docs(base): fix the angle_std formula and the angle_mean and angle_wrap parameter docs

spatialmath/base/vectors.py

@@ -683,14 +683,28 @@ def angle_std(theta: ArrayLike) -> float:
     r"""
     Standard deviation of angular values
 
-    :param theta: angular values
+    :param theta: angular values, in radians
     :type theta: array_like
-    :return: circular standard deviation
+    :return: circular standard deviation, in radians
     :rtype: float
 
+    The circular standard deviation is
+
     .. math::
 
-        \sigma_{\theta} = \sqrt{-2 \log \| \left[ \frac{\sum \sin \theta_i}{N}, \frac{\sum \sin \theta_i}{N} \right] \|} \in [0, \infty)
+        \sigma_{\theta} = \sqrt{-2 \log R} \in [0, \infty), \quad
+        R = \left\| \left[ \frac{\sum \cos \theta_i}{N}, \frac{\sum \sin \theta_i}{N} \right] \right\|
+
+    where :math:`R` is the length of the mean of the unit vectors at angles
+    :math:`\theta_i`.  :math:`R = 1` if all the angles are equal, giving a
+    standard deviation of zero, and :math:`R \to 0` as the angles spread evenly
+    around the circle, when the standard deviation grows without bound.
+
+    This is the same quantity as ``scipy.stats.circstd`` with its default
+    arguments.
+
+    .. note:: If :math:`R` is exactly zero the result is ``inf``, with a NumPy
+        divide-by-zero warning.
 
     :seealso: :func:`angle_mean`
     """
@@ -705,16 +719,23 @@ def angle_mean(theta: ArrayLike) -> float:
     r"""
     Mean of angular values
 
-    :param theta: angular values
-    :type v: array_like
-    :return: circular mean
+    :param theta: angular values, in radians
+    :type theta: array_like
+    :return: circular mean, in radians
     :rtype: float
 
-    The circular mean is given by
+    The circular mean is the angle of the mean of the unit vectors at angles
+    :math:`\theta_i`
 
     .. math::
 
-        \bar{\theta} = \tan^{-1} \frac{\sum \sin \theta_i}{\sum \cos \theta_i} \in [-\pi, \pi)]
+        \bar{\theta} = \tan^{-1} \frac{\sum \sin \theta_i}{\sum \cos \theta_i} \in [-\pi, \pi]
+
+    computed with the two-argument arctangent so that the quadrant is correct.
+
+    .. note:: If the unit vectors cancel, for example the angles :math:`0` and
+        :math:`\pi`, the mean direction is undefined and the result is decided by
+        rounding error.
 
     :seealso: :func:`angle_std`
     """
@@ -727,8 +748,8 @@ def angle_wrap(theta: ArrayLike, mode: str = "-pi:pi") -> Union[float, NDArray]:
     """
     Generalized angle-wrapping
 
-    :param v: angles to wrap
-    :type v: array_like
+    :param theta: angles to wrap
+    :type theta: array_like
     :param mode: wrapping mode, one of: ``"0:2pi"``, ``"0:pi"``, ``"-pi/2:pi/2"`` or ``"-pi:pi"`` [default]
     :type mode: str, optional
     :return: wrapped angles