python利用八叉树划分三维点云代码

以下是Python使用八叉树划分三维点云的示例代码：

import numpy as np

class OctreeNode:
    def __init__(self, center, radius):
        self.center = center
        self.radius = radius
        self.points = []
        self.children = []

    def insert(self, point):
        if len(self.children) > 0:
            index = self.get_child_index(point)
            if index != -1:
                self.children[index].insert(point)
                return
        self.points.append(point)
        if len(self.points) > 8:
            self.subdivide()

    def subdivide(self):
        radius = self.radius / 2
        for i in range(8):
            x = self.center[0] + radius * (-1)**(i%2)
            y = self.center[1] + radius * (-1)**(i//2%2)
            z = self.center[2] + radius * (-1)**(i//4)
            child_center = np.array([x, y, z])
            child_node = OctreeNode(child_center, radius)
            for point in self.points:
                child_node.insert(point)
            self.children.append(child_node)
        self.points = []

    def get_child_index(self, point):
        for i, child in enumerate(self.children):
            if child.contains(point):
                return i
        return -1

    def contains(self, point):
        return np.linalg.norm(point - self.center) <= self.radius

    def get_points_in_sphere(self, center, radius):
        points = []
        if not self.intersects_sphere(center, radius):
            return points
        for point in self.points:
            if np.linalg.norm(point - center) <= radius:
                points.append(point)
        for child in self.children:
            points.extend(child.get_points_in_sphere(center, radius))
        return points

    def intersects_sphere(self, center, radius):
        return np.linalg.norm(center - self.center) <= self.radius + radius

class Octree:
    def __init__(self, points, center, radius):
        self.root = OctreeNode(center, radius)
        for point in points:
            self.root.insert(point)

    def get_points_in_sphere(self, center, radius):
        return self.root.get_points_in_sphere(center, radius)

# 示例使用
points = np.random.rand(1000, 3) * 10 - 5
octree = Octree(points, np.array([0, 0, 0]), 5)
points_in_sphere = octree.get_points_in_sphere(np.array([1, 2, 3]), 2)
print(len(points_in_sphere))

在此示例中，我们首先定义了一个`OctreeNode`类表示八叉树节点，其中`center`和`radius`属性表示节点的中心和半径。`points`属性是节点包含的点列表，而`children`属性则是子节点列表。`insert`方法将一个点插入节点，如果节点包含子节点，则将点插入适当的子节点中。如果节点包含的点数超过8，则将节点细分为8个子节点。`subdivide`方法创建8个子节点，并将原来节点包含的点分散到子节点中。`get_child_index`方法根据点的位置返回子节点的索引。`contains`方法检查节点是否包含给定的点。`get_points_in_sphere`方法返回在给定半径内的球体中的所有点的列表。`intersects_sphere`方法检查节点是否与球体相交。

`Octree`类使用`OctreeNode`类构建八叉树。在构造函数中，我们首先创建一个根节点，然后将所有点插入该节点。`get_points_in_sphere`方法使用根节点的`get_points_in_sphere`方法来查找在给定球体内的点。

在示例中，我们使用`numpy`生成1000个随机三维点，并使用它们创建一个八叉树。然后，我们使用`get_points_in_sphere`方法找到距离点`(1, 2, 3)`不超过2的所有点，并输出它们的数量。