import tkinter as tk import math import random # ------------------ 3D 数学工具 ------------------ def rotate_x(point, angle): """绕 X 轴旋转""" x, y, z = point rad = math.radians(angle) cos_a, sin_a = math.cos(rad), math.sin(rad) return (x, y * cos_a - z * sin_a, y * sin_a + z * cos_a) def rotate_y(point, angle): """绕 Y 轴旋转""" x, y, z = point rad = math.radians(angle) cos_a, sin_a = math.cos(rad), math.sin(rad) return (x * cos_a + z * sin_a, y, -x * sin_a + z * cos_a) def rotate_z(point, angle): """绕 Z 轴旋转""" x, y, z = point rad = math.radians(angle) cos_a, sin_a = math.cos(rad), math.sin(rad) return (x * cos_a - y * sin_a, x * sin_a + y * cos_a, z) def project(point, fov=300, viewer_distance=500): """ 将 3D 点投影到 2D 平面（透视投影） fov: 视野系数，viewer_distance: 观察距离 """ x, y, z = point factor = fov / (viewer_distance + z) return (x * factor, y * factor) # ------------------ 主程序 ------------------ class ComplexGraphics: def __init__(self, root): self.root = root self.root.title("3D 交互式旋转立方体 - Tkinter 复杂图形示例") self.root.geometry("800x600") # 创建 Canvas self.canvas = tk.Canvas(root, bg='black', width=800, height=600, highlightthickness=0) self.canvas.pack(fill=tk.BOTH, expand=True) # 立方体顶点（边长 100，中心在原点） half = 50 self.vertices = [ (-half, -half, -half), ( half, -half, -half), ( half, half, -half), (-half, half, -half), (-half, -half, half), ( half, -half, half), ( half, half, half), (-half, half, half) ] # 定义棱（顶点索引对） self.edges = [ (0,1), (1,2), (2,3), (3,0), # 前面 (4,5), (5,6), (6,7), (7,4), # 后面 (0,4), (1,5), (2,6), (3,7) # 连接前后 ] # 定义面（用于填充颜色，按顶点索引） self.faces = [ (0,1,2,3), # 前面 (z = -half) (4,5,6,7), # 后面 (z = +half) (0,1,5,4), # 底面 (y = -half) (2,3,7,6), # 顶面 (y = +half) (0,3,7,4), # 左面 (x = -half) (1,2,6,5) # 右面 (x = +half) ] # 为每个面赋予不同颜色（带透明度效果，但 Tkinter 不支持半透明，仅用纯色） self.face_colors = ['#FF6B6B', '#4ECDC4', '#45B7D1', '#96CEB4', '#FFEAA7', '#DDA0DD'] # 控制旋转角度（可被鼠标拖动修改） self.angle_x = 30 self.angle_y = 45 self.angle_z = 0 # 鼠标拖拽相关 self.dragging = False self.last_x = 0 self.last_y = 0 # 生成星空背景（随机点） self.stars = [] for _ in range(150): x = random.randint(0, 800) y = random.randint(0, 600) size = random.randint(1, 3) brightness = random.randint(100, 255) color = f'#{brightness:02x}{brightness:02x}{brightness:02x}' self.stars.append((x, y, size, color)) # 绑定鼠标事件 self.canvas.bind("", self.on_mouse_down) self.canvas.bind("", self.on_mouse_drag) self.canvas.bind("", self.on_mouse_up) # 鼠标滚轮缩放（模拟远近） self.canvas.bind("", self.on_mouse_wheel) # 全局缩放系数 self.scale = 1.0 # 启动动画循环 self.animate() # ------------------ 鼠标事件处理 ------------------ def on_mouse_down(self, event): self.dragging = True self.last_x = event.x self.last_y = event.y def on_mouse_drag(self, event): if self.dragging: dx = event.x - self.last_x dy = event.y - self.last_y # 根据拖拽方向改变旋转角度 self.angle_y += dx * 0.5 # 水平拖拽绕 Y 轴 self.angle_x += dy * 0.5 # 垂直拖拽绕 X 轴 self.last_x = event.x self.last_y = event.y def on_mouse_up(self, event): self.dragging = False def on_mouse_wheel(self, event): # Windows 下 event.delta 为 ±120；Linux 可能需要调整 delta = event.delta // 120 if event.delta else 0 self.scale *= (1.0 + delta * 0.02) self.scale = max(0.2, min(3.0, self.scale)) # 限制缩放范围 # ------------------ 绘制核心 ------------------ def draw_cube(self): # 清空画布（保留背景星空） self.canvas.delete("cube") self.canvas.delete("axis") # 1. 