In some applications, it is necessary to calculate the shortest distance between a point and a set of line segments defined by pairs of points. To find the distance between a point and each line segment, one approach is to use a loop to iterate over each line segment and calculate the distance using a formula or algorithm. However, this can be slow for large datasets.
The optimal solution can be achieved using the following NumPy arrays and functions.
1. Using the “np.linalg.norm()” function:
NumPy provides several built-in functions that can simplify the calculation of distances between points and lines. One such function is np.linalg.norm()
, which calculates the Euclidean norm of an array.
- import the NumPy library and assign it the alias
np
. - Then, we calculate the projection of
p
onto each line segment using the dot product betweenT
and the vector fromP0
top
. - We then clip the values of
U
to ensure that the projection falls within the bounds of the line segment. - Finally, we calculate the closest point
C
on the line segment top
using the projectionU
and the vectorT
, and compute the Euclidean distance betweenp
andC
.
2. Using “cross product”:
- import the NumPy library and assign it the alias
np
. - The function
distance
calculates the shortest distance between a pointp
and a set of line segments defined by pairs of pointsP0
andP1
. - it first calculates the vector
T
representing the direction and magnitude of each line segment by subtractingP0
fromP1
. - It also calculates the vector
V
betweenP0
andp
. - it uses the cross product of
T
andV
to calculate the area of a parallelogram formed by these vectors. - The absolute value of the cross product is divided by the length of
T
to get the distance between the point and the line segment. - The function returns an array of distances, where each distance corresponds to a line segment defined by
P0
andP1
.