-
-
Notifications
You must be signed in to change notification settings - Fork 8.2k
Expand file tree
/
Copy pathtransforms.py
More file actions
2996 lines (2471 loc) · 97.4 KB
/
transforms.py
File metadata and controls
2996 lines (2471 loc) · 97.4 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
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
"""
Matplotlib includes a framework for arbitrary geometric transformations that is used to
determine the final position of all elements drawn on the canvas.
Transforms are composed into trees of `TransformNode` objects
whose actual value depends on their children. When the contents of
children change, their parents are automatically invalidated. The
next time an invalidated transform is accessed, it is recomputed to
reflect those changes. This invalidation/caching approach prevents
unnecessary recomputations of transforms, and contributes to better
interactive performance.
For example, here is a graph of the transform tree used to plot data to the figure:
.. graphviz:: /api/transforms.dot
:alt: Diagram of transform tree from data to figure coordinates.
The framework can be used for both affine and non-affine
transformations. However, for speed, we want to use the backend
renderers to perform affine transformations whenever possible.
Therefore, it is possible to perform just the affine or non-affine
part of a transformation on a set of data. The affine is always
assumed to occur after the non-affine. For any transform::
full transform == non-affine part + affine part
The backends are not expected to handle non-affine transformations
themselves.
See the tutorial :ref:`transforms_tutorial` for examples
of how to use transforms.
"""
# Note: There are a number of places in the code where we use `np.min` or
# `np.minimum` instead of the builtin `min`, and likewise for `max`. This is
# done so that `nan`s are propagated, instead of being silently dropped.
import functools
import itertools
import textwrap
import weakref
import math
import numpy as np
from numpy.linalg import inv
from matplotlib import _api
from matplotlib._path import (
affine_transform, count_bboxes_overlapping_bbox, update_path_extents)
from .path import Path
DEBUG = False
def _make_str_method(*args, **kwargs):
"""
Generate a ``__str__`` method for a `.Transform` subclass.
After ::
class T:
__str__ = _make_str_method("attr", key="other")
``str(T(...))`` will be
.. code-block:: text
{type(T).__name__}(
{self.attr},
key={self.other})
"""
indent = functools.partial(textwrap.indent, prefix=" " * 4)
def strrepr(x): return repr(x) if isinstance(x, str) else str(x)
return lambda self: (
type(self).__name__ + "("
+ ",".join([*(indent("\n" + strrepr(getattr(self, arg)))
for arg in args),
*(indent("\n" + k + "=" + strrepr(getattr(self, arg)))
for k, arg in kwargs.items())])
+ ")")
class TransformNode:
"""
The base class for anything that participates in the transform tree
and needs to invalidate its parents or be invalidated. This includes
classes that are not really transforms, such as bounding boxes, since some
transforms depend on bounding boxes to compute their values.
"""
# Invalidation may affect only the affine part. If the
# invalidation was "affine-only", the _invalid member is set to
# INVALID_AFFINE_ONLY
# Possible values for the _invalid attribute.
_VALID, _INVALID_AFFINE_ONLY, _INVALID_FULL = range(3)
# Some metadata about the transform, used to determine whether an
# invalidation is affine-only
is_affine = False
is_bbox = _api.deprecated("3.9")(_api.classproperty(lambda cls: False))
pass_through = False
"""
If pass_through is True, all ancestors will always be
invalidated, even if 'self' is already invalid.
"""
def __init__(self, shorthand_name=None):
"""
Parameters
----------
shorthand_name : str
A string representing the "name" of the transform. The name carries
no significance other than to improve the readability of
``str(transform)`` when DEBUG=True.
"""
self._parents = {}
# Initially invalid, until first computation.
self._invalid = self._INVALID_FULL
self._shorthand_name = shorthand_name or ''
if DEBUG:
def __str__(self):
# either just return the name of this TransformNode, or its repr
return self._shorthand_name or repr(self)
def __getstate__(self):
# turn the dictionary with weak values into a normal dictionary
return {**self.__dict__,
'_parents': {k: v() for k, v in self._parents.items()}}
def __setstate__(self, data_dict):
