如何确定一个点是位于 ConvexHull 的内部还是外部？

Question

我在 numpy 中有一组点，我通过 (scipy.spatial.ConvexHull 而不是 scipy.spatial.Delaunay.convex_hull) 计算它们的 ConvexHull，现在我想知道我是否向我的数组添加新点是这个点位于点云与否？在 numoy 中最好的方法是什么？

我应该提到我看到了这个问题并且它没有解决我的问题（因为它使用 cipy.spatial.Delaunay.convex_hull 来计算 ConvexHull）

Answer 1

I know this question is old, but in case some people find it as I did, here is the answer: I'm using scipy 1.1.0 and python 3.6

def isInHull(P,hull):
    '''
    Datermine if the list of points P lies inside the hull
    :return: list
    List of boolean where true means that the point is inside the convex hull
    '''
    A = hull.equations[:,0:-1]
    b = np.transpose(np.array([hull.equations[:,-1]]))
    isInHull = np.all((A @ np.transpose(P)) <= np.tile(-b,(1,len(P))),axis=0)

Here we use the equations of all the plan to determine if the point is outside the hull. We never build the Delaunay object. This function takes as insput P mxn an array of m points in n dimensions. The hull is constrcuted using

hull = ConvexHull(X)

where X is the pxn array of p points that constitute the cloud of points on which the convex hull should be constructed.