Convex hull area in Python?

Convex hull is simply a convex polygon so you can easily try {this} or {this} to find area of 2D polygon.

Something like the following (our version):

def PolyArea2D(pts):
    lines = np.hstack([pts,np.roll(pts,-1,axis=0)])
    area = 0.5*abs(sum(x1*y2-x2*y1 for x1,y1,x2,y2 in lines))
    return area

in which pts is array of polygon's vertices i.e., a (nx2) array.

Full usage:

import numpy as np

def PolyArea2D(pts):
    lines = np.hstack([pts,np.roll(pts,-1,axis=0)])
    area = 0.5*abs(sum(x1*y2-x2*y1 for x1,y1,x2,y2 in lines))
    return area

pts = [[0,0],[1,0],[1,1],[0,1]]
print PolyArea2D(pts)    

pts = [[0,0],[1,0],[0,1]]
print PolyArea2D(pts)    

pts = [[0,0],[1,0],[0.5,0.5]] 
print PolyArea2D(pts)    

>>>
1.0
0.5
0.25

You could just use the ConvexHull class from scipy.spatial. It will not only give you the hull's area, but it will compute the hull for you as well. But if you do use it, BEWARE! In 2D, the attribute you want to use is not area, it is volume, because the former will actually give you the hull's perimeter.

That's because the attributes are named after their values in 3D, where area will indeed be the hull's area, and volume, well, its volume. For 2D hulls, the names are the same, but what they actually contain is not quite what it says on the tin. Worse, the documentation does not warn you about this.

(You can easily check this with trivial examples such as an isosceles right triangle of length 1 on its legs: the perimeter should be 2+sqrt(2), or about 3.414213562, and the area should be 0.5.)