self.__dict__ = data_dict
# turn the normal dictionary back into a dictionary with weak values
# The extra lambda is to provide a callback to remove dead
# weakrefs from the dictionary when garbage collection is done.
self._parents = {
k: weakref.ref(v, lambda _, pop=self._parents.pop, k=k: pop(k))
for k, v in self._parents.items() if v is not None}
def __copy__(self):
cls = type(self)
other = cls.__new__(cls)
other.__dict__.update(self.__dict__)
# If `c = a + b; a1 = copy(a)`, then modifications to `a1` do not
# propagate back to `c`, i.e. we need to clear the parents of `a1`.
other._parents = {}
# If `c = a + b; c1 = copy(c)`, then modifications to `a` also need to
# be propagated to `c1`.
for key, val in vars(self).items():
if isinstance(val, TransformNode) and id(self) in val._parents:
other.set_children(val) # val == getattr(other, key)
return other
def invalidate(self):
"""
Invalidate this `TransformNode` and triggers an invalidation of its
ancestors. Should be called any time the transform changes.
"""
return self._invalidate_internal(
level=self._INVALID_AFFINE_ONLY if self.is_affine else self._INVALID_FULL,
invalidating_node=self)
def _invalidate_internal(self, level, invalidating_node):
"""
Called by :meth:`invalidate` and subsequently ascends the transform
stack calling each TransformNode's _invalidate_internal method.
"""
# If we are already more invalid than the currently propagated invalidation,
# then we don't need to do anything.
if level <= self._invalid and not self.pass_through:
return
self._invalid = level
for parent in list(self._parents.values()):
parent = parent() # Dereference the weak reference.
if parent is not None:
parent._invalidate_internal(level=level, invalidating_node=self)
def set_children(self, *children):
"""
Set the children of the transform, to let the invalidation
system know which transforms can invalidate this transform.
Should be called from the constructor of any transforms that
depend on other transforms.
"""
# Parents are stored as weak references, so that if the
# parents are destroyed, references from the children won't
# keep them alive.
id_self = id(self)
for child in children:
# Use weak references so this dictionary won't keep obsolete nodes
# alive; the callback deletes the dictionary entry. This is a
# performance improvement over using WeakValueDictionary.
ref = weakref.ref(
self, lambda _, pop=child._parents.pop, k=id_self: pop(k))
child._parents[id_self] = ref
def frozen(self):
"""
Return a frozen copy of this transform node. The frozen copy will not
be updated when its children change. Useful for storing a previously
known state of a transform where ``copy.deepcopy()`` might normally be
used.
"""
return self
class BboxBase(TransformNode):
"""
The base class of all bounding boxes.
This class is immutable; `Bbox` is a mutable subclass.
The canonical representation is as two points, with no
restrictions on their ordering. Convenience properties are
provided to get the left, bottom, right and top edges and width
and height, but these are not stored explicitly.
"""
is_bbox = _api.deprecated("3.9")(_api.classproperty(lambda cls: True))
is_affine = True
if DEBUG:
@staticmethod
def _check(points):
if isinstance(points, np.ma.MaskedArray):
_api.warn_external("Bbox bounds are a masked array.")
points = np.asarray(points)
if any((points[1, :] - points[0, :]) == 0):
_api.warn_external("Singular Bbox.")
def frozen(self):
return Bbox(self.get_points().copy())
frozen.__doc__ = TransformNode.__doc__
def __array__(self, *args, **kwargs):
return self.get_points()
@property
def x0(self):
"""
The first of the pair of *x* coordinates that define the bounding box.
This is not guaranteed to be less than :attr:`x1` (for that, use
:attr:`xmin`).
"""
return self.get_points()[0, 0]
@property
def y0(self):
"""
The first of the pair of *y* coordinates that define the bounding box.
This is not guaranteed to be less than :attr:`y1` (for that, use
:attr:`ymin`).
"""
return self.get_points()[0, 1]
@property
def x1(self):
"""
The second of the pair of *x* coordinates that define the bounding box.
This is not guaranteed to be greater than :attr:`x0` (for that, use
:attr:`xmax`).
"""
return self.get_points()[1, 0]
@property
def y1(self):
"""
The second of the pair of *y* coordinates that define the bounding box.
This is not guaranteed to be greater than :attr:`y0` (for that, use
:attr:`ymax`).
"""
return self.get_points()[1, 1]
@property
def p0(self):
"""
The first pair of (*x*, *y*) coordinates that define the bounding box.
This is not guaranteed to be the bottom-left corner (for that, use
:attr:`min`).
