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Commite2f403a

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committed
code to compute bezier segment / path lengths
1 parent0037abd commite2f403a

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4 files changed

+129
-1
lines changed

4 files changed

+129
-1
lines changed

‎lib/matplotlib/bezier.py

Lines changed: 91 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -4,6 +4,7 @@
44

55
importmath
66
importwarnings
7+
fromcollectionsimportdeque
78

89
importnumpyasnp
910

@@ -206,6 +207,96 @@ def point_at_t(self, t):
206207
"""Return the point on the Bezier curve for parameter *t*."""
207208
returntuple(self(t))
208209

210+
defsplit_at_t(self,t):
211+
"""Split into two Bezier curves using de casteljau's algorithm.
212+
213+
Parameters
214+
----------
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t : float
216+
Point in [0,1] at which to split into two curves
217+
218+
Returns
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-------
220+
B1, B2 : BezierSegment
221+
The two sub-curves.
222+
"""
223+
new_cpoints=split_de_casteljau(self._cpoints,t)
224+
returnBezierSegment(new_cpoints[0]),BezierSegment(new_cpoints[1])
225+
226+
defcontrol_net_length(self):
227+
"""Sum of lengths between control points"""
228+
L=0
229+
N,d=self._cpoints.shape
230+
foriinrange(N-1):
231+
L+=np.linalg.norm(self._cpoints[i+1]-self._cpoints[i])
232+
returnL
233+
234+
defarc_length(self,rtol=None,atol=None):
235+
"""Estimate the length using iterative refinement.
236+
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Our estimate is just the average between the length of the chord and
238+
the length of the control net.
239+
240+
Since the chord length and control net give lower and upper bounds
241+
(respectively) on the length, this maximum possible error is tested
242+
against an absolute tolerance threshold at each subdivision.
243+
244+
However, sometimes this estimator converges much faster than this error
245+
esimate would suggest. Therefore, the relative change in the length
246+
estimate between subdivisions is compared to a relative error tolerance
247+
after each set of subdivisions.
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Parameters
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----------
251+
rtol : float, default 1e-4
252+
If :code:`abs(est[i+1] - est[i]) <= rtol * est[i+1]`, we return
253+
:code:`est[i+1]`.
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atol : float, default 1e-6
255+
If the distance between chord length and control length at any
256+
point falls below this number, iteration is terminated.
257+
"""
258+
ifrtolisNone:
259+
rtol=1e-4
260+
ifatolisNone:
261+
atol=1e-6
262+
263+
chord=np.linalg.norm(self._cpoints[-1]-self._cpoints[0])
264+
net=self.control_net_length()
265+
max_err= (net-chord)/2
266+
curr_est=chord+max_err
267+
# early exit so we don't try to "split" paths of zero length
268+
ifmax_err<atol:
269+
returncurr_est
270+
271+
prev_est=np.inf
272+
curves=deque([self])
273+
errs=deque([max_err])
274+
lengths=deque([curr_est])
275+
whilenp.abs(curr_est-prev_est)>rtol*curr_est:
276+
# subdivide the *whole* curve before checking relative convergence
277+
# again
278+
prev_est=curr_est
279+
num_curves=len(curves)
280+
foriinrange(num_curves):
281+
curve=curves.popleft()
282+
new_curves=curve.split_at_t(0.5)
283+
max_err-=errs.popleft()
284+
curr_est-=lengths.popleft()
285+
forncurveinnew_curves:
286+
chord=np.linalg.norm(
287+
ncurve._cpoints[-1]-ncurve._cpoints[0])
288+
net=ncurve.control_net_length()
289+
nerr= (net-chord)/2
290+
nlength=chord+nerr
291+
max_err+=nerr
292+
curr_est+=nlength
293+
curves.append(ncurve)
294+
errs.append(nerr)
295+
lengths.append(nlength)
296+
ifmax_err<atol:
297+
returncurr_est
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returncurr_est
299+
209300
defarc_area(self):
210301
r"""
211302
(Signed) area swept out by ray from origin to curve.

‎lib/matplotlib/path.py

Lines changed: 21 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -642,6 +642,27 @@ def intersects_bbox(self, bbox, filled=True):
642642
return_path.path_intersects_rectangle(
643643
self,bbox.x0,bbox.y0,bbox.x1,bbox.y1,filled)
644644

645+
deflength(self,rtol=None,atol=None,**kwargs):
646+
"""Get length of Path.
647+
648+
Equivalent to (but not computed as)
649+
650+
.. math::
651+
652+
\sum_{j=1}^N \int_0^1 ||B'_j(t)|| dt
653+
654+
where the sum is over the :math:`N` Bezier curves that comprise the
655+
Path. Notice that this measure of length will assign zero weight to all
656+
isolated points on the Path.
657+
658+
Returns
659+
-------
660+
length : float
661+
The path length.
662+
"""
663+
returnnp.sum([B.arc_length(rtol,atol)
664+
forB,codeinself.iter_bezier(**kwargs)])
665+
645666
defsigned_area(self,**kwargs):
646667
"""
647668
Get signed area filled by path.

‎lib/matplotlib/tests/test_bezier.py

Lines changed: 13 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -20,6 +20,13 @@
2020
]
2121

2222

23+
def_integral_arc_length(B):
24+
dB=B.differentiate(B)
25+
defintegrand(t):
26+
returnnp.linalg.norm(dB(t))
27+
returnscipy.integrate.quad(integrand,0,1)[0]
28+
29+
2330
def_integral_arc_area(B):
2431
"""(Signed) area swept out by ray from origin to curve."""
2532
dB=B.differentiate(B)
@@ -33,3 +40,9 @@ def integrand(t):
3340
deftest_area_formula():
3441
forBintest_curves:
3542
assert(np.isclose(_integral_arc_area(B),B.arc_area()))
43+
44+
45+
deftest_length_iteration():
46+
forBintest_curves:
47+
assert(np.isclose(_integral_arc_length(B),B.arc_length(
48+
rtol=1e-5,atol=1e-8),rtol=1e-5,atol=1e-8))

‎lib/matplotlib/tests/test_path.py

Lines changed: 4 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -1,7 +1,6 @@
11
importcopy
22

33
importnumpyasnp
4-
54
fromnumpy.testingimportassert_array_equal
65
importpytest
76

@@ -72,6 +71,10 @@ def test_signed_area_unit_rectangle():
7271
assert(np.isclose(rect.signed_area(),1))
7372

7473

74+
deftest_length_curve():
75+
assert(np.isclose(_hard_curve.length(),2.0))
76+
77+
7578
deftest_point_in_path_nan():
7679
box=np.array([[0,0], [1,0], [1,1], [0,1], [0,0]])
7780
p=Path(box)

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