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Commitd7084de

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committed
correctly compute bounding box for path
1 parent696b64c commitd7084de

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3 files changed

+199
-9
lines changed

3 files changed

+199
-9
lines changed

‎lib/matplotlib/bezier.py

Lines changed: 103 additions & 8 deletions
Original file line numberDiff line numberDiff line change
@@ -3,11 +3,19 @@
33
"""
44

55
importmath
6+
importwarnings
67

78
importnumpyasnp
89

910
importmatplotlib.cbookascbook
1011

12+
# same algorithm as 3.8's math.comb
13+
@np.vectorize
14+
def_comb(n,k):
15+
k=min(k,n-k)
16+
i=np.arange(1,k+1)
17+
returnnp.prod((n+1-i)/i).astype(int)
18+
1119

1220
classNonIntersectingPathException(ValueError):
1321
pass
@@ -177,27 +185,114 @@ def find_bezier_t_intersecting_with_closedpath(
177185

178186
classBezierSegment:
179187
"""
180-
AD-dimensional Bezier segment.
188+
Ad-dimensional Bezier segment.
181189
182190
Parameters
183191
----------
184-
control_points : (N,D) array
192+
control_points : (N,d) array
185193
Location of the *N* control points.
186194
"""
187195

188196
def__init__(self,control_points):
189-
n=len(control_points)
190-
self._orders=np.arange(n)
191-
coeff= [math.factorial(n-1)
192-
// (math.factorial(i)*math.factorial(n-1-i))
193-
foriinrange(n)]
194-
self._px=np.asarray(control_points).T*coeff
197+
self._cpoints=np.asarray(control_points)
198+
self._N,self._d=self._cpoints.shape
199+
self._orders=np.arange(self._N)
200+
coeff= [math.factorial(self._N-1)
201+
// (math.factorial(i)*math.factorial(self._N-1-i))
202+
foriinrange(self._N)]
203+
self._px=self._cpoints.T*coeff
204+
205+
def__call__(self,t):
206+
returnself.point_at_t(t)
195207

196208
defpoint_at_t(self,t):
197209
"""Return the point on the Bezier curve for parameter *t*."""
198210
returntuple(
199211
self._px @ (((1-t)**self._orders)[::-1]*t**self._orders))
200212

213+
@property
214+
defcontrol_points(self):
215+
"""The control points of the curve."""
216+
returnself._cpoints
217+
218+
@property
219+
defdimension(self):
220+
"""The dimension of the curve."""
221+
returnself._d
222+
223+
@property
224+
defdegree(self):
225+
"""The number of control points in the curve."""
226+
returnself._N-1
227+
228+
@property
229+
defpolynomial_coefficients(self):
230+
r"""The polynomial coefficients of the Bezier curve.
231+
232+
Returns
233+
-------
234+
coefs : float, (n+1, d) array_like
235+
Coefficients after expanding in polynomial basis, where :math:`n`
236+
is the degree of the bezier curve and :math:`d` its dimension.
237+
These are the numbers (:math:`C_j`) such that the curve can be
238+
written :math:`\sum_{j=0}^n C_j t^j`.
239+
240+
Notes
241+
-----
242+
The coefficients are calculated as
243+
244+
.. math::
245+
246+
{n \choose j} \sum_{i=0}^j (-1)^{i+j} {j \choose i} P_i
247+
248+
where :math:`P_i` are the control points of the curve.
249+
"""
250+
n=self.degree
251+
# matplotlib uses n <= 4. overflow plausible starting around n = 15.
252+
ifn>10:
253+
warnings.warn("Polynomial coefficients formula unstable for high "
254+
"order Bezier curves!",RuntimeWarning)
255+
d=self.dimension
256+
P=self.control_points
257+
coefs=np.zeros((n+1,d))
258+
forjinrange(n+1):
259+
i=np.arange(j+1)
260+
prefactor=np.power(-1,i+j)*_comb(j,i)
261+
prefactor=np.tile(prefactor, (d,1)).T
262+
coefs[j]=_comb(n,j)*np.sum(prefactor*P[i],axis=0)
263+
returncoefs
264+
265+
@property
266+
defaxis_aligned_extrema(self):
267+
"""
268+
Return the location along the curve's interior where its partial
269+
derivative is zero, along with the dimension along which it is zero for
270+
each such instance.
271+
272+
Returns
273+
-------
274+
dims : int, array_like
275+
dimension :math:`i` along which the corresponding zero occurs
276+
dzeros : float, array_like
277+
of same size as dims. the :math:`t` such that :math:`d/dx_i B(t) =
278+
0`
279+
"""
280+
n=self.degree
281+
Cj=self.polynomial_coefficients
282+
dCj=np.atleast_2d(np.arange(1,n+1)).T*Cj[1:]
283+
iflen(dCj)==0:
284+
returnnp.array([]),np.array([])
285+
dims= []
286+
roots= []
287+
fori,piinenumerate(dCj.T):
288+
r=np.roots(pi[::-1])
289+
roots.append(r)
290+
dims.append(i*np.ones_like(r))
291+
roots=np.concatenate(roots)
292+
dims=np.concatenate(dims)
293+
in_range=np.isreal(roots)& (roots>=0)& (roots<=1)
294+
returndims[in_range],np.real(roots)[in_range]
295+
201296

202297
defsplit_bezier_intersecting_with_closedpath(
203298
bezier,inside_closedpath,tolerance=0.01):

