@@ -271,8 +271,10 @@ def polynomial_coefficients(self):
271271 Returns
272272 -------
273273 coefs : float, (n+1, d) array_like
274- coefficients after expanding in polynomial basis, where n is the
275- degree of the bezier curve
274+ Coefficients after expanding in polynomial basis, where :math:`n`
275+ is the degree of the bezier curve and :math:`d` its dimension.
276+ These are the numbers (:math:`C_j`) such that the curve can be
277+ written :math:`\sum_{j=0}^n C_j t^j`.
276278
277279 Notes
278280 -----
@@ -282,6 +284,7 @@ def polynomial_coefficients(self):
282284
283285 {n \choose j} \sum_{i=0}^j (-1)^{i+j} {j \choose i} P_i
284286
287+ where :math:`P_i` are the control points of the curve.
285288 """
286289 n = self .degree
287290 # matplotlib uses n <= 4. overflow plausible starting around n = 15.
@@ -299,18 +302,19 @@ def polynomial_coefficients(self):
299302 return coefs
300303
301304 @property
302- def interior_extrema (self ):
305+ def axis_aligned_extrema (self ):
303306 """
304307 Return the location along the curve's interior where its partial
305308 derivative is zero, along with the dimension along which it is zero for
306- each instance.
309+ each such instance.
307310
308311 Returns
309312 -------
310313 dims : int, array_like
311- dimension $i$ along which the corresponding zero occurs
314+ dimension :math:`i` along which the corresponding zero occurs
312315 dzeros : float, array_like
313- of same size as dims. the $t$ such that $d/dx_i B(t) = 0$
316+ of same size as dims. the :math:`t` such that :math:`d/dx_i B(t) =
317+ 0`
314318 """
315319 n = self .degree
316320 Cj = self .polynomial_coefficients
@@ -325,7 +329,7 @@ def interior_extrema(self):
325329 dims .append (i * np .ones_like (r ))
326330 roots = np .concatenate (roots )
327331 dims = np .concatenate (dims )
328- in_range = np .isreal (roots ) & (roots > 0 ) & (roots < 1 )
332+ in_range = np .isreal (roots ) & (roots >= 0 ) & (roots <= 1 )
329333 return dims [in_range ], np .real (roots )[in_range ]
330334
331335
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