### 移动立方体算法 Python 实现 #### 使用 Pygame 和 NumPy 库创建移动立方体 为了实现一个可以在二维屏幕上显示并移动的三维立方体，可以采用 Pygame 来处理图形渲染以及事件循环，并利用 NumPy 进行矩阵运算来简化几何变换操作。 ```python import numpy as np import pygame from math import radians, cos, sin class Cube: vertices = [ [-1, -1, -1], [1, -1, -1], [1, 1, -1], [-1, 1, -1], [-1, -1, 1], [1, -1, 1], [1, 1, 1], [-1, 1, 1]] edges = [(0, 1), (1, 2), (2, 3), (3, 0), (4, 5), (5, 6), (6, 7), (7, 4), (0, 4), (1, 5), (2, 6), (3, 7)] def __init__(self): self.angle_x = self.angle_y = self.angle_z = 0 def rotate(self, axis='x', angle=1): """Rotate the cube around specified axis.""" theta = radians(angle) if axis == 'x': rotation_matrix = [[1, 0, 0], [0, cos(theta), -sin(theta)], [0, sin(theta), cos(theta)]] elif axis == 'y': rotation_matrix = [[cos(theta), 0, sin(theta)], [0, 1, 0], [-sin(theta), 0, cos(theta)]] elif axis == 'z': rotation_matrix = [[cos(theta), -sin(theta), 0], [sin(theta), cos(theta), 0], [0, 0, 1]] rot_mat = np.array(rotation_matrix) rotated_vertices = [] for vertex in self.vertices: v = np.dot(rot_mat, vertex) rotated_vertices.append(v.tolist()) self.vertices = rotated_vertices def project(self, width, height, fov, distance): factor =fov / (vertex[2]+distance) for vertex in self.vertices] projected = [] for i, vertex in enumerate(self.vertices): projection = [width/2 + factor[i]*vertex[0], height/2 - factor[i]*vertex[1]] projected.append(projection) return projected def main(): pygame.init() screen = pygame.display.set_mode((800, 600)) clock = pygame.time.Clock() cube = Cube() running = True while running: for event in pygame.event.get(): if event.type == pygame.QUIT: running = False keys = pygame.key.get_pressed() if keys[pygame.K_LEFT]: cube.rotate('y', -2) if keys[pygame.K_RIGHT]: cube.rotate('y', 2) if keys[pygame.K_UP]: cube.rotate('x', -2) if keys[pygame.K_DOWN]: cube.rotate('x', 2) screen.fill((0, 0, 0)) points = cube.project(800, 600, 256, 4) for edge in cube.edges: p1 = tuple(map(int, points[edge[0]])) p2 = tuple(map(int, points[edge[1]])) pygame.draw.line(screen, (255, 255, 255), p1, p2, 1) pygame.display.flip() clock.tick(60) if __name__ == "__main__": main() ``` 这段代码展示了如何使用 Python 创建一个简单的交互式 3D 立方体模拟器。用户可以通过键盘方向键使立方体沿不同轴向旋转[^1]。