我想画一个平行六面体。实际上我从绘制多维数据集的python脚本开始:
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
points = np.array([[-1, -1, -1],
[1, -1, -1 ],
[1, 1, -1],
[-1, 1, -1],
[-1, -1, 1],
[1, -1, 1 ],
[1, 1, 1],
[-1, 1, 1]])
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
r = [-1,1]
X, Y = np.meshgrid(r, r)
ax.plot_surface(X,Y,1, alpha=0.5)
ax.plot_surface(X,Y,-1, alpha=0.5)
ax.plot_surface(X,-1,Y, alpha=0.5)
ax.plot_surface(X,1,Y, alpha=0.5)
ax.plot_surface(1,X,Y, alpha=0.5)
ax.plot_surface(-1,X,Y, alpha=0.5)
ax.scatter3D(points[:, 0], points[:, 1], points[:, 2])
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
plt.show()
为了获得平行六面体,我将点矩阵乘以下面的矩阵:
P =
[[2.06498904e-01 -6.30755443e-07 1.07477548e-03]
[1.61535574e-06 1.18897198e-01 7.85307721e-06]
[7.08353661e-02 4.48415767e-06 2.05395893e-01]]
如:
Z = np.zeros((8,3))
for i in range(8):
Z[i,:] = np.dot(points[i,:],P)
Z = 10.0*Z
我的想法是表示如下:
ax.scatter3D(Z[:, 0], Z[:, 1], Z[:, 2])
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
plt.show()
这就是我得到的:
然后我如何将表面放在这些不同的点上以形成平行六面体(在上面的立方体的方式)?
使用3D PolyCollection(example)绘制曲面
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection, Line3DCollection
import matplotlib.pyplot as plt
points = np.array([[-1, -1, -1],
[1, -1, -1 ],
[1, 1, -1],
[-1, 1, -1],
[-1, -1, 1],
[1, -1, 1 ],
[1, 1, 1],
[-1, 1, 1]])
P = [[2.06498904e-01 , -6.30755443e-07 , 1.07477548e-03],
[1.61535574e-06 , 1.18897198e-01 , 7.85307721e-06],
[7.08353661e-02 , 4.48415767e-06 , 2.05395893e-01]]
Z = np.zeros((8,3))
for i in range(8): Z[i,:] = np.dot(points[i,:],P)
Z = 10.0*Z
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
r = [-1,1]
X, Y = np.meshgrid(r, r)
# plot vertices
ax.scatter3D(Z[:, 0], Z[:, 1], Z[:, 2])
# list of sides' polygons of figure
verts = [[Z[0],Z[1],Z[2],Z[3]],
[Z[4],Z[5],Z[6],Z[7]],
[Z[0],Z[1],Z[5],Z[4]],
[Z[2],Z[3],Z[7],Z[6]],
[Z[1],Z[2],Z[6],Z[5]],
[Z[4],Z[7],Z[3],Z[0]]]
# plot sides
ax.add_collection3d(Poly3DCollection(verts,
facecolors='cyan', linewidths=1, edgecolors='r', alpha=.25))
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
plt.show()
鉴于这个问题的标题是'python draw 3D cube',这是我在Google上搜索这个问题时发现的文章。
为了那些和我一样的人,他们只是想画一个立方体,我创造了以下函数,它取一个立方体的四个点,一个角落,然后是那个角落的三个相邻点。
然后绘制立方体。
功能如下:
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection, Line3DCollection
def plot_cube(cube_definition):
cube_definition_array = [
np.array(list(item))
for item in cube_definition
]
points = []
points += cube_definition_array
vectors = [
cube_definition_array[1] - cube_definition_array[0],
cube_definition_array[2] - cube_definition_array[0],
cube_definition_array[3] - cube_definition_array[0]
]
points += [cube_definition_array[0] + vectors[0] + vectors[1]]
points += [cube_definition_array[0] + vectors[0] + vectors[2]]
points += [cube_definition_array[0] + vectors[1] + vectors[2]]
points += [cube_definition_array[0] + vectors[0] + vectors[1] + vectors[2]]
points = np.array(points)
edges = [
[points[0], points[3], points[5], points[1]],
[points[1], points[5], points[7], points[4]],
[points[4], points[2], points[6], points[7]],
[points[2], points[6], points[3], points[0]],
[points[0], points[2], points[4], points[1]],
[points[3], points[6], points[7], points[5]]
]
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
faces = Poly3DCollection(edges, linewidths=1, edgecolors='k')
faces.set_facecolor((0,0,1,0.1))
ax.add_collection3d(faces)
# Plot the points themselves to force the scaling of the axes
ax.scatter(points[:,0], points[:,1], points[:,2], s=0)
ax.set_aspect('equal')
cube_definition = [
(0,0,0), (0,1,0), (1,0,0), (0,0,1)
]
plot_cube(cube_definition)
给出结果:
请参阅我的其他答案(https://stackoverflow.com/a/49766400/3912576)以获得更简单的解决方案。
这是一组更复杂的函数,它使matplotlib更好地扩展,并始终强制输入为多维数据集。
传递给cubify_cube_definition的第一个参数是起点,第二个参数是第二个点,立方体长度是从这一点定义的,第三个是旋转点,它将被移动以匹配第一个和第二个的长度。
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection, Line3DCollection
