带 2D 投影的 3D 线框图：空间组织和投影频率
3D wireframe plot with 2D projections: Spatial organiszation & frequency of projection
我正在处理由线框显示的 3D 图，其中 2D 图分别投影在 x、y 和 z 表面上。您可以在下面找到一个最小示例。
我有两个问题：
- 使用 contourf，每个 x=10、x=20... 或 y=10、y=20... 的 2D 图都显示在图墙上。是否有可能分别定义显示等高线图的 x 或 y？例如，如果我只想将 y = 0.5 的 xz 等值线图镜像到墙上？
补充：为了显示我所说的“2D 图”，我将代码中的“contourf”更改为“contour”，并将生成的图添加到这个问题中。在这里，您现在可以看到不同 y 值的 xz 线，都偏移到 y=90。如果我不想拥有所有的线，而只想要其中的两条用于定义的 y 值怎么办？
3D_plot_with_2D_contours
- 正如您在最小示例中看到的那样，2D 等高线图在视觉上覆盖了线框 3D 图。通过使用 alpha=0.5 增加透明度，我可以增加 2D 轮廓的透明度以至少看到线框，但它在视觉上仍然是错误的。是否可以正确排序对象？
import matplotlib.pyplot as plt,numpy as np
import pylab as pl
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt,numpy as np
plt.clf()
fig = plt.figure(1,figsize=(35,17),dpi=600,facecolor='w',edgecolor='k')
fig.set_size_inches(10.5,8)
ax = fig.gca(projection='3d')
X, Y, Z = axes3d.get_test_data(0.05)
Xnew = X + 50
Ynew = Y + 50
cset = ax.contourf(Xnew, Ynew, Z, zdir='z', offset=-100, cmap=plt.cm.coolwarm, alpha=0.5)
cset = ax.contourf(Xnew, Ynew, Z, zdir='x', offset=10, cmap=plt.cm.coolwarm, alpha=0.5)
cset = ax.contourf(Xnew, Ynew, Z, zdir='y', offset=90, cmap=plt.cm.coolwarm, alpha = 0.5)
ax.plot_wireframe(Xnew, Ynew, Z, rstride=5, cstride=5, color='black')
Z=Z-Z.min()
Z=Z/Z.max()
from scipy.ndimage.interpolation import zoom
Xall=zoom(Xnew,5)
Yall=zoom(Ynew,5)
Z=zoom(Z,5)
ax.set_xlim(10, 90)
ax.set_ylim(10, 90)
ax.set_zlim(-100, 100)
ax.tick_params(axis='z', which='major', pad=10)
ax.set_xlabel('X',labelpad=10)
ax.set_ylabel('Y',labelpad=10)
ax.set_zlabel('Z',labelpad=17)
ax.view_init(elev=35., azim=-70)
fig.tight_layout()
plt.show()
补充 2：这是我正在使用的实际代码。然而，原始数据隐藏在 csv 文件中，这些文件太大而无法包含在最小示例中。这就是为什么最初用测试数据替换它们的原因。然而，也许实际的代码仍然有帮助。
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt,numpy as np
import pylab as pl
from matplotlib.markers import MarkerStyle
import csv
with open("X.csv", 'r') as f:
X = list(csv.reader(f, delimiter=";"))
import numpy as np
X = np.array(X[1:], dtype=np.float)
import csv
with open("Z.csv", 'r') as f:
Z = list(csv.reader(f, delimiter=";"))
import numpy as np
Z = np.array(Z[1:], dtype=np.float)
Y = [[7,7.1,7.2,7.3,7.4,7.5,7.6,7.7,7.8,7.9,8,8.1,8.2,8.3,8.4,8.5,8.6,8.7,8.8,8.9,9]]
Xall = np.repeat(X[:],21,axis=1)
Yall = np.repeat(Y[:],30,axis=0)
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt,numpy as np
plt.clf()
fig = plt.figure(1,figsize=(35,17),dpi=600,facecolor='w',edgecolor='k')
fig.set_size_inches(10.5,8)
ax = fig.gca(projection='3d')
cset = ax.contourf(Xall, Yall, Z, 2, zdir='x', offset=0, cmap=plt.cm.coolwarm, shade = False, edgecolor='none', alpha=0.5)
cset = ax.contourf(Xall, Yall, Z, 2, zdir='y', offset=9, cmap=plt.cm.coolwarm, shade = False, edgecolor='none', alpha=0.5)
ax.plot_wireframe(Xall, Yall, Z, rstride=1, cstride=1, color='black')
Z=Z-Z.min()
Z=Z/Z.max()
from scipy.ndimage.interpolation import zoom
