def uniform_frechet_distance(
polyline1: Sequence[Sequence[float]],
polyline2: Sequence[Sequence[float]],
) -> float:
"""Compute the maximum distance between two curves if walk on a constant speed on a curve.
Arguments:
polyline1: The first polyline consists of multiple points.
polyline2: The second polyline consists of multiple points.
Returns:
The computed distance between the two polylines.
Examples:
>>> polyline_1 = [[1, 1], [1, 2], [2, 2]]
>>> polyline_2 = [[4, 5], [2, 1], [3, 3]]
>>> Polyline2D.uniform_frechet_distance(polyline_1, polyline_2)
3.605551275463989
"""
# forward:
line1 = Polyline2D(polyline1)
line2 = Polyline2D(polyline2)
polyline_info1 = Polyline2D._get_polyline_info(line1)
polyline_info2 = Polyline2D._get_polyline_info(line2)
insert_args1, insert_args2 = Polyline2D._get_insert_args(
polyline_info1, polyline_info2)
for arg in reversed(insert_args1):
line1.insert(*arg)
for arg in reversed(insert_args2):
line2.insert(*arg)
distance_forward = max(_dist(*args) for args in zip(line1, line2))
# backward:
line1 = Polyline2D(polyline1)
line2_reverse = Polyline2D(reversed(polyline2))
polyline_info2_reverse = Polyline2D._get_polyline_info(line2_reverse)
insert_args1, insert_args2 = Polyline2D._get_insert_args(
polyline_info1, polyline_info2_reverse)
for arg in reversed(insert_args1):
line1.insert(*arg)
for arg in reversed(insert_args2):
line2_reverse.insert(*arg)
distance_reverse = max(
_dist(*args) for args in zip(line1, line2_reverse))
return min(distance_forward, distance_reverse)
def similarity(
polyline1: Sequence[Sequence[float]],
polyline2: Sequence[Sequence[float]],
) -> float:
"""Calculate the similarity between two polylines, range from 0 to 1.
Arguments:
polyline1: The first polyline consists of multiple points.
polyline2: The second polyline consisting of multiple points.
Returns:
The similarity between the two polylines.
The larger the value, the higher the similarity.
Examples:
>>> polyline_1 = [[1, 1], [1, 2], [2, 2]]
>>> polyline_2 = [[4, 5], [2, 1], [3, 3]]
>>> Polyline2D.similarity(polyline_1, polyline_2)
0.2788897449072022
"""
min_distance = Polyline2D.uniform_frechet_distance(
polyline1, polyline2)
max_distance = max(
_dist(*args) for args in product(polyline1, polyline2))
return 1 - min_distance / max_distance