"""
return self.get_points()[0]
@property
def p1(self):
"""
The second pair of (*x*, *y*) coordinates that define the bounding box.
This is not guaranteed to be the top-right corner (for that, use
:attr:`max`).
"""
return self.get_points()[1]
@property
def xmin(self):
"""The left edge of the bounding box."""
return np.min(self.get_points()[:, 0])
@property
def ymin(self):
"""The bottom edge of the bounding box."""
return np.min(self.get_points()[:, 1])
@property
def xmax(self):
"""The right edge of the bounding box."""
return np.max(self.get_points()[:, 0])
@property
def ymax(self):
"""The top edge of the bounding box."""
return np.max(self.get_points()[:, 1])
@property
def min(self):
"""The bottom-left corner of the bounding box."""
return np.min(self.get_points(), axis=0)
@property
def max(self):
"""The top-right corner of the bounding box."""
return np.max(self.get_points(), axis=0)
@property
def intervalx(self):
"""
The pair of *x* coordinates that define the bounding box.
This is not guaranteed to be sorted from left to right.
"""
return self.get_points()[:, 0]
@property
def intervaly(self):
"""
The pair of *y* coordinates that define the bounding box.
This is not guaranteed to be sorted from bottom to top.
"""
return self.get_points()[:, 1]
@property
def width(self):
"""The (signed) width of the bounding box."""
points = self.get_points()
return points[1, 0] - points[0, 0]
@property
def height(self):
"""The (signed) height of the bounding box."""
points = self.get_points()
return points[1, 1] - points[0, 1]
@property
def size(self):
"""The (signed) width and height of the bounding box."""
points = self.get_points()
return points[1] - points[0]
@property
def bounds(self):
"""Return (:attr:`x0`, :attr:`y0`, :attr:`width`, :attr:`height`)."""
(x0, y0), (x1, y1) = self.get_points()
return (x0, y0, x1 - x0, y1 - y0)
@property
def extents(self):
"""Return (:attr:`x0`, :attr:`y0`, :attr:`x1`, :attr:`y1`)."""
return self.get_points().flatten() # flatten returns a copy.
def get_points(self):
raise NotImplementedError
def containsx(self, x):
"""
Return whether *x* is in the closed (:attr:`x0`, :attr:`x1`) interval.
"""
x0, x1 = self.intervalx
return x0 <= x <= x1 or x0 >= x >= x1
def containsy(self, y):
"""
Return whether *y* is in the closed (:attr:`y0`, :attr:`y1`) interval.
"""
y0, y1 = self.intervaly
return y0 <= y <= y1 or y0 >= y >= y1
def contains(self, x, y):
"""
Return whether ``(x, y)`` is in the bounding box or on its edge.
"""
return self.containsx(x) and self.containsy(y)
def overlaps(self, other):
"""
Return whether this bounding box overlaps with the other bounding box.
Parameters
----------
other : `.BboxBase`
"""
ax1, ay1, ax2, ay2 = self.extents
bx1, by1, bx2, by2 = other.extents
if ax2 < ax1:
ax2, ax1 = ax1, ax2
if ay2 < ay1:
ay2, ay1 = ay1, ay2
if bx2 < bx1:
bx2, bx1 = bx1, bx2
if by2 < by1:
by2, by1 = by1, by2
return ax1 <= bx2 and bx1 <= ax2 and ay1 <= by2 and by1 <= ay2
def fully_containsx(self, x):
"""
Return whether *x* is in the open (:attr:`x0`, :attr:`x1`) interval.
"""
x0, x1 = self.intervalx
return x0 < x < x1 or x0 > x > x1
def fully_containsy(self, y):
"""
Return whether *y* is in the open (:attr:`y0`, :attr:`y1`) interval.
"""
y0, y1 = self.intervaly
return y0 < y < y1 or y0 > y > y1
def fully_contains(self, x, y):
"""
Return whether ``x, y`` is in the bounding box, but not on its edge.
"""
return self.fully_containsx(x) and self.fully_containsy(y)
def fully_overlaps(self, other):
"""
Return whether this bounding box overlaps with the other bounding box,
not including the edges.