‎lib/matplotlib/path.py

Lines changed: 90 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -17,7 +17,18 @@
1717
importmatplotlibasmpl
1818
from .import_path,cbook
1919
from .cbookimport_to_unmasked_float_array,simple_linear_interpolation
20-
from .bezierimportsplit_bezier_intersecting_with_closedpath
20+
from .bezierimportBezierSegment,split_bezier_intersecting_with_closedpath
21+
22+
23+
def_update_extents(extents,point):
24+
dim=len(point)
25+
fori,xiinenumerate(point):
26+
ifxi<extents[i]:
27+
extents[i]=xi
28+
# elif here would fail to correctly update from "null" extents of
29+
# np.array([np.inf, np.inf, -np.inf, -np.inf])
30+
ifextents[i+dim]<xi:
31+
extents[i+dim]=xi
2132

2233

2334
classPath:
@@ -421,6 +432,54 @@ def iter_segments(self, transform=None, remove_nans=True, clip=None,
421432
curr_vertices=np.append(curr_vertices,next(vertices))
422433
yieldcurr_vertices,code
423434

435+
defiter_curves(self,**kwargs):
436+
"""
437+
Iterate over each bezier curve (lines included) in a Path.
438+
439+
This is in contrast to iter_segments, which omits the first control
440+
point of each curve.
441+
442+
Parameters
443+
----------
444+
kwargs : Dict[str, object]
445+
Forwareded to iter_segments.
446+
447+
Yields
448+
------
449+
vertices : float, (N, 2) array_like
450+
The N control points of the next 2-dimensional bezier curve making
451+
up self. Note in particular that freestanding points are bezier
452+
curves of order 0, and lines are bezier curves of order 1 (with two
453+
control points).
454+
code : Path.code_type
455+
The code describing what kind of curve is being returned.
456+
Path.MOVETO, Path.LINETO, Path.CURVE3, Path.CURVE4 correspond to
457+
bezier curves with 1, 2, 3, and 4 control points (respectively).
458+
"""
459+
first_vertex=None
460+
prev_vertex=None
461+
forvertices,codeinself.iter_segments(**kwargs):
462+
iffirst_vertexisNone:
463+
ifcode!=Path.MOVETO:
464+
raiseValueError("Malformed path, must start with MOVETO.")
465+
ifcode==Path.MOVETO:# a point is like "CURVE1"
466+
first_vertex=vertices
467+
yieldnp.array([first_vertex]),code
468+
elifcode==Path.LINETO:# "CURVE2"
469+
yieldnp.array([prev_vertex,vertices]),code
470+
elifcode==Path.CURVE3:
471+
yieldnp.array([prev_vertex,vertices[:2],vertices[2:]]),code
472+
elifcode==Path.CURVE4:
473+
yieldnp.array([prev_vertex,vertices[:2],vertices[2:4],
474+
vertices[4:]]),code
475+
elifcode==Path.CLOSEPOLY:
476+
yieldnp.array([prev_vertex,first_vertex]),code
477+
elifcode==Path.STOP:
478+
return
479+
else:
480+
raiseValueError("Invalid Path.code_type: "+str(code))
481+
prev_vertex=vertices[-2:]
482+
424483
@cbook._delete_parameter("3.3","quantize")
425484
defcleaned(self,transform=None,remove_nans=False,clip=None,
426485
quantize=False,simplify=False,curves=False,
@@ -546,6 +605,36 @@ def get_extents(self, transform=None):
546605
transform=None
547606
returnBbox(_path.get_path_extents(path,transform))
548607

608+
defget_exact_extents(self,**kwargs):
609+
"""Get size of Bbox of curve (instead of Bbox of control points).
610+
611+
Parameters
612+
----------
613+
kwargs : Dict[str, object]
614+
Forwarded to self.iter_curves.
615+
616+
Returns
617+
-------
618+
extents : (4,) float, array_like
619+
The extents of the path (xmin, ymin, xmax, ymax).
620+
"""
621+
maxi=2# [xmin, ymin, *xmax, ymax]
622+
# return value for empty paths to match _path.h
623+
extents=np.array([np.inf,np.inf,-np.inf,-np.inf])
624+
forcurve,codeinself.iter_curves(**kwargs):
625+
curve=BezierSegment(curve)
626+
# start and endpoints can be extrema of the curve
627+
_update_extents(extents,curve(0))# start point
628+
_update_extents(extents,curve(1))# end point
629+
# interior extrema where d/ds B(s) == 0
630+
_,dzeros=curve.axis_aligned_extrema
631+
iflen(dzeros)==0:
632+
continue
633+
forzeroindzeros:
634+
potential_extrema=curve.point_at_t(zero)
635+
_update_extents(extents,potential_extrema)
636+
returnextents
637+
549638
defintersects_path(self,other,filled=True):
550639
"""
551640
Returns *True* if this path intersects another given path.

‎lib/matplotlib/tests/test_path.py

Lines changed: 6 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -49,6 +49,12 @@ def test_contains_points_negative_radius():
4949
np.testing.assert_equal(result, [True,False,False])
5050

5151

52+
deftest_exact_extents_cubic():
53+
hard_curve=Path([[0,0], [1,0], [1,1], [0,1]],
54+
[Path.MOVETO,Path.CURVE4,Path.CURVE4,Path.CURVE4])
55+
np.testing.assert_equal(hard_curve.get_exact_extents(), [0.,0.,0.75,1.])
56+
57+
5258
deftest_point_in_path_nan():
5359
box=np.array([[0,0], [1,0], [1,1], [0,1], [0,0]])
5460
p=Path(box)

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