arange(0, 10, 0.005)
y = np.exp(-x/2.) * np.sin(2*np.pi*x)
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(x, y)
ax.set_xlim(0, 10)
ax.set_ylim(-1, 1)
plt.show()
###############################################################################
# You can use the ``ax.transData`` instance to transform from your
# `data` to your `display` coordinate system, either a single point or a
# sequence of points as shown below:
#
# .. sourcecode:: ipython
#
# In [14]: type(ax.transData)
# Out[14]: <class 'matplotlib.transforms.CompositeGenericTransform'>
#
# In [15]: ax.transData.transform((5, 0))
# Out[15]: array([ 335.175, 247. ])
#
# In [16]: ax.transData.transform([(5, 0), (1, 2)])
# Out[16]:
# array([[ 335.175, 247. ],
# [ 132.435, 642.2 ]])
#
# You can use the :meth:`~matplotlib.transforms.Transform.inverted`
# method to create a transform which will take you from display to data
# coordinates:
#
# .. sourcecode:: ipython
#
# In [41]: inv = ax.transData.inverted()
#
# In [42]: type(inv)
# Out[42]: <class 'matplotlib.transforms.CompositeGenericTransform'>
#
# In [43]: inv.transform((335.175, 247.))
# Out[43]: array([ 5., 0.])
#
# If your are typing along with this tutorial, the exact values of the
# display 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.
x = np.arange(0, 10, 0.005)
y = np.exp(-x/2.) * np.sin(2*np.pi*x)
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(x, y)
ax.set_xlim(0, 10)
ax.set_ylim(-1, 1)
xdata, ydata = 5, 0
xdisplay, ydisplay = ax.transData.transform_point((xdata, ydata))
bbox = dict(boxstyle="round", fc="0.8")
arrowprops = dict(
arrowstyle="->",
connectionstyle="angle,angleA=0,angleB=90,rad=10")
offset = 72
ax.annotate('data = (%.1f, %.1f)' % (xdata, ydata),
(xdata, ydata), xytext=(-2*offset, offset), textcoords='offset points',
bbox=bbox, arrowprops=arrowprops)
disp = ax.annotate('display = (%.1f, %.1f)' % (xdisplay, ydisplay),
(xdisplay, ydisplay), xytext=(0.5*offset, -offset),
xycoords='figure pixels',
textcoords='offset points',
bbox=bbox, arrowprops=arrowprops)
plt.show()
###############################################################################
# .. note::
#
# If you run the source code in the example above in a GUI backend,
# you may also find that the two arrows for the `data` and `display`
# 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 display
# space, but you can connect to the ``'on_draw'``
# :class:`~matplotlib.backend_bases.Event` to update figure
# coordinates on figure draws; see :ref:`event-handling-tutorial`.
#
# 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
# :class:`~matplotlib.transforms.Bbox`.
#
# .. sourcecode:: ipython
#
# In [54]: ax.transData.transform((5, 0))
# Out[54]: array([ 335.175, 247. ])
#
# In [55]: ax.set_ylim(-1, 2)
# Out[55]: (-1, 2)
#
# In [56]: ax.transData.transform((5, 0))
# Out[56]: array([ 335.175 , 181.13333333])
#
# In [57]: ax.set_xlim(10, 20)
# Out[57]: (10, 20)
#
# In [58]: ax.transData.transform((5, 0))
# Out[58]: array([-171.675 , 181.13333333])
#
#
# .. _axes-coords:
#
# Axes coordinates
# ================
#
# After the `data` coordinate system, `axes` 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.
fig = plt.figure()
for i, label in enumerate(('A', 'B', 'C', 'D')):
ax = fig.add_subplot(2, 2, i+1)
ax.text(0.05, 0.95, label, transform=ax.transAxes,
fontsize=16, fontweight='bold', va='top')
plt.show()