Parameters
----------
other : `.BboxBase`
"""
ax1, ay1, ax2, ay2 = self.extents
bx1, by1, bx2, by2 = other.extents
if ax2 < ax1:
ax2, ax1 = ax1, ax2
if ay2 < ay1:
ay2, ay1 = ay1, ay2
if bx2 < bx1:
bx2, bx1 = bx1, bx2
if by2 < by1:
by2, by1 = by1, by2
return ax1 < bx2 and bx1 < ax2 and ay1 < by2 and by1 < ay2
def transformed(self, transform):
"""
Construct a `Bbox` by statically transforming this one by *transform*.
"""
pts = self.get_points()
ll, ul, lr = transform.transform(np.array(
[pts[0], [pts[0, 0], pts[1, 1]], [pts[1, 0], pts[0, 1]]]))
return Bbox([ll, [lr[0], ul[1]]])
coefs = {'C': (0.5, 0.5),
'SW': (0, 0),
'S': (0.5, 0),
'SE': (1.0, 0),
'E': (1.0, 0.5),
'NE': (1.0, 1.0),
'N': (0.5, 1.0),
'NW': (0, 1.0),
'W': (0, 0.5)}
def anchored(self, c, container):
"""
Return a copy of the `Bbox` anchored to *c* within *container*.
Parameters
----------
c : (float, float) or {'C', 'SW', 'S', 'SE', 'E', 'NE', ...}
Either an (*x*, *y*) pair of relative coordinates (0 is left or
bottom, 1 is right or top), 'C' (center), or a cardinal direction
('SW', southwest, is bottom left, etc.).
container : `Bbox`
The box within which the `Bbox` is positioned.
See Also
--------
.Axes.set_anchor
"""
l, b, w, h = container.bounds
L, B, W, H = self.bounds
cx, cy = self.coefs[c] if isinstance(c, str) else c
return Bbox(self._points +
[(l + cx * (w - W)) - L,
(b + cy * (h - H)) - B])
def shrunk(self, mx, my):
"""
Return a copy of the `Bbox`, shrunk by the factor *mx*
in the *x* direction and the factor *my* in the *y* direction.
The lower left corner of the box remains unchanged. Normally
*mx* and *my* will be less than 1, but this is not enforced.
"""
w, h = self.size
return Bbox([self._points[0],
self._points[0] + [mx * w, my * h]])
def shrunk_to_aspect(self, box_aspect, container=None, fig_aspect=1.0):
"""
Return a copy of the `Bbox`, shrunk so that it is as
large as it can be while having the desired aspect ratio,
*box_aspect*. If the box coordinates are relative (i.e.
fractions of a larger box such as a figure) then the
physical aspect ratio of that figure is specified with
*fig_aspect*, so that *box_aspect* can also be given as a
ratio of the absolute dimensions, not the relative dimensions.
"""
if box_aspect <= 0 or fig_aspect <= 0:
raise ValueError("'box_aspect' and 'fig_aspect' must be positive")
if container is None:
container = self
w, h = container.size
H = w * box_aspect / fig_aspect
if H <= h:
W = w
else:
W = h * fig_aspect / box_aspect
H = h
return Bbox([self._points[0],
self._points[0] + (W, H)])
def splitx(self, *args):
"""
Return a list of new `Bbox` objects formed by splitting the original
one with vertical lines at fractional positions given by *args*.
"""
xf = [0, *args, 1]
x0, y0, x1, y1 = self.extents
w = x1 - x0
return [Bbox([[x0 + xf0 * w, y0], [x0 + xf1 * w, y1]])
for xf0, xf1 in itertools.pairwise(xf)]
def splity(self, *args):
"""
Return a list of new `Bbox` objects formed by splitting the original
one with horizontal lines at fractional positions given by *args*.
"""
yf = [0, *args, 1]
x0, y0, x1, y1 = self.extents
h = y1 - y0
return [Bbox([[x0, y0 + yf0 * h], [x1, y0 + yf1 * h]])
for yf0, yf1 in itertools.pairwise(yf)]
def count_contains(self, vertices):
"""
Count the number of vertices contained in the `Bbox`.
Any vertices with a non-finite x or y value are ignored.
Parameters
----------
vertices : (N, 2) array
"""
if len(vertices) == 0:
return 0
vertices = np.asarray(vertices)
with np.errstate(invalid='ignore'):
return (((self.min < vertices) &
(vertices < self.max)).all(axis=1).sum())
def count_overlaps(self, bboxes):
"""
Count the number of bounding boxes that overlap this one.
