如何利用矩阵变换后的长方体顶点绘制3D图形？

Hey there! Let's get that transformed cuboid plotted properly—sounds like the main hurdles were probably messy vertex data formatting or incorrect edge/face connections. Here's a straightforward solution with two common plotting approaches (wireframe and filled surfaces) that should work for your setup:

Step 1: Clean Up Your Transformed Vertex Data #

First, your new_corner entries are nested arrays (like [[array([[1.95]])], [array([[0.3]])], [array([[-0.708]])]]), which aren't easy to work with for plotting. Let's extract the raw numerical coordinates into a clean numpy array:

import numpy as np

# Replace this with your actual list of 8 transformed vertices
new_corners = [
    [[np.array([[1.95]])], [np.array([[0.3]])], [np.array([[-0.708]])]],
    # ... add the other 7 vertices here
]

def extract_clean_vertices(transformed_corners):
    vertices = []
    for corner in transformed_corners:
        # Pull out the scalar values from the nested arrays
        x = corner[0][0][0]
        y = corner[1][0][0]
        z = corner[2][0][0]
        vertices.append((x, y, z))
    return np.array(vertices)

# Get a (8, 3) array of clean (x,y,z) coordinates
clean_vertices = extract_clean_vertices(new_corners)

Step 2: Plot as a Wireframe Cuboid #

If you prefer a simple outlined shape, we'll define all 12 edges of the cuboid and plot each one individually. This works great for verifying vertex positions:

import matplotlib.pyplot as plt

# Define the 12 edges of the cuboid (index pairs of connected vertices)
# Note: This assumes your original cuboid function generates vertices in a standard order
# If your vertex order is different, adjust these pairs after checking clean_vertices
edges = [
    [0,1], [1,2], [2,3], [3,0],  # Bottom face edges
    [4,5], [5,6], [6,7], [7,4],  # Top face edges
    [0,4], [1,5], [2,6], [3,7]   # Vertical connecting edges
]

# Set up 3D plot
fig = plt.figure(figsize=(8,6))
ax = fig.add_subplot(111, projection='3d')

# Plot each edge
for start_idx, end_idx in edges:
    x_vals = [clean_vertices[start_idx, 0], clean_vertices[end_idx, 0]]
    y_vals = [clean_vertices[start_idx, 1], clean_vertices[end_idx, 1]]
    z_vals = [clean_vertices[start_idx, 2], clean_vertices[end_idx, 2]]
    ax.plot3D(x_vals, y_vals, z_vals, color='darkblue', linewidth=2)

# Add labels and adjust view
ax.set_xlabel('X Axis')
ax.set_ylabel('Y Axis')
ax.set_zlabel('Z Axis')
ax.view_init(elev=30, azim=45)  # Adjust viewing angle as needed
plt.tight_layout()
plt.show()

Step 3: Plot as a Filled Surface Cuboid #

For a solid-looking cuboid, use Poly3DCollection to render filled faces with optional transparency:

from mpl_toolkits.mplot3d.art3d import Poly3DCollection

# Define the 6 faces of the cuboid (each face is 4 vertex indices)
faces = [
    [0,1,2,3],  # Bottom face
    [4,5,6,7],  # Top face
    [0,1,5,4],  # Front face
    [1,2,6,5],  # Right face
    [2,3,7,6],  # Back face
    [3,0,4,7]   # Left face
]

# Set up 3D plot
fig = plt.figure(figsize=(8,6))
ax = fig.add_subplot(111, projection='3d')

# Create 3D polygons for each face
face_polygons = []
for face in faces:
    face_coords = [clean_vertices[idx] for idx in face]
    face_polygons.append(face_coords)

# Add the collection to the plot
ax.add_collection3D(Poly3DCollection(
    face_polygons,
    facecolors='lightcyan',
    edgecolors='darkblue',
    linewidths=1,
    alpha=0.6  # Adjust transparency here
))

# Auto-scale axes to fit the cuboid
ax.set_xlim(clean_vertices[:,0].min() - 0.1, clean_vertices[:,0].max() + 0.1)
ax.set_ylim(clean_vertices[:,1].min() - 0.1, clean_vertices[:,1].max() + 0.1)
ax.set_zlim(clean_vertices[:,2].min() - 0.1, clean_vertices[:,2].max() + 0.1)

# Add labels
ax.set_xlabel('X Axis')
ax.set_ylabel('Y Axis')
ax.set_zlabel('Z Axis')
plt.tight_layout()
plt.show()

Quick Troubleshooting Tip #

If the cuboid looks distorted or disconnected, double-check the vertex order from your cuboid function. Print clean_vertices to see how the 8 points are arranged, then adjust the edges and faces index pairs to match your actual vertex ordering.

内容的提问来源于stack exchange，提问作者Pradeep Chakravarthi Nutakki