Xall=zoom(Xall,5)
Yall=zoom(Yall,5)
Z=zoom(Z,5)
cset = ax.plot_surface(Xall, Yall, np.zeros_like(Z)-0,facecolors=plt.cm.coolwarm(Z),shade=False,alpha=0.5,linewidth=False)
ax.set_xlim(-0.5, 31)
ax.set_ylim(6.9, 9.1)
ax.set_zlim(0, 500)
labelsx = [item.get_text() for item in ax.get_xticklabels()]
empty_string_labelsx = ['']*len(labelsx)
ax.set_xticklabels(empty_string_labelsx)
labelsy = [item.get_text() for item in ax.get_yticklabels()]
empty_string_labelsy = ['']*len(labelsy)
ax.set_yticklabels(empty_string_labelsy)
labelsz = [item.get_text() for item in ax.get_zticklabels()]
empty_string_labelsz = ['']*len(labelsz)
ax.set_zticklabels(empty_string_labelsz)
import matplotlib.ticker as ticker
ax.xaxis.set_major_locator(ticker.MultipleLocator(5))
ax.xaxis.set_minor_locator(ticker.MultipleLocator(1))
ax.yaxis.set_major_locator(ticker.MultipleLocator(0.5))
ax.yaxis.set_minor_locator(ticker.MultipleLocator(0.25))
ax.zaxis.set_major_locator(ticker.MultipleLocator(100))
ax.zaxis.set_minor_locator(ticker.MultipleLocator(50))
ax.tick_params(axis='z', which='major', pad=10)
ax.set_xlabel('X',labelpad=5,fontsize=15)
ax.set_ylabel('Y',labelpad=5,fontsize=15)
ax.set_zlabel('Z',labelpad=5,fontsize=15)
ax.view_init(elev=35., azim=-70)
fig.tight_layout()
plt.show()
（问题 1 的答案）要绘制曲面与指定平面（y=-20 和 y=20）之间的交点，需要找到 Y[?]=-20 和 20。通过检查，发现Y[100]=20, Y[20]=-20.
绘制相交线的相关代码：
# By inspection, Y[100]=20, Y[20]=-20
ax.plot3D(X[100], Y[100], Z[100], color='red', lw=6) # line-1 at y=20
ax.plot3D(X[20], Y[20], Z[20], color='green', lw=6) # line-2 at y=-20
# Project them on Z=-100 plane
ax.plot3D(X[100], Y[100], -100, color='red', lw=3) # projection of Line-1
ax.plot3D(X[20], Y[20], -100, color='green', lw=3) # projection of Line-2
输出图：
（问题 2 的答案）从曲面图中突出线框以获得更好的绘图。曲面图必须部分透明，这是通过设置选项 alpha=0.6 实现的。相关代码如下
Z1 = Z-Z.min()
Z1 = Z1/Z.max()
Xall = zoom(X,3)
Yall = zoom(Y,3)
Zz = zoom(Z1, 3)
surf = ax.plot_surface(Xall, Yall, Zz, rstride=10, cstride=10,
facecolors = cm.jet(Zz/np.amax(Zz)),
linewidth=0, antialiased=True,
alpha= 0.6)
# Wireframe
ax.plot_wireframe(X, Y, Z, rstride=5, cstride=5, color='black', alpha=1, lw=0.8)
剧情是：
其他可能的答案。
此代码演示
- 表面图及其对应的线框
- 在指定的 x 和 y 值处创建数据及其 3d 线图（覆盖在 1 中的表面上）
- 3d 线（在 2 中）在框架墙上的投影
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
from scipy import interpolate
import numpy as np
# use the test data for plotting
fig = plt.figure(1, figsize=(6,6), facecolor='w', edgecolor='gray')
ax = fig.gca(projection='3d')
X, Y, Z = axes3d.get_test_data(0.1) #get 3d data at appropriate density
# create an interpolating function
# can take a long time if data is too large
f1 = interpolate.interp2d(X, Y, Z, kind='linear')
# in general, one can use a set of other X,Y,Z that cover a surface
# preferably, (X,Y) are in grid arrangement
# make up a new set of 3d data to plot
# ranges of x1, and y1 will be inside (X,Y) of the data obtained above
# related grid, x1g,y1g,z1g will be obtained from meshgrid and the interpolated function
x1 = np.linspace(-15,15,10)
