Shortest Distance Between Points and Line Segments

Python
#1

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.