11""" 
2- A module providing some utility functions regarding Bezier  path manipulation. 
2+ A module providing some utility functions regarding Bézier  path manipulation. 
33""" 
44
55from  functools  import  lru_cache 
@@ -94,7 +94,7 @@ def _de_casteljau1(beta, t):
9494
9595def  split_de_casteljau (beta , t ):
9696    """ 
97-     Split a Bezier  segment defined by its control points *beta* into two 
97+     Split a Bézier  segment defined by its control points *beta* into two 
9898    separate segments divided at *t* and return their control points. 
9999    """ 
100100    beta  =  np .asarray (beta )
@@ -113,7 +113,7 @@ def split_de_casteljau(beta, t):
113113def  find_bezier_t_intersecting_with_closedpath (
114114        bezier_point_at_t , inside_closedpath , t0 = 0. , t1 = 1. , tolerance = 0.01 ):
115115    """ 
116-     Find the intersection of the Bezier  curve with a closed path. 
116+     Find the intersection of the Bézier  curve with a closed path. 
117117
118118    The intersection point *t* is approximated by two parameters *t0*, *t1* 
119119    such that *t0* <= *t* <= *t1*. 
@@ -126,7 +126,7 @@ def find_bezier_t_intersecting_with_closedpath(
126126    Parameters 
127127    ---------- 
128128    bezier_point_at_t : callable 
129-         A function returning x, y coordinates of the Bezier  at parameter *t*. 
129+         A function returning x, y coordinates of the Bézier  at parameter *t*. 
130130        It must have the signature:: 
131131
132132            bezier_point_at_t(t: float) -> tuple[float, float] 
@@ -146,7 +146,7 @@ def find_bezier_t_intersecting_with_closedpath(
146146    Returns 
147147    ------- 
148148    t0, t1 : float 
149-         The Bezier  path parameters. 
149+         The Bézier  path parameters. 
150150    """ 
151151    start  =  bezier_point_at_t (t0 )
152152    end  =  bezier_point_at_t (t1 )
@@ -180,7 +180,7 @@ def find_bezier_t_intersecting_with_closedpath(
180180
181181class  BezierSegment :
182182    """ 
183-     A d-dimensional Bezier  segment. 
183+     A d-dimensional Bézier  segment. 
184184
185185    Parameters 
186186    ---------- 
@@ -199,7 +199,7 @@ def __init__(self, control_points):
199199
200200    def  __call__ (self , t ):
201201        """ 
202-         Evaluate the Bezier  curve at point(s) t  in [0, 1]. 
202+         Evaluate the Bézier  curve at point(s) *t*  in [0, 1]. 
203203
204204        Parameters 
205205        ---------- 
@@ -239,15 +239,15 @@ def degree(self):
239239    @property  
240240    def  polynomial_coefficients (self ):
241241        r""" 
242-         The polynomial coefficients of the Bezier  curve. 
242+         The polynomial coefficients of the Bézier  curve. 
243243
244244        .. warning:: Follows opposite convention from `numpy.polyval`. 
245245
246246        Returns 
247247        ------- 
248248        (n+1, d) array 
249249            Coefficients after expanding in polynomial basis, where :math:`n` 
250-             is the degree of the bezier  curve and :math:`d` its dimension. 
250+             is the degree of the Bézier  curve and :math:`d` its dimension. 
251251            These are the numbers (:math:`C_j`) such that the curve can be 
252252            written :math:`\sum_{j=0}^n C_j t^j`. 
253253
@@ -308,12 +308,12 @@ def axis_aligned_extrema(self):
308308def  split_bezier_intersecting_with_closedpath (
309309        bezier , inside_closedpath , tolerance = 0.01 ):
310310    """ 
311-     Split a Bezier  curve into two at the intersection with a closed path. 
311+     Split a Bézier  curve into two at the intersection with a closed path. 
312312
313313    Parameters 
314314    ---------- 
315315    bezier : (N, 2) array-like 
316-         Control points of the Bezier  segment. See `.BezierSegment`. 