###############################################################################
# You can also make lines or patches in the axes coordinate system, but
# this is less useful in my experience than using ``ax.transAxes`` for
# placing text. Nonetheless, here is a silly example which plots some
# random dots in `data` space, and overlays a semi-transparent
# :class:`~matplotlib.patches.Circle` centered in the middle of the axes
# with a radius one quarter of the axes -- if your axes does not
# preserve aspect ratio (see :meth:`~matplotlib.axes.Axes.set_aspect`),
# 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 `data`
# coordinates and will always remain at the center of the axes.
import matplotlib.patches as patches
fig = plt.figure()
ax = fig.add_subplot(111)
x, y = 10*np.random.rand(2, 1000)
ax.plot(x, y, 'go') # plot some data in data coordinates
circ = patches.Circle((0.5, 0.5), 0.25, transform=ax.transAxes,
facecolor='yellow', alpha=0.5)
ax.add_patch(circ)
plt.show()
###############################################################################
# .. blended_transformations:
#
# Blended transformations
# =======================
#
# Drawing in `blended` coordinate spaces which mix `axes` with `data`
# 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
# :meth:`~matplotlib.axes.Axes.axhline`,
# :meth:`~matplotlib.axes.Axes.axvline`,
# :meth:`~matplotlib.axes.Axes.axhspan`,
# :meth:`~matplotlib.axes.Axes.axvspan`) 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
# :class:`~matplotlib.projections.polar.PolarAxes.PolarTransform`.
import matplotlib.transforms as transforms
fig = plt.figure()
ax = fig.add_subplot(111)
x = np.random.randn(1000)
ax.hist(x, 30)
ax.set_title(r'$\sigma=1 \/ \dots \/ \sigma=2$', fontsize=16)
# the x coords of this transformation are data, and the
# y coord are axes
trans = transforms.blended_transform_factory(
ax.transData, ax.transAxes)
# highlight the 1..2 stddev region with a span.
# We want x to be in data coordinates and y to
# span from 0..1 in axes coords
rect = patches.Rectangle((1, 0), width=1, height=1,
transform=trans, color='yellow',
alpha=0.5)
ax.add_patch(rect)
plt.show()
###############################################################################
# .. note::
#
# The blended transformations where x is in data coords and y in axes
# coordinates is so useful that we have helper methods to return the
# versions mpl uses internally for drawing ticks, ticklabels, etc.
# The methods are :meth:`matplotlib.axes.Axes.get_xaxis_transform` and
# :meth:`matplotlib.axes.Axes.get_yaxis_transform`. So in the example
# above, the call to
# :meth:`~matplotlib.transforms.blended_transform_factory` can be
# replaced by ``get_xaxis_transform``::
#
# trans = ax.get_xaxis_transform()
#
# .. offset-transforms-shadow:
#
# Using offset transforms to create a shadow effect
# =================================================
#
# One use of transformations 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 data
# coordinates, so that the shift effect is constant at different zoom
# levels and dpi settings.
#
# 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. The transforms module has a
# helper transformation
# :class:`~matplotlib.transforms.ScaledTranslation`. It is
# instantiated with::
#
# trans = ScaledTranslation(xt, yt, scale_trans)
#
# where `xt` and `yt` are the translation offsets, and `scale_trans` is
# a transformation which scales `xt` and `yt` at transformation time
# before applying the offsets. A typical use case is to use the figure
# ``fig.dpi_scale_trans`` transformation for the `scale_trans` argument,
# to first scale `xt` and `yt` specified in points to `display` space
# before doing the final offset. The dpi and inches offset is a
# common-enough use case that we have a special helper function to
# create it in :func:`matplotlib.transforms.offset_copy`, which returns
# a new transform with an added offset. But in the example below, we'll
# create the offset transform ourselves. Note the use of the plus
# operator in::
#
# offset = transforms.ScaledTranslation(dx, dy,
# fig.dpi_scale_trans)
# shadow_transform = ax.transData + offset
#
# showing that can chain transformations using the addition operator.
# This code says: first apply the data transformation ``ax.transData``
# and then translate the data by `dx` and `dy` points. In typography,
# a`point <https://en.wikipedia.org/wiki/Point_%28typography%29>`_ 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.