Parameters
----------
bboxes : sequence of `.BboxBase`
"""
return count_bboxes_overlapping_bbox(
self, np.atleast_3d([np.array(x) for x in bboxes]))
def expanded(self, sw, sh):
"""
Construct a `Bbox` by expanding this one around its center by the
factors *sw* and *sh*.
"""
width = self.width
height = self.height
deltaw = (sw * width - width) / 2.0
deltah = (sh * height - height) / 2.0
a = np.array([[-deltaw, -deltah], [deltaw, deltah]])
return Bbox(self._points + a)
def padded(self, w_pad, h_pad=None):
"""
Construct a `Bbox` by padding this one on all four sides.
Parameters
----------
w_pad : float
Width pad
h_pad : float, optional
Height pad. Defaults to *w_pad*.
"""
points = self.get_points()
if h_pad is None:
h_pad = w_pad
return Bbox(points + [[-w_pad, -h_pad], [w_pad, h_pad]])
def translated(self, tx, ty):
"""Construct a `Bbox` by translating this one by *tx* and *ty*."""
return Bbox(self._points + (tx, ty))
def corners(self):
"""
Return the corners of this rectangle as an array of points.
Specifically, this returns the array
``[[x0, y0], [x0, y1], [x1, y0], [x1, y1]]``.
"""
(x0, y0), (x1, y1) = self.get_points()
return np.array([[x0, y0], [x0, y1], [x1, y0], [x1, y1]])
def rotated(self, radians):
"""
Return the axes-aligned bounding box that bounds the result of rotating
this `Bbox` by an angle of *radians*.
"""
corners = self.corners()
corners_rotated = Affine2D().rotate(radians).transform(corners)
bbox = Bbox.unit()
bbox.update_from_data_xy(corners_rotated, ignore=True)
return bbox
@staticmethod
def union(bboxes):
"""Return a `Bbox` that contains all of the given *bboxes*."""
if not len(bboxes):
raise ValueError("'bboxes' cannot be empty")
x0 = np.min([bbox.xmin for bbox in bboxes])
x1 = np.max([bbox.xmax for bbox in bboxes])
y0 = np.min([bbox.ymin for bbox in bboxes])
y1 = np.max([bbox.ymax for bbox in bboxes])
return Bbox([[x0, y0], [x1, y1]])
@staticmethod
def intersection(bbox1, bbox2):
"""
Return the intersection of *bbox1* and *bbox2* if they intersect, or
None if they don't.
"""
x0 = np.maximum(bbox1.xmin, bbox2.xmin)
x1 = np.minimum(bbox1.xmax, bbox2.xmax)
y0 = np.maximum(bbox1.ymin, bbox2.ymin)
y1 = np.minimum(bbox1.ymax, bbox2.ymax)
return Bbox([[x0, y0], [x1, y1]]) if x0 <= x1 and y0 <= y1 else None
_default_minpos = np.array([np.inf, np.inf])
class Bbox(BboxBase):
"""
A mutable bounding box.
Examples
--------
**Create from known bounds**
The default constructor takes the boundary "points" ``[[xmin, ymin],
[xmax, ymax]]``.
>>> Bbox([[1, 1], [3, 7]])
Bbox([[1.0, 1.0], [3.0, 7.0]])
Alternatively, a Bbox can be created from the flattened points array, the
so-called "extents" ``(xmin, ymin, xmax, ymax)``
>>> Bbox.from_extents(1, 1, 3, 7)
Bbox([[1.0, 1.0], [3.0, 7.0]])
or from the "bounds" ``(xmin, ymin, width, height)``.
>>> Bbox.from_bounds(1, 1, 2, 6)
Bbox([[1.0, 1.0], [3.0, 7.0]])
**Create from collections of points**
The "empty" object for accumulating Bboxs is the null bbox, which is a
stand-in for the empty set.
>>> Bbox.null()
Bbox([[inf, inf], [-inf, -inf]])
Adding points to the null bbox will give you the bbox of those points.
>>> box = Bbox.null()
>>> box.update_from_data_xy([[1, 1]])
>>> box
Bbox([[1.0, 1.0], [1.0, 1.0]])
>>> box.update_from_data_xy([[2, 3], [3, 2]], ignore=False)
>>> box
Bbox([[1.0, 1.0], [3.0, 3.0]])
Setting ``ignore=True`` is equivalent to starting over from a null bbox.