316+         Control points of the Bézier  segment. See `.BezierSegment`. 
317317    inside_closedpath : callable 
318318        A function returning True if a given point (x, y) is inside the 
319319        closed path. See also `.find_bezier_t_intersecting_with_closedpath`. 
@@ -324,7 +324,7 @@ def split_bezier_intersecting_with_closedpath(
324324    Returns 
325325    ------- 
326326    left, right 
327-         Lists of control points for the two Bezier  segments. 
327+         Lists of control points for the two Bézier  segments. 
328328    """ 
329329
330330    bz  =  BezierSegment (bezier )
@@ -461,13 +461,13 @@ def check_if_parallel(dx1, dy1, dx2, dy2, tolerance=1.e-5):
461461
462462def  get_parallels (bezier2 , width ):
463463    """ 
464-     Given the quadratic Bezier  control points *bezier2*, returns 
465-     control points of quadratic Bezier  lines roughly parallel to given 
464+     Given the quadratic Bézier  control points *bezier2*, returns 
465+     control points of quadratic Bézier  lines roughly parallel to given 
466466    one separated by *width*. 
467467    """ 
468468
469469    # The parallel Bezier lines are constructed by following ways. 
470-     #  c1 and c2 are control points representing the begin  and end of the 
470+     #  c1 and c2 are control points representing the start  and end of the 
471471    #  Bezier line. 
472472    #  cm is the middle point 
473473
@@ -485,7 +485,7 @@ def get_parallels(bezier2, width):
485485        cos_t2 , sin_t2  =  cos_t1 , sin_t1 
486486    else :
487487        # t1 and t2 is the angle between c1 and cm, cm, c2.  They are 
488-         # also a  angle of the tangential line of the path at c1 and c2 
488+         # also an  angle of the tangential line of the path at c1 and c2 
489489        cos_t1 , sin_t1  =  get_cos_sin (c1x , c1y , cmx , cmy )
490490        cos_t2 , sin_t2  =  get_cos_sin (cmx , cmy , c2x , c2y )
491491
@@ -535,7 +535,7 @@ def get_parallels(bezier2, width):
535535
536536def  find_control_points (c1x , c1y , mmx , mmy , c2x , c2y ):
537537    """ 
538-     Find control points of the Bezier  curve passing through (*c1x*, *c1y*), 
538+     Find control points of the Bézier  curve passing through (*c1x*, *c1y*), 
539539    (*mmx*, *mmy*), and (*c2x*, *c2y*), at parametric values 0, 0.5, and 1. 
540540    """ 
541541    cmx  =  .5  *  (4  *  mmx  -  (c1x  +  c2x ))
@@ -545,8 +545,8 @@ def find_control_points(c1x, c1y, mmx, mmy, c2x, c2y):
545545
546546def  make_wedged_bezier2 (bezier2 , width , w1 = 1. , wm = 0.5 , w2 = 0. ):
547547    """ 
548-     Being similar to get_parallels, returns control points of two quadratic 
549-     Bezier  lines having a width roughly parallel to given one separated by 
548+     Being similar to ` get_parallels` , returns control points of two quadratic 
549+     Bézier  lines having a width roughly parallel to given one separated by 
550550    *width*. 
551551    """ 
552552
@@ -556,7 +556,7 @@ def make_wedged_bezier2(bezier2, width, w1=1., wm=0.5, w2=0.):
556556    c3x , c3y  =  bezier2 [2 ]
557557
558558    # t1 and t2 is the angle between c1 and cm, cm, c3. 
559-     # They are also a  angle of the tangential line of the path at c1 and c3 
559+     # They are also an  angle of the tangential line of the path at c1 and c3 
560560    cos_t1 , sin_t1  =  get_cos_sin (c1x , c1y , cmx , cmy )
561561    cos_t2 , sin_t2  =  get_cos_sin (cmx , cmy , c3x , c3y )
562562
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