python实现三维的最短路径并绘制3维图像中的最短路径

实现三维的最短路径可以使用 Dijkstra 算法或者 A*算法。这里我们以 Dijkstra 算法为例。

首先，为了方便计算，我们可以将三维图像转化为一个带权有向图，其中每个像素点对应一个节点，相邻像素点之间的边权重为它们之间的距离。然后，我们可以以起点为起点，使用 Dijkstra 算法计算出到所有节点的最短路径。最后，我们可以根据最短路径来在三维图像中绘制出最短路径。

下面是 Python 代码实现：

import numpy as np
import heapq
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# 构建带权有向图
def build_graph(matrix):
    graph = {}
    rows, cols, depths = matrix.shape
    for row in range(rows):
        for col in range(cols):
            for depth in range(depths):
                node = (row, col, depth)
                neighbors = []
                if row > 0:
                    neighbors.append(((row-1, col, depth), matrix[row-1, col, depth]))
                if row < rows-1:
                    neighbors.append(((row+1, col, depth), matrix[row+1, col, depth]))
                if col > 0:
                    neighbors.append(((row, col-1, depth), matrix[row, col-1, depth]))
                if col < cols-1:
                    neighbors.append(((row, col+1, depth), matrix[row, col+1, depth]))
                if depth > 0:
                    neighbors.append(((row, col, depth-1), matrix[row, col, depth-1]))
                if depth < depths-1:
                    neighbors.append(((row, col, depth+1), matrix[row, col, depth+1]))
                graph[node] = neighbors
    return graph

# Dijkstra 算法
def dijkstra(graph, start):
    distances = {node: float('inf') for node in graph}
    distances[start] = 0
    queue = [(0, start)]
    while queue:
        current_distance, current_node = heapq.heappop(queue)
        if current_distance > distances[current_node]:
            continue
        for neighbor, weight in graph[current_node]:
            distance = current_distance + weight
            if distance < distances[neighbor]:
                distances[neighbor] = distance
                heapq.heappush(queue, (distance, neighbor))
    return distances

# 绘制最短路径
def plot_shortest_path(matrix, start, end, distances):
    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')
    rows, cols, depths = matrix.shape
    for row in range(rows):
        for col in range(cols):
            for depth in range(depths):
                if matrix[row, col, depth] == 1:
                    ax.scatter(row, col, depth, c='black', marker='o')
                else:
                    ax.scatter(row, col, depth, c='white', marker='o')
    node = end
    path = [end]
    while node != start:
        shortest_distance = float('inf')
        shortest_node = None
        for neighbor, weight in graph[node]:
            if distances[neighbor] < shortest_distance:
                shortest_distance = distances[neighbor]
                shortest_node = neighbor
        path.append(shortest_node)
        node = shortest_node
    path.reverse()
    for i in range(len(path)-1):
        x1, y1, z1 = path[i]
        x2, y2, z2 = path[i+1]
        ax.plot([x1, x2], [y1, y2], [z1, z2], c='red')
    ax.set_xlabel('X Label')
    ax.set_ylabel('Y Label')
    ax.set_zlabel('Z Label')
    plt.show()

# 测试
matrix = np.array([
    [[0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 1, 0], [0, 0, 1, 0]],
    [[0, 0, 1, 0], [1, 1, 1, 0], [0, 0, 0, 0], [0, 1, 1, 1]],
    [[1, 1, 0, 0], [0, 0, 0, 1], [0, 1, 1, 1], [0, 1, 0, 0]],
    [[1, 0, 0, 0], [1, 1, 0, 0], [1, 1, 1, 0], [0, 0, 0, 0]]
])
graph = build_graph(matrix)
start = (0, 0, 0)
end = (3, 3, 3)
distances = dijkstra(graph, start)
plot_shortest_path(matrix, start, end, distances)

运行以上代码可以得到一个三维图像，并在图像中绘制出了起点到终点的最短路径。