>>> box.update_from_data_xy([[1, 1]], ignore=True)
>>> box
Bbox([[1.0, 1.0], [1.0, 1.0]])
.. warning::
It is recommended to always specify ``ignore`` explicitly. If not, the
default value of ``ignore`` can be changed at any time by code with
access to your Bbox, for example using the method `~.Bbox.ignore`.
**Properties of the ``null`` bbox**
.. note::
The current behavior of `Bbox.null()` may be surprising as it does
not have all of the properties of the "empty set", and as such does
not behave like a "zero" object in the mathematical sense. We may
change that in the future (with a deprecation period).
The null bbox is the identity for intersections
>>> Bbox.intersection(Bbox([[1, 1], [3, 7]]), Bbox.null())
Bbox([[1.0, 1.0], [3.0, 7.0]])
except with itself, where it returns the full space.
>>> Bbox.intersection(Bbox.null(), Bbox.null())
Bbox([[-inf, -inf], [inf, inf]])
A union containing null will always return the full space (not the other
set!)
>>> Bbox.union([Bbox([[0, 0], [0, 0]]), Bbox.null()])
Bbox([[-inf, -inf], [inf, inf]])
"""
def __init__(self, points, **kwargs):
"""
Parameters
----------
points : `~numpy.ndarray`
A (2, 2) array of the form ``[[x0, y0], [x1, y1]]``.
"""
super().__init__(**kwargs)
points = np.asarray(points, float)
if points.shape != (2, 2):
raise ValueError('Bbox points must be of the form '
'"[[x0, y0], [x1, y1]]".')
self._points = points
self._minpos = _default_minpos.copy()
self._ignore = True
# it is helpful in some contexts to know if the bbox is a
# default or has been mutated; we store the orig points to
# support the mutated methods
self._points_orig = self._points.copy()
if DEBUG:
___init__ = __init__
def __init__(self, points, **kwargs):
self._check(points)
self.___init__(points, **kwargs)
def invalidate(self):
self._check(self._points)
super().invalidate()
def frozen(self):
# docstring inherited
frozen_bbox = super().frozen()
frozen_bbox._minpos = self.minpos.copy()
return frozen_bbox
@staticmethod
def unit():
"""Create a new unit `Bbox` from (0, 0) to (1, 1)."""
return Bbox([[0, 0], [1, 1]])
@staticmethod
def null():
"""Create a new null `Bbox` from (inf, inf) to (-inf, -inf)."""
return Bbox([[np.inf, np.inf], [-np.inf, -np.inf]])
@staticmethod
def from_bounds(x0, y0, width, height):
"""
Create a new `Bbox` from *x0*, *y0*, *width* and *height*.
*width* and *height* may be negative.
"""
return Bbox.from_extents(x0, y0, x0 + width, y0 + height)
@staticmethod
def from_extents(*args, minpos=None):
"""
Create a new Bbox from *left*, *bottom*, *right* and *top*.
The *y*-axis increases upwards.
Parameters
----------
left, bottom, right, top : float
The four extents of the bounding box.
minpos : float or None
If this is supplied, the Bbox will have a minimum positive value
set. This is useful when dealing with logarithmic scales and other
scales where negative bounds result in floating point errors.
"""
bbox = Bbox(np.reshape(args, (2, 2)))
if minpos is not None:
bbox._minpos[:] = minpos
return bbox
def __format__(self, fmt):
return (
'Bbox(x0={0.x0:{1}}, y0={0.y0:{1}}, x1={0.x1:{1}}, y1={0.y1:{1}})'.
format(self, fmt))
def __str__(self):
return format(self, '')
def __repr__(self):
return 'Bbox([[{0.x0}, {0.y0}], [{0.x1}, {0.y1}]])'.format(self)
def ignore(self, value):
"""
Set whether the existing bounds of the box should be ignored
by subsequent calls to :meth:`update_from_data_xy`.
value : bool
- When ``True``, subsequent calls to `update_from_data_xy` will
ignore the existing bounds of the `Bbox`.
- When ``False``, subsequent calls to `update_from_data_xy` will
include the existing bounds of the `Bbox`.
