irfpy.util.vectortools

Vector (numpy array) related functions

Vector tools for numpy array. Most of the funcitons (are intended to) support the 2-D (or >2-D) array, namely, (N, 3) (or (N0, N1, …, 3)) array.

Related modules:

Code author: Yoshifumi Futaana

distance_to_cylinder_center(vector, center_axis)

Calculate the distance to the center axis of the cylinder.

cone_angle(vector, cone_axis[, cone_center])

Return cone angle in radians.
irfpy.util.vectortools.distance_to_cylinder_center(vector, center_axis, cylinder_center=(0, 0, 0))[source]

Calculate the distance to the center axis of the cylinder.

Calculate the distance between a given vector, v, and the center of the given cylinder. The cylinder is defined by a vector, cylinder_center p, together with the axis vector, center_axis n.

Parameters:

  • vector – Vector(s) for which the distance(s) are calculated. (3,) or (…, 3) array.

  • cylinder_center – Specifies the center of the cylinder. A single point on the axis. (3,) array

  • cylinder_axis – Specifies the axis vector of the cylinder. A single vector. (3,) array.

Examples follow.

>>> p = (2, 1, 0)
>>> n = (0, 0.5, 0)
>>> v = (0, 0, 0)
>>> distance_to_cylinder_center(v, n, cylinder_center=p)
2.0

>>> v = (2, 0, 0)
>>> distance_to_cylinder_center(v, n, cylinder_center=p)
0.0

>>> v = [(0, 0, 0), (0, 1, 0), (1, 0, 0), (0, 0, 1)]
>>> distance_to_cylinder_center(v, n, cylinder_center=p) 
array([2. ,  2.  ,  1. ,  2.23606798])

The implementaion is as follows.

First, the cylinder_center is translated to the origin (0, 0, 0). The transformation does not change the center axis, n, but the given vector v is converted to \(\vec{v}' = \vec{v} - \vec{p}\).

The distance d is now calculated by \(d = |v'| \sin\alpha\) where \(\alpha\) is the angle between the v’ and n vectors. Thus, \(\cos\alpha = \vec{v'}\cdot{n} / |v'||n|\), and therefore, the distance is

\[\begin{split}d = |v'| \sin\alpha = |v'| \sqrt{1 - \cos^2\alpha} \\ = \sqrt{|v'|^2 - \frac{\vec{n}\cdot\vec{v'}}{|n|^2}}\end{split}\]
irfpy.util.vectortools.cone_angle(vector, cone_axis, cone_center=(0, 0, 0))[source]

Return cone angle in radians.

Parameters:

  • vector – Vector for input. (3, ) or (…, 3) array

  • cone_axis – Vector of the axis, along the line.

  • cone_center – The top of the cone.

Returns:

The cone angle in radians. Scalar or (…) shaped.

>>> p = (1, 3, 0)
>>> a = (0, 2, 0)

>>> v = (1, 0, 0)
>>> print(np.rad2deg(cone_angle(v, a, cone_center=p)))
180.0

>>> v = (1, 4, 0)
>>> print(np.rad2deg(cone_angle(v, a, cone_center=p)))
0.0

>>> v = [(1, 0, 0), (1, 1, 0), (1, 2, 0), (1, 4, 0), (2, 3, 0)]
>>> print(np.rad2deg(cone_angle(v, a, cone_center=p)))  
[180.  180.  180.  0.  90.]

>>> v = [2, 3, 0]