找到点是否位于点云的凸包中的有效方法是什么? [英] What's an efficient way to find if a point lies in the convex hull of a point cloud?

问题描述

我在 numpy 中有一个坐标点云.对于大量点，我想找出这些点是否位于点云的凸包中.

I have a point cloud of coordinates in numpy. For a high number of points, I want to find out if the points lie in the convex hull of the point cloud.

我尝试了 pyhull，但我不知道如何检查一个点是否在 ConvexHull 中:

I tried pyhull but I cant figure out how to check if a point is in the ConvexHull:

hull = ConvexHull(np.array([(1, 2), (3, 4), (3, 6)]))
for s in hull.simplices:
    s.in_simplex(np.array([2, 3]))

引发 LinAlgError: Array must be square.

raises LinAlgError: Array must be square.

推荐答案

这里有一个简单的解决方案，只需要 scipy:

Here is an easy solution that requires only scipy:

def in_hull(p, hull):
    """
    Test if points in `p` are in `hull`

    `p` should be a `NxK` coordinates of `N` points in `K` dimensions
    `hull` is either a scipy.spatial.Delaunay object or the `MxK` array of the 
    coordinates of `M` points in `K`dimensions for which Delaunay triangulation
    will be computed
    """
    from scipy.spatial import Delaunay
    if not isinstance(hull,Delaunay):
        hull = Delaunay(hull)

    return hull.find_simplex(p)>=0

它返回一个布尔数组，其中 True 值表示位于给定凸包中的点.可以这样使用:

It returns a boolean array where True values indicate points that lie in the given convex hull. It can be used like this:

tested = np.random.rand(20,3)
cloud  = np.random.rand(50,3)

print in_hull(tested,cloud)

如果您安装了 matplotlib，您还可以使用以下函数调用第一个函数并绘制结果.仅适用于 2D 数据，由 Nx2 数组给出:

If you have matplotlib installed, you can also use the following function that calls the first one and plots the results. For 2D data only, given by Nx2 arrays:

def plot_in_hull(p, hull):
    """
    plot relative to `in_hull` for 2d data
    """
    import matplotlib.pyplot as plt
    from matplotlib.collections import PolyCollection, LineCollection

    from scipy.spatial import Delaunay
    if not isinstance(hull,Delaunay):
        hull = Delaunay(hull)

    # plot triangulation
    poly = PolyCollection(hull.points[hull.vertices], facecolors='w', edgecolors='b')
    plt.clf()
    plt.title('in hull')
    plt.gca().add_collection(poly)
    plt.plot(hull.points[:,0], hull.points[:,1], 'o', hold=1)


    # plot the convex hull
    edges = set()
    edge_points = []

    def add_edge(i, j):
        """Add a line between the i-th and j-th points, if not in the list already"""
        if (i, j) in edges or (j, i) in edges:
            # already added
            return
        edges.add( (i, j) )
        edge_points.append(hull.points[ [i, j] ])

    for ia, ib in hull.convex_hull:
        add_edge(ia, ib)

    lines = LineCollection(edge_points, color='g')
    plt.gca().add_collection(lines)
    plt.show()    

    # plot tested points `p` - black are inside hull, red outside
    inside = in_hull(p,hull)
    plt.plot(p[ inside,0],p[ inside,1],'.k')
    plt.plot(p[-inside,0],p[-inside,1],'.r')

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