y1 = np.linspace(-15,15,10)
x1g, y1g = np.meshgrid(x1, y1)
z1g = f1(x1, y1) #dont use (x1g, y1g)
# prep data for 3d line on the surface (X,Y,Z) at x=7.5
n = 12
x_pf = 7.5
x5 = x_pf*np.ones(n)
y5 = np.linspace(-15, 15, n)
z5 = f1(x_pf, y5)
# x5,y5,z5 can be used to plot 3d line on the surface (X,Y,Z)
# prep data for 3d line on the surface (X,Y,Z) at y=6
y_pf = 6
x6 = np.linspace(-15, 15, n)
y6 = x_pf*np.ones(n)
z6 = f1(x6, y_pf)
# x6,y6,z6 can be used to plot 3d line on the surface (X,Y,Z)
ax = fig.gca(projection='3d')
ax.plot_surface(x1g, y1g, z1g, alpha=0.25)
ax.plot_wireframe(x1g, y1g, z1g, rstride=2, cstride=2, color='black', zorder=10, alpha=1, lw=0.8)
# 3D lines that follow the surface
ax.plot(x5,y5,z5.flatten(), color='red', lw=4)
ax.plot(x6,y6,z6.flatten(), color='green', lw=4)
# projections of 3d curves
# project red and green lines to the walls
ax.plot(-15*np.ones(len(y5)), y5, z5.flatten(), color='red', lw=4, linestyle=':', alpha=0.6)
ax.plot(x6, 15*np.ones(len(x6)), z6.flatten(), color='green', lw=4, linestyle=':', alpha=0.6)
# projections on other sides (become vertical lines)
# change to if True, to plot these
if False:
ax.plot(x5, 15*np.ones(len(x5)), z5.flatten(), color='red', lw=4, alpha=0.3)
ax.plot(-15*np.ones(len(x6)), y6, z6.flatten(), color='green', lw=4, alpha=0.3)
ax.set_title("Projections of 3D lines")
# set limits
ax.set_xlim(-15, 15.5)
ax.set_ylim(-15.5, 15)
plt.show();
我正在处理由线框显示的 3D 图，其中 2D 图分别投影在 x、y 和 z 表面上。您可以在下面找到一个最小示例。
我有两个问题：
- 使用 contourf，每个 x=10、x=20... 或 y=10、y=20... 的 2D 图都显示在图墙上。是否有可能分别定义显示等高线图的 x 或 y？例如，如果我只想将 y = 0.5 的 xz 等值线图镜像到墙上？
补充：为了显示我所说的“2D 图”，我将代码中的“contourf”更改为“contour”，并将生成的图添加到这个问题中。在这里，您现在可以看到不同 y 值的 xz 线，都偏移到 y=90。如果我不想拥有所有的线，而只想要其中的两条用于定义的 y 值怎么办？
3D_plot_with_2D_contours
- 正如您在最小示例中看到的那样，2D 等高线图在视觉上覆盖了线框 3D 图。通过使用 alpha=0.5 增加透明度，我可以增加 2D 轮廓的透明度以至少看到线框，但它在视觉上仍然是错误的。是否可以正确排序对象？
import matplotlib.pyplot as plt,numpy as np
import pylab as pl
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt,numpy as np
plt.clf()
fig = plt.figure(1,figsize=(35,17),dpi=600,facecolor='w',edgecolor='k')
fig.set_size_inches(10.5,8)
ax = fig.gca(projection='3d')
X, Y, Z = axes3d.get_test_data(0.05)
Xnew = X + 50
Ynew = Y + 50
cset = ax.contourf(Xnew, Ynew, Z, zdir='z', offset=-100, cmap=plt.cm.coolwarm, alpha=0.5)
cset = ax.contourf(Xnew, Ynew, Z, zdir='x', offset=10, cmap=plt.cm.coolwarm, alpha=0.5)
cset = ax.contourf(Xnew, Ynew, Z, zdir='y', offset=90, cmap=plt.cm.coolwarm, alpha = 0.5)
ax.plot_wireframe(Xnew, Ynew, Z, rstride=5, cstride=5, color='black')
Z=Z-Z.min()
Z=Z/Z.max()
from scipy.ndimage.interpolation import zoom
Xall=zoom(Xnew,5)
Yall=zoom(Ynew,5)
Z=zoom(Z,5)
ax.set_xlim(10, 90)