绘制星空（静态） for x, y, size, color in self.stars: self.canvas.create_oval(x-size, y-size, x+size, y+size, fill=color, outline='', tags="star") # 2. 变换所有顶点 transformed = [] for v in self.vertices: # 应用旋转 v = rotate_x(v, self.angle_x) v = rotate_y(v, self.angle_y) v = rotate_z(v, self.angle_z) # 应用缩放 v = (v[0] * self.scale, v[1] * self.scale, v[2] * self.scale) transformed.append(v) # 3. 投影到 2D projected = [project(v, fov=300, viewer_distance=600) for v in transformed] # 计算每个面的平均 Z 值（用于排序，实现简单画家算法） face_z = [] for face in self.faces: avg_z = sum(transformed[i][2] for i in face) / len(face) face_z.append(avg_z) # 按 Z 从远到近排序（先绘制远的） face_order = sorted(range(len(self.faces)), key=lambda i: face_z[i], reverse=False) # 4. 绘制填充面（先绘制远处，再近处覆盖） for idx in face_order: face = self.faces[idx] points = [] for i in face: x, y = projected[i] # 平移使中心在画布中央 x += 400 y += 300 points.extend([x, y]) self.canvas.create_polygon(points, fill=self.face_colors[idx], outline='white', width=1, tags="cube") # 5. 绘制棱（线框，覆盖在面上增加清晰度） for edge in self.edges: p1 = projected[edge[0]] p2 = projected[edge[1]] x1, y1 = p1[0] + 400, p1[1] + 300 x2, y2 = p2[0] + 400, p2[1] + 300 self.canvas.create_line(x1, y1, x2, y2, fill='white', width=2, tags="cube") # 6. 绘制坐标轴（辅助线） axis_length = 100 * self.scale origin = (400, 300) # X轴（红） end_x = project((axis_length, 0, 0), fov=300, viewer_distance=600) self.canvas.create_line(origin[0], origin[1], end_x[0]+400, end_x[1]+300, fill='red', width=2, arrow=tk.LAST, tags="axis") # Y轴（绿） end_y = project((0, axis_length, 0), fov=300, viewer_distance=600) self.canvas.create_line(origin[0], origin[1], end_y[0]+400, end_y[1]+300, fill='green', width=2, arrow=tk.LAST, tags="axis") # Z轴（蓝） end_z = project((0, 0, axis_length), fov=300, viewer_distance=600) self.canvas.create_line(origin[0], origin[1], end_z[0]+400, end_z[1]+300, fill='blue', width=2, arrow=tk.LAST, tags="axis") # 添加文字标注 self.canvas.create_text(420, 280, text='X', fill='red', tags="axis") self.canvas.create_text(420, 320, text='Y', fill='green', tags="axis") self.canvas.create_text(380, 300, text='Z', fill='blue', tags="axis") # 显示角度信息 info = f"角度 X: {self.angle_x:.1f}° Y: {self.angle_y:.1f}° Z: {self.angle_z:.1f}° | 缩放: {self.scale:.2f}" self.canvas.create_text(400, 20, text=info, fill='yellow', font=('Arial', 12), tags="cube") def animate(self): """动画循环：每帧更新角度并重绘""" # 如果不拖拽，可以自动旋转（这里不自动旋转，交给用户拖拽） # 但为了让效果更生动，可以增加微小的自转（可选） # 这里我们保持用户控制，所以只重绘 self.draw_cube() self.root.after(30, self.animate) # 约 33 FPS # ------------------ 启动 ------------------ if __name__ == "__main__": root = tk.Tk() app = ComplexGraphics(root) root.mainloop()