Calculate area of polygon given (x,y) coordinates

Implementation of Shoelace formula could be done in Numpy. Assuming these vertices:

import numpy as np
x = np.arange(0,1,0.001)
y = np.sqrt(1-x**2)

We can redefine the function in numpy to find the area:

def PolyArea(x,y):
    return 0.5*np.abs(np.dot(x,np.roll(y,1))-np.dot(y,np.roll(x,1)))

And getting results:

print PolyArea(x,y)
# 0.26353377782163534

Avoiding for loop makes this function ~50X faster than PolygonArea:

%timeit PolyArea(x,y)
# 10000 loops, best of 3: 42 µs per loop
%timeit PolygonArea(zip(x,y))
# 100 loops, best of 3: 2.09 ms per loop.

Timing is done in Jupyter notebook.