用于在 python 中查找点云边界的 3D alpha 形状

Question

我正在尝试使用 3D alpha 形状算法找到点云的表面。当我计算外接半径时，行列式 a 等于零，导致错误“在 double_scalars 中除以零”。我该怎么办？非常感谢！代码如下：

def alpha_shape_3D(points, alpha):
    tetra = Delaunay(points)
    edge = []
    for i1, i2, i3, i4 in tetra.vertices:
        pa = points[i1]
        pb = points[i2]
        pc = points[i3]
        pd = points[i4]
        pa2 = np.dot(pa, pa)
        pb2 = np.dot(pb, pb)
        pc2 = np.dot(pc, pc)
        pd2 = np.dot(pd, pd)
        a = np.linalg.det(np.array([np.append(pa, 1), np.append(pb, 1), np.append(pc, 1), np.append(pd, 1)]))

        Dx = np.linalg.det(np.array([np.array([pa2, pa[1], pa[2], 1]),
                                     np.array([pb2, pb[1], pb[2], 1]),
                                     np.array([pc2, pc[1], pc[2], 1]),
                                     np.array([pd2, pd[1], pd[2], 1])]))

        Dy = - np.linalg.det(np.array([np.array([pa2, pa[0], pa[2], 1]),
                                       np.array([pb2, pb[0], pb[2], 1]),
                                       np.array([pc2, pc[0], pc[2], 1]),
                                       np.array([pd2, pd[0], pd[2], 1])]))

        Dz = np.linalg.det(np.array([np.array([pa2, pa[0], pa[1], 1]),
                                     np.array([pb2, pb[0], pb[1], 1]),
                                     np.array([pc2, pc[0], pc[1], 1]),
                                     np.array([pd2, pd[0], pd[1], 1])]))

        c = np.linalg.det(np.array([np.array([pa2, pa[0], pa[1], pa[2]]),
                                    np.array([pb2, pb[0], pb[1], pb[2]]),
                                    np.array([pc2, pc[0], pc[1], pc[2]]),
                                    np.array([pd2, pd[0], pd[1], pd[2]])]))
       
        r = math.sqrt(math.pow(Dx, 2) + math.pow(Dy, 2) + math.pow(Dz, 2) - 4 * a * c) / (2 * abs(a))  # error occurs here, since some value of a is zero.
        if r<alpha:
            edge.append([pa,pb,pc,pd])
    tetras = np.array(edge)
    # triangles
    TriComb = np.array([(0, 1, 2), (0, 1, 3), (0, 2, 3), (1, 2, 3)])
    Triangles = tetras[:,TriComb].reshape(-1,3)
    Triangles = np.sort(Triangles,axis=1)
    # Remove triangles that occurs twice, because they are within shapes
    TrianglesDict = defaultdict(int)
    for tri in Triangles:TrianglesDict[tuple(tri)] += 1
    Triangles=np.array([tri for tri in TrianglesDict if TrianglesDict[tri] ==1])
    #edges
    EdgeComb=np.array([(0, 1), (0, 2), (1, 2)])
    Edges=Triangles[:,EdgeComb].reshape(-1,2)
    Edges=np.sort(Edges,axis=1)
    Edges=np.unique(Edges,axis=0)

    Vertices = np.unique(Edges)
    return Vertices,Edges,Triangles

Answer 1

如果没有您的 points 数据，很难确定，但看起来您的数据已退化。例如，如果您的所有点都在同一平面上，您可以得到这个结果。