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 between`T`

and the vector from`P0`

to`p`

. - 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 to`p`

using the projection`U`

and the vector`T`

, and compute the Euclidean distance between`p`

and`C`

.

#### 2. Using “cross product”:

- import the NumPy library and assign it the alias
`np`

. - The function
`distance`

calculates the shortest distance between a point`p`

and a set of line segments defined by pairs of points`P0`

and`P1`

. - it first calculates the vector
`T`

representing the direction and magnitude of each line segment by subtracting`P0`

from`P1`

. - It also calculates the vector
`V`

between`P0`

and`p`

. - it uses the cross product of
`T`

and`V`

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`

and`P1`

.