fig = plt.figure()
ax = fig.add_subplot(111)
# make a simple sine wave
x = np.arange(0., 2., 0.01)
y = np.sin(2*np.pi*x)
line, = ax.plot(x, y, lw=3, color='blue')
# shift the object over 2 points, and down 2 points
dx, dy = 2/72., -2/72.
offset = transforms.ScaledTranslation(dx, dy, fig.dpi_scale_trans)
shadow_transform = ax.transData + offset
# now plot the same data with our offset transform;
# use the zorder to make sure we are below the line
ax.plot(x, y, lw=3, color='gray',
transform=shadow_transform,
zorder=0.5*line.get_zorder())
ax.set_title('creating a shadow effect with an offset transform')
plt.show()
###############################################################################
# .. transformation-pipeline:
#
# The transformation pipeline
# ===========================
#
# The ``ax.transData`` transform we have been working with in this
# tutorial is a composite of three different transformations that
# comprise the transformation pipeline from `data` -> `display`
# 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.
#
#
# Here is how the ``ax.transData`` instance is defined in the basic
# separable axis :class:`~matplotlib.axes.Axes` class::
#
# self.transData = self.transScale + (self.transLimits + self.transAxes)
#
# We've been introduced to the ``transAxes`` instance above in
# :ref:`axes-coords`, which maps the (0, 0), (1, 1) corners of the
# axes or subplot bounding box to `display` space, so let's look at
# these other two pieces.
#
# ``self.transLimits`` is the transformation that takes you from
# ``data`` to ``axes`` coordinates; i.e., it maps your view xlim and ylim
# to the unit space of the axes (and ``transAxes`` then takes that unit
# space to display space). We can see this in action here
#
# .. sourcecode:: ipython
#
# In [80]: ax = subplot(111)
#
# In [81]: ax.set_xlim(0, 10)
# Out[81]: (0, 10)
#
# In [82]: ax.set_ylim(-1, 1)
# Out[82]: (-1, 1)
#
# In [84]: ax.transLimits.transform((0, -1))
# Out[84]: array([ 0., 0.])
#
# In [85]: ax.transLimits.transform((10, -1))
# Out[85]: array([ 1., 0.])
#
# In [86]: ax.transLimits.transform((10, 1))
# Out[86]: array([ 1., 1.])
#
# In [87]: ax.transLimits.transform((5, 0))
# Out[87]: array([ 0.5, 0.5])
#
# and we can use this same inverted transformation to go from the unit
# `axes` coordinates back to `data` coordinates.
#
# .. sourcecode:: ipython
#
# In [90]: inv.transform((0.25, 0.25))
# Out[90]: array([ 2.5, -0.5])
#
# The final piece is the ``self.transScale`` 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
# :meth:`~matplotlib.axes.Axes.semilogx` or explicitly set the scale to
# logarithmic with :meth:`~matplotlib.axes.Axes.set_xscale`, then the
# ``ax.transScale`` attribute is set to handle the nonlinear projection.
# The scales transforms are properties of the respective ``xaxis`` and
# ``yaxis`` :class:`~matplotlib.axis.Axis` instances. For example, when
# you call ``ax.set_xscale('log')``, the xaxis updates its scale to a
# :class:`matplotlib.scale.LogScale` instance.
#
# For non-separable axes the PolarAxes, there is one more piece to
# consider, the projection transformation. The ``transData``
# :class:`matplotlib.projections.polar.PolarAxes` is similar to that for
# the typical separable matplotlib Axes, with one additional piece
# ``transProjection``::
#
# self.transData = self.transScale + self.transProjection + \
# (self.transProjectionAffine + self.transAxes)
#
# ``transProjection`` handles the projection from the space,
# e.g., latitude and longitude for map data, or radius and theta for polar
# data, to a separable Cartesian coordinate system. There are several
# projection examples in the ``matplotlib.projections`` package, and the
# best way to learn more is to open the source for those packages and
# see how to make your own, since Matplotlib supports extensible axes
# and projections. Michael Droettboom has provided a nice tutorial
# example of creating a Hammer projection axes; see
# :ref:`sphx_glr_gallery_misc_custom_projection.py`.