NumPy: Calculate the distance between a Point and a Line

# NumPy: Calculate the distance between a Point and a Line

The example assumes that you have a line drawn between P1 and P2 and need to calculate the distance from P3 to the line.

You can use the numpy.cross() method to get the cross-product of the arrays of vectors and divide the result by the norm of the matrix of vectors.

main.py

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import numpy as np

p1 = np.array([0, 0])
p2 = np.array([20, 20])
p3 = np.array([10, 14])


distance = np.cross(p2 - p1, p3 - p1) / np.linalg.norm(p2 - p1)

print(distance)  # 👉️ 2.82842712474619

numpy calculate distance between point and line

The code for this article is available on GitHub

Make sure the values you pass to numpy.cross() and numpy.linalg.norm() and NumPy arrays.

You can use the numpy.array() method if you need to convert a list or a tuple to an array.

main.py

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tup = (0, 0)

print(type(tup)) # <class 'tuple'>

arr = np.array(tup)

print(type(arr)) # <class 'numpy.ndarray'>

The numpy.cross() method returns the cross product of two arrays of vectors.

The only arguments we passed to numpy.cross() are a and b:

a - components of the first vector(s).
b components of the second vector(s).

main.py

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distance = np.cross(p2 - p1, p3 - p1) / np.linalg.norm(p2 - p1)

print(distance)  # 👉️ 2.82842712474619

The cross product of a and b is a vector perpendicular to both a and b.

The numpy.cross() method returns the vector cross product(s).

main.py

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import numpy as np

p1 = np.array([0, 0])
p2 = np.array([20, 20])
p3 = np.array([10, 14])

print(np.cross(p2 - p1, p3 - p1)) # 👉️ 80

The numpy.linalg.norm() method returns the norm of the matrix or vectors.

main.py

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import numpy as np

p1 = np.array([0, 0])
p2 = np.array([20, 20])
p3 = np.array([10, 14])

# 👇️ 28.284271247461902
print(np.linalg.norm(p2 - p1))

The code for this article is available on GitHub

The last step is to divide the result of calling numpy.cross() by the result of calling numpy.linalg.norm().

main.py

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import numpy as np

p1 = np.array([0, 0])
p2 = np.array([20, 20])
p3 = np.array([10, 14])


distance = np.cross(p2 - p1, p3 - p1) / np.linalg.norm(p2 - p1)

print(distance)  # 👉️ 2.82842712474619

numpy calculate distance between point and line

If you want to calculate the distance and get the absolute (non-negative) value, use the numpy.absolute() method.

main.py

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import numpy as np

p1 = np.array([0, 0])
p2 = np.array([20, 20])
p3 = np.array([10, 14])

distance = np.abs(np.cross(p2 - p1, p1 - p3)) / np.linalg.norm(p2 - p1)

print(distance)  # 👉️ 2.82842712474619

get absolute value after calculating distance

The code for this article is available on GitHub

The absolute value of a number is its non-negative value.

For example, the absolute value of 10 is 10, and the absolute value of -10 is also 10.

# Additional Resources

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NumPy: Calculate the distance between a Point and a Line

# NumPy: Calculate the distance between a Point and a Line

# Additional Resources

Borislav Hadzhiev