如何用Python Matplotlib闭合半圆柱曲面及顶点弧绘制圆柱？

问题 #

1. 绘制的半圆柱曲面未闭合，如何实现曲面完全闭合？
2. 能否通过顶点和边来绘制圆柱，让两个顶点之间形成一段弧？

一、实现半圆柱曲面闭合 #

你当前的代码里，theta只取了0到π的区间，且首尾点不重合，同时缺少半圆柱的两个端面，导致曲面呈开放状态。要实现闭合，需要两步操作：

1. 让曲面的弧边首尾重合；
2. 添加半圆柱的两个半圆端面。

修改后的完整代码：

from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
import numpy as np

def data_for_cylinder_along_z(center_x,center_y,radius,height_z):
    z = np.linspace(0, height_z, 50)
    # 重复起点，让弧边首尾闭合
    theta = np.linspace(0, np.pi, 50)
    theta = np.append(theta, theta[0])
    theta_grid, z_grid=np.meshgrid(theta, z)
    x_grid = radius*np.cos(theta_grid) + center_x
    y_grid = radius*np.sin(theta_grid) + center_y
    return x_grid,y_grid,z_grid

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

# 绘制半圆柱曲面
center_x, center_y = 0.2, 0.2
radius = 0.05
height_z = 0.1
Xc,Yc,Zc = data_for_cylinder_along_z(center_x,center_y,radius,height_z)
ax.plot_surface(Xc, Yc, Zc, alpha=0.5)

# 生成并添加两个半圆端面
theta_end = np.linspace(0, np.pi, 50)
x_end = radius*np.cos(theta_end) + center_x
y_end = radius*np.sin(theta_end) + center_y

# z=0处的端面
end1 = np.column_stack((x_end, y_end, np.zeros_like(x_end)))
# z=height_z处的端面
end2 = np.column_stack((x_end, y_end, np.full_like(x_end, height_z)))

ax.add_collection3d(Poly3DCollection([end1], alpha=0.5, facecolor='blue'))
ax.add_collection3d(Poly3DCollection([end2], alpha=0.5, facecolor='blue'))

ax.set_title("Closed Half Cylinder")
plt.show()

二、通过顶点和边绘制带弧段的圆柱 #

完全可以手动通过顶点和边构建半圆柱。你可以自定义弧的顶点坐标，再用Poly3DCollection绘制曲面，或用Line3DCollection绘制边缘线条，示例代码如下：

from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d.art3d import Poly3DCollection, Line3DCollection
import numpy as np

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

center_x, center_y = 0.2, 0.2
radius = 0.05
height_z = 0.1

# 定义半圆弧的顶点
theta = np.linspace(0, np.pi, 50)
x_arc = radius*np.cos(theta) + center_x
y_arc = radius*np.sin(theta) + center_y

# 生成上下两个弧的z坐标
z0 = np.zeros_like(x_arc)
z1 = np.full_like(x_arc, height_z)

# 构建曲面的小四边形顶点
surface_verts = []
for i in range(len(theta)-1):
    verts = [
        (x_arc[i], y_arc[i], z0[i]),
        (x_arc[i+1], y_arc[i+1], z0[i+1]),
        (x_arc[i+1], y_arc[i+1], z1[i+1]),
        (x_arc[i], y_arc[i], z1[i])
    ]
    surface_verts.append(verts)

# 添加半圆柱曲面
ax.add_collection3d(Poly3DCollection(surface_verts, alpha=0.5, facecolor='cyan'))

# 添加边缘线条（可选）
edges = []
# 上下弧的分段边
for i in range(len(theta)-1):
    edges.append([(x_arc[i], y_arc[i], z0[i]), (x_arc[i+1], y_arc[i+1], z0[i+1])])
    edges.append([(x_arc[i], y_arc[i], z1[i]), (x_arc[i+1], y_arc[i+1], z1[i+1])])
# 两端的竖直边
edges.append([(x_arc[0], y_arc[0], z0[0]), (x_arc[0], y_arc[0], z1[0])])
edges.append([(x_arc[-1], y_arc[-1], z0[-1]), (x_arc[-1], y_arc[-1], z1[-1])])

ax.add_collection3d(Line3DCollection(edges, color='black', linewidths=0.5))

ax.set_title("Half Cylinder via Vertices & Edges")
plt.show()

你可以通过调整theta的采样数量，控制弧段的平滑程度。

内容的提问来源于stack exchange，提问作者Freya the Goddess