ax.set_ylim(10, 90)
ax.set_zlim(-100, 100)
ax.tick_params(axis='z', which='major', pad=10)
ax.set_xlabel('X',labelpad=10)
ax.set_ylabel('Y',labelpad=10)
ax.set_zlabel('Z',labelpad=17)
ax.view_init(elev=35., azim=-70)
fig.tight_layout()
plt.show()
补充 2：这是我正在使用的实际代码。然而，原始数据隐藏在 csv 文件中，这些文件太大而无法包含在最小示例中。这就是为什么最初用测试数据替换它们的原因。然而，也许实际的代码仍然有帮助。
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt,numpy as np
import pylab as pl
from matplotlib.markers import MarkerStyle
import csv
with open("X.csv", 'r') as f:
X = list(csv.reader(f, delimiter=";"))
import numpy as np
X = np.array(X[1:], dtype=np.float)
import csv
with open("Z.csv", 'r') as f:
Z = list(csv.reader(f, delimiter=";"))
import numpy as np
Z = np.array(Z[1:], dtype=np.float)
Y = [[7,7.1,7.2,7.3,7.4,7.5,7.6,7.7,7.8,7.9,8,8.1,8.2,8.3,8.4,8.5,8.6,8.7,8.8,8.9,9]]
Xall = np.repeat(X[:],21,axis=1)
Yall = np.repeat(Y[:],30,axis=0)
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt,numpy as np
plt.clf()
fig = plt.figure(1,figsize=(35,17),dpi=600,facecolor='w',edgecolor='k')
fig.set_size_inches(10.5,8)
ax = fig.gca(projection='3d')
cset = ax.contourf(Xall, Yall, Z, 2, zdir='x', offset=0, cmap=plt.cm.coolwarm, shade = False, edgecolor='none', alpha=0.5)
cset = ax.contourf(Xall, Yall, Z, 2, zdir='y', offset=9, cmap=plt.cm.coolwarm, shade = False, edgecolor='none', alpha=0.5)
ax.plot_wireframe(Xall, Yall, Z, rstride=1, cstride=1, color='black')
Z=Z-Z.min()
Z=Z/Z.max()
from scipy.ndimage.interpolation import zoom
Xall=zoom(Xall,5)
Yall=zoom(Yall,5)
Z=zoom(Z,5)
cset = ax.plot_surface(Xall, Yall, np.zeros_like(Z)-0,facecolors=plt.cm.coolwarm(Z),shade=False,alpha=0.5,linewidth=False)
ax.set_xlim(-0.5, 31)
ax.set_ylim(6.9, 9.1)
ax.set_zlim(0, 500)
labelsx = [item.get_text() for item in ax.get_xticklabels()]
empty_string_labelsx = ['']*len(labelsx)
ax.set_xticklabels(empty_string_labelsx)
labelsy = [item.get_text() for item in ax.get_yticklabels()]
empty_string_labelsy = ['']*len(labelsy)
ax.set_yticklabels(empty_string_labelsy)
labelsz = [item.get_text() for item in ax.get_zticklabels()]
empty_string_labelsz = ['']*len(labelsz)
ax.set_zticklabels(empty_string_labelsz)
import matplotlib.ticker as ticker
ax.xaxis.set_major_locator(ticker.MultipleLocator(5))
ax.xaxis.set_minor_locator(ticker.MultipleLocator(1))
ax.yaxis.set_major_locator(ticker.MultipleLocator(0.5))
ax.yaxis.set_minor_locator(ticker.MultipleLocator(0.25))
ax.zaxis.set_major_locator(ticker.MultipleLocator(100))
ax.zaxis.set_minor_locator(ticker.MultipleLocator(50))
ax.tick_params(axis='z', which='major', pad=10)
ax.set_xlabel('X',labelpad=5,fontsize=15)
ax.set_ylabel('Y',labelpad=5,fontsize=15)
ax.set_zlabel('Z',labelpad=5,fontsize=15)
ax.view_init(elev=35., azim=-70)
fig.tight_layout()
plt.show()
（问题 1 的答案）要绘制曲面与指定平面（y=-20 和 y=20）之间的交点，需要找到 Y[?]=-20 和 20。通过检查，发现Y[100]=20, Y[20]=-20.
