def test_sum_vectors(self):
m = 10
n = 3
vectors = [[j for j in range(n)] for i in range(m)]
r0 = basic.sum_vectors(vectors, axis=0)
r1 = basic.sum_vectors(vectors, axis=1)
self.assertEqual(len(r0), n)
self.assertEqual(len(r1), m)
def circle_from_points(a, b, c):
"""Construct a circle from three points.
Parameters
----------
a : sequence of float
XYZ coordinates.
b : sequence of float
XYZ coordinates.
c : sequence of float
XYZ coordinates.
Returns
-------
circle : tuple
Center, radius, normal of the circle.
References
----------
https://en.wikipedia.org/wiki/Circumscribed_circle
Examples
--------
>>>
"""
ab = subtract_vectors(b, a)
cb = subtract_vectors(b, c)
ba = subtract_vectors(a, b)
ca = subtract_vectors(a, c)
ac = subtract_vectors(c, a)
bc = subtract_vectors(c, b)
normal = normalize_vector(cross_vectors(ab, ac))
d = 2 * length_vector_sqrd(cross_vectors(ba, cb))
A = length_vector_sqrd(cb) * dot_vectors(ba, ca) / d
B = length_vector_sqrd(ca) * dot_vectors(ab, cb) / d
C = length_vector_sqrd(ba) * dot_vectors(ac, bc) / d
Aa = scale_vector(a, A)
Bb = scale_vector(b, B)
Cc = scale_vector(c, C)
center = sum_vectors([Aa, Bb, Cc])
radius = length_vector(subtract_vectors(a, center))
return center, radius, normal
def weighted_centroid_points(points, weights):
"""Compute the weighted centroid of a set of points. The weights can be any between minus and plus infinity.
Parameters
----------
points : list
A list of point coordinates.
weights : list
A list of weight floats.
Returns
-------
list
The coordinates of the weighted centroid.
"""
vectors = [scale_vector(point, weight) for point, weight in zip(points, weights)]
vector = scale_vector(sum_vectors(vectors), 1. / sum(weights))
return vector