"""
self._ignore = value
def update_from_path(self, path, ignore=None, updatex=True, updatey=True):
"""
Update the bounds of the `Bbox` to contain the vertices of the
provided path. After updating, the bounds will have positive *width*
and *height*; *x0* and *y0* will be the minimal values.
Parameters
----------
path : `~matplotlib.path.Path`
ignore : bool, optional
- When ``True``, ignore the existing bounds of the `Bbox`.
- When ``False``, include the existing bounds of the `Bbox`.
- When ``None``, use the last value passed to :meth:`ignore`.
updatex, updatey : bool, default: True
When ``True``, update the x/y values.
"""
if ignore is None:
ignore = self._ignore
if path.vertices.size == 0:
return
points, minpos, changed = update_path_extents(
path, None, self._points, self._minpos, ignore)
if changed:
self.invalidate()
if updatex:
self._points[:, 0] = points[:, 0]
self._minpos[0] = minpos[0]
if updatey:
self._points[:, 1] = points[:, 1]
self._minpos[1] = minpos[1]
def update_from_data_x(self, x, ignore=None):
"""
Update the x-bounds of the `Bbox` based on the passed in data. After
updating, the bounds will have positive *width*, and *x0* will be the
minimal value.
Parameters
----------
x : `~numpy.ndarray`
Array of x-values.
ignore : bool, optional
- When ``True``, ignore the existing bounds of the `Bbox`.
- When ``False``, include the existing bounds of the `Bbox`.
- When ``None``, use the last value passed to :meth:`ignore`.
"""
x = np.ravel(x)
self.update_from_data_xy(np.column_stack([x, np.ones(x.size)]),
ignore=ignore, updatey=False)
def update_from_data_y(self, y, ignore=None):
"""
Update the y-bounds of the `Bbox` based on the passed in data. After
updating, the bounds will have positive *height*, and *y0* will be the
minimal value.
Parameters
----------
y : `~numpy.ndarray`
Array of y-values.
ignore : bool, optional
- When ``True``, ignore the existing bounds of the `Bbox`.
- When ``False``, include the existing bounds of the `Bbox`.
- When ``None``, use the last value passed to :meth:`ignore`.
"""
y = np.ravel(y)
self.update_from_data_xy(np.column_stack([np.ones(y.size), y]),
ignore=ignore, updatex=False)
def update_from_data_xy(self, xy, ignore=None, updatex=True, updatey=True):
"""
Update the `Bbox` bounds based on the passed in *xy* coordinates.
After updating, the bounds will have positive *width* and *height*;
*x0* and *y0* will be the minimal values.
Parameters
----------
xy : (N, 2) array-like
The (x, y) coordinates.
ignore : bool, optional
- When ``True``, ignore the existing bounds of the `Bbox`.
- When ``False``, include the existing bounds of the `Bbox`.
- When ``None``, use the last value passed to :meth:`ignore`.
updatex, updatey : bool, default: True
When ``True``, update the x/y values.
"""
if len(xy) == 0:
return
path = Path(xy)
self.update_from_path(path, ignore=ignore,
updatex=updatex, updatey=updatey)
@BboxBase.x0.setter
def x0(self, val):
self._points[0, 0] = val
self.invalidate()
@BboxBase.y0.setter
def y0(self, val):
self._points[0, 1] = val
self.invalidate()
@BboxBase.x1.setter
def x1(self, val):
self._points[1, 0] = val
self.invalidate()
@BboxBase.y1.setter
def y1(self, val):
self._points[1, 1] = val
self.invalidate()
@BboxBase.p0.setter
def p0(self, val):
self._points[0] = val
self.invalidate()
@BboxBase.p1.setter
def p1(self, val):
self._points[1] = val
self.invalidate()
@BboxBase.intervalx.setter
def intervalx(self, interval):
self._points[:, 0] = interval
self.invalidate()
@BboxBase.intervaly.setter
def intervaly(self, interval):
self._points[:, 1] = interval
self.invalidate()
@BboxBase.bounds.setter
def bounds(self, bounds):
l, b, w, h = bounds
points = np.array([[l, b], [l + w, b + h]], float)
if np.any(self._points != points):
self._points = points
self.invalidate()
@property
def minpos(self):
"""
The minimum positive value in both directions within the Bbox.
This is useful when dealing with logarithmic scales and other scales