def cubify_cube_definition(cube_definition):
cube_definition_array = [
np.array(list(item))
for item in cube_definition
]
start = cube_definition_array[0]
length_decider_vector = cube_definition_array[1] - cube_definition_array[0]
length = np.linalg.norm(length_decider_vector)
rotation_decider_vector = (cube_definition_array[2] - cube_definition_array[0])
rotation_decider_vector = rotation_decider_vector / np.linalg.norm(rotation_decider_vector) * length
orthogonal_vector = np.cross(length_decider_vector, rotation_decider_vector)
orthogonal_vector = orthogonal_vector / np.linalg.norm(orthogonal_vector) * length
orthogonal_length_decider_vector = np.cross(rotation_decider_vector, orthogonal_vector)
orthogonal_length_decider_vector = (
orthogonal_length_decider_vector / np.linalg.norm(orthogonal_length_decider_vector) * length)
final_points = [
tuple(start),
tuple(start + orthogonal_length_decider_vector),
tuple(start + rotation_decider_vector),
tuple(start + orthogonal_vector)
]
return final_points
def cube_vertices(cube_definition):
cube_definition_array = [
np.array(list(item))
for item in cube_definition
]
points = []
points += cube_definition_array
vectors = [
cube_definition_array[1] - cube_definition_array[0],
cube_definition_array[2] - cube_definition_array[0],
cube_definition_array[3] - cube_definition_array[0]
]
points += [cube_definition_array[0] + vectors[0] + vectors[1]]
points += [cube_definition_array[0] + vectors[0] + vectors[2]]
points += [cube_definition_array[0] + vectors[1] + vectors[2]]
points += [cube_definition_array[0] + vectors[0] + vectors[1] + vectors[2]]
points = np.array(points)
return points
def get_bounding_box(points):
x_min = np.min(points[:,0])
x_max = np.max(points[:,0])
y_min = np.min(points[:,1])
y_max = np.max(points[:,1])
z_min = np.min(points[:,2])
z_max = np.max(points[:,2])
max_range = np.array(
[x_max-x_min, y_max-y_min, z_max-z_min]).max() / 2.0
mid_x = (x_max+x_min) * 0.5
mid_y = (y_max+y_min) * 0.5
mid_z = (z_max+z_min) * 0.5
return [
[mid_x - max_range, mid_x + max_range],
[mid_y - max_range, mid_y + max_range],
[mid_z - max_range, mid_z + max_range]
]
def plot_cube(cube_definition):
points = cube_vertices(cube_definition)
edges = [
[points[0], points[3], points[5], points[1]],
[points[1], points[5], points[7], points[4]],
[points[4], points[2], points[6], points[7]],
[points[2], points[6], points[3], points[0]],
[points[0], points[2], points[4], points[1]],
[points[3], points[6], points[7], points[5]]
]
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
faces = Poly3DCollection(edges, linewidths=1, edgecolors='k')
faces.set_facecolor((0,0,1,0.1))
ax.add_collection3d(faces)
bounding_box = get_bounding_box(points)
ax.set_xlim(bounding_box[0])
ax.set_ylim(bounding_box[1])
ax.set_zlim(bounding_box[2])
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
ax.set_aspect('equal')
cube_definition = cubify_cube_definition([(0,0,0), (0,3,0), (1,1,0.3)])
plot_cube(cube_definition)
这产生以下结果:
使用matplotlib和坐标几何完成
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
def cube_coordinates(edge_len,step_size):
X = np.arange(0,edge_len+step_size,step_size)
Y = np.arange(0,edge_len+step_size,step_size)
Z = np.arange(0,edge_len+step_size,step_size)
temp=list()
for i in range(len(X)):
temp.append((X[i],0,0))
temp.append((0,Y[i],0))
temp.append((0,0,Z[i]))
temp.append((X[i],edge_len,0))
temp.append((edge_len,Y[i],0))
temp.append((0,edge_len,Z[i]))
temp.append((X[i],edge_len,edge_len))
temp.append((edge_len,Y[i],edge_len))
temp.append((edge_len,edge_len,Z[i]))
temp.append((edge_len,0,Z[i]))
temp.append((X[i],0,edge_len))
temp.append((0,Y[i],edge_len))
return temp
edge_len = 10
A=cube_coordinates(edge_len,0.01)
A=list(set(A))
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
A=zip(*A)
X,Y,Z=list(A[0]),list(A[1]),list(A[2])
ax.scatter(X,Y,Z,c='g')
plt.show()