计算 scipy 中凸包的面积

Question

I wanted to compute the convex hull for a couple of points on a plane, using scipy .

Here is my code:

import numpy as np
from scipy.spatial import ConvexHull

points = np.array([[10, 10], [30, 10], [30, 20], [10, 20]])
hull = ConvexHull(points)
print(hull.vertices, hull.area)

It prints: [0 1 2 3] 60.0

So, the perimeter rather than area is returned (I checked another example, same behavior). Is this a bug? Python 3.7.4 (64-bit), scipy 1.3.1.

Answer 1

I suppose hull.area refers to the perimeter in 1D and to the area in 2D. If you want the area delimited by a 1D hull or the volume delimited by a 2D hull, call hull.volume instead.

Answer 2

The definition of the Convex Hull is based upon the perimeter, not the area:

In mathematics, the convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X.

So this is an expected result. Although it seems to me that you have printed both the perimeter points ( [0 1 2 3] ) and the area ( 60.0 )?