绘制相交线的相关代码：
# By inspection, Y[100]=20, Y[20]=-20
ax.plot3D(X[100], Y[100], Z[100], color='red', lw=6) # line-1 at y=20
ax.plot3D(X[20], Y[20], Z[20], color='green', lw=6) # line-2 at y=-20
# Project them on Z=-100 plane
ax.plot3D(X[100], Y[100], -100, color='red', lw=3) # projection of Line-1
ax.plot3D(X[20], Y[20], -100, color='green', lw=3) # projection of Line-2
输出图：
（问题 2 的答案）从曲面图中突出线框以获得更好的绘图。曲面图必须部分透明，这是通过设置选项 alpha=0.6 实现的。相关代码如下
Z1 = Z-Z.min()
Z1 = Z1/Z.max()
Xall = zoom(X,3)
Yall = zoom(Y,3)
Zz = zoom(Z1, 3)
surf = ax.plot_surface(Xall, Yall, Zz, rstride=10, cstride=10,
facecolors = cm.jet(Zz/np.amax(Zz)),
linewidth=0, antialiased=True,
alpha= 0.6)
# Wireframe
ax.plot_wireframe(X, Y, Z, rstride=5, cstride=5, color='black', alpha=1, lw=0.8)
剧情是：
其他可能的答案。
此代码演示
- 表面图及其对应的线框
- 在指定的 x 和 y 值处创建数据及其 3d 线图（覆盖在 1 中的表面上）
- 3d 线（在 2 中）在框架墙上的投影
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
from scipy import interpolate
import numpy as np
# use the test data for plotting
fig = plt.figure(1, figsize=(6,6), facecolor='w', edgecolor='gray')
ax = fig.gca(projection='3d')
X, Y, Z = axes3d.get_test_data(0.1) #get 3d data at appropriate density
# create an interpolating function
# can take a long time if data is too large
f1 = interpolate.interp2d(X, Y, Z, kind='linear')
# in general, one can use a set of other X,Y,Z that cover a surface
# preferably, (X,Y) are in grid arrangement
# make up a new set of 3d data to plot
# ranges of x1, and y1 will be inside (X,Y) of the data obtained above
# related grid, x1g,y1g,z1g will be obtained from meshgrid and the interpolated function
x1 = np.linspace(-15,15,10)
y1 = np.linspace(-15,15,10)
x1g, y1g = np.meshgrid(x1, y1)
z1g = f1(x1, y1) #dont use (x1g, y1g)
# prep data for 3d line on the surface (X,Y,Z) at x=7.5
n = 12
x_pf = 7.5
x5 = x_pf*np.ones(n)
y5 = np.linspace(-15, 15, n)
z5 = f1(x_pf, y5)
# x5,y5,z5 can be used to plot 3d line on the surface (X,Y,Z)
# prep data for 3d line on the surface (X,Y,Z) at y=6
y_pf = 6
x6 = np.linspace(-15, 15, n)
y6 = x_pf*np.ones(n)
z6 = f1(x6, y_pf)
# x6,y6,z6 can be used to plot 3d line on the surface (X,Y,Z)
ax = fig.gca(projection='3d')
ax.plot_surface(x1g, y1g, z1g, alpha=0.25)
ax.plot_wireframe(x1g, y1g, z1g, rstride=2, cstride=2, color='black', zorder=10, alpha=1, lw=0.8)
# 3D lines that follow the surface
ax.plot(x5,y5,z5.flatten(), color='red', lw=4)
ax.plot(x6,y6,z6.flatten(), color='green', lw=4)
# projections of 3d curves
# project red and green lines to the walls
ax.plot(-15*np.ones(len(y5)), y5, z5.flatten(), color='red', lw=4, linestyle=':', alpha=0.6)
ax.plot(x6, 15*np.ones(len(x6)), z6.flatten(), color='green', lw=4, linestyle=':', alpha=0.6)
# projections on other sides (become vertical lines)
# change to if True, to plot these
if False:
ax.plot(x5, 15*np.ones(len(x5)), z5.flatten(), color='red', lw=4, alpha=0.3)
ax.plot(-15*np.ones(len(x6)), y6, z6.flatten(), color='green', lw=4, alpha=0.3)
ax.set_title("Projections of 3D lines")
# set limits
ax.set_xlim(-15, 15.5)
ax.set_ylim(-15.5, 15)
plt.show();