def distance_point_line_sqrd_xy(point, line):
"""Compute the squared distance between a point and a line lying in the XY-plane.
Parameters
----------
point : sequence of float
XY(Z) coordinates of a 2D or 3D point (Z will be ignored).
line : list, tuple
Line defined by two points.
Returns
-------
float
The squared distance between the point and the line.
Notes
-----
This implementation computes the orthogonal squared distance from a point P to a
line defined by points A and B as twice the area of the triangle ABP divided
by the length of AB [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_xy(b, a)
pa = subtract_vectors_xy(a, point)
pb = subtract_vectors_xy(b, point)
l = cross_vectors_xy(pa, pb)[2]**2
l_ab = length_vector_sqrd_xy(ab)
return l / l_ab
def distance_point_point_sqrd_xy(a, b):
"""Compute the squared distance between points a and b lying in the XY plane.
Parameters
----------
a : sequence of float
XY(Z) coordinates of the first point.
b : sequence of float)
XY(Z) coordinates of the second point.
Returns
-------
float
Squared distance between a and b in the XY-plane.
Examples
--------
>>> distance([0.0, 0.0], [2.0, 0.0])
4.0
>>> distance([0.0, 0.0, 0.0], [2.0, 0.0, 0.0])
4.0
>>> distance([0.0, 0.0, 1.0], [2.0, 0.0, 1.0])
4.0
"""
ab = subtract_vectors_xy(b, a)
return length_vector_sqrd_xy(ab)