def distance_point_line_sqrd(point, line):
"""Compute the squared distance between a point and a line.
Parameters
----------
point : sequence of float
XYZ coordinates of the point.
line : list, tuple
Line defined by two points.
Returns
-------
float
The squared distance between the point and the line.
Notes
-----
For more info, see [1]_.
References
----------
.. [1] Wikipedia. *Distance from a point to a line*.
Available at: https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line.
"""
a, b = line
ab = subtract_vectors(b, a)
pa = subtract_vectors(a, point)
pb = subtract_vectors(b, point)
l = length_vector_sqrd(cross_vectors(pa, pb))
l_ab = length_vector_sqrd(ab)
return l / l_ab
def distance_point_line_sqrd(point, line):
"""Compute the squared distance between a point and a line."""
a, b = line
ab = subtract_vectors(b, a)
pa = subtract_vectors(a, point)
pb = subtract_vectors(b, point)
l = length_vector_sqrd(cross_vectors(pa, pb))
l_ab = length_vector_sqrd(ab)
return l / l_ab
def distance_point_point_sqrd(a, b):
"""Compute the squared distance bewteen points a and b.
Parameters
----------
a : sequence of float
XYZ coordinates of point a.
b : sequence of float
XYZ coordinates of point b.
Returns
-------
d2 : float
Squared distance bewteen a and b.
Examples
--------
>>> distance_point_point_sqrd([0.0, 0.0, 0.0], [2.0, 0.0, 0.0])
4.0
See Also
--------
distance_point_point_sqrd_xy
"""
ab = subtract_vectors(b, a)
return length_vector_sqrd(ab)
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