使用mplot3d绘制凹面形状(镜头焦点)

Question

我目前正在尝试使用matplotlib来可视化镜头的焦距形状，特别是mplot3d工具箱。我将椭圆拟合到一组不同焦距的显微镜图像上，作为主要major和次要minor半径，以及这些椭圆的旋转角ang。由此，我生成了包含椭圆坐标的x、y和z数组，如下所示。

i = 100
omega = np.linspace(0, 2 * np.pi, i, endpoint=True)

x = [major * np.cos(omega) * np.cos(np.deg2rad(ang + 90)) - minor * np.sin(omega) * np.sin(np.deg2rad(ang + 90)) for major, minor, ang in zip(maj_avg, min_avg, ang_avg)]
y = [major * np.cos(omega) * np.sin(np.deg2rad(ang + 90)) + minor * np.sin(omega) * np.cos(np.deg2rad(ang + 90)) for major, minor, ang in zip(maj_avg, min_avg, ang_avg)]
z = [np.full(i, zi) for zi in zs]

如果我现在在3D空间中绘制单个椭圆，一切都会按预期进行。

fig = plt.figure(figsize=(16, 12))
ax = fig.add_subplot(111, projection='3d')
for x_arr, y_arr, z_arr in zip(x, y, z):
    ax.plot(x_arr, y_arr, z_arr)

plt.show()

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我正在尝试做的是从这个数据集生成一个曲面图，它显示了透镜的焦点形状。到目前为止，我尝试了plot_surface和meshgrid/griddata，如下所示：

xi = np.arange(-300, 300, 0.1)
yi = np.arange(-300, 300, 0.1)

xgrid, ygrid = np.meshgrid(xi, yi)
zgrid = griddata(np.ravel(x), np.ravel(y), np.ravel(z), xi, yi, interp='linear')

fig = plt.figure(figsize=(16, 12))
ax = fig.add_subplot(111, projection='3d')

surf = ax.plot_surface(xgrid, ygrid, zgrid)
plt.show()

​

​

同样，plot_trisurf也给出了同样不令人满意的结果：

triang = mtri.Triangulation(np.ravel(x), np.ravel(y))

fig = plt.figure(figsize=(16, 12))
ax = fig.add_subplot(111, projection='3d')
ax.plot_trisurf(triang, np.ravel(z), cmap=plt.cm.CMRmap)
plt.show()

​

​

有人能建议一种方法在曲面图中正确显示我的数据集的高z区域吗？

Answer 1

问题是，您正在尝试插值栅格上的参数曲线。由于要绘制的形状是非双射的，非猜想的，所以你会得到一个完全混乱的图形。

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您可以直接绘制这些点，而不是尝试插值这些点。

X = np.array(x)
Y = np.array(y)
Z = np.array(z)
ax.plot_surface(X,Y,Z, cmap="RdYlBu")
plt.show()

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完整的复制示例：

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np

maj_avg = 50*(np.linspace(0,1,20)-0.6)**2+50
min_avg = 60*(np.linspace(0,1,20)-0.7)**2+60
ang_avg = np.linspace(0,90,20)
zs = np.arange(0,40,2)

i = 100
omega = np.linspace(0, 2 * np.pi, i, endpoint=True)

x = [major * np.cos(omega) * np.cos(np.deg2rad(ang + 90)) \
     - minor * np.sin(omega) * np.sin(np.deg2rad(ang + 90)) \
     for major, minor, ang in zip(maj_avg, min_avg, ang_avg)]
y = [major * np.cos(omega) * np.sin(np.deg2rad(ang + 90)) \
     + minor * np.sin(omega) * np.cos(np.deg2rad(ang + 90)) \
     for major, minor, ang in zip(maj_avg, min_avg, ang_avg)]
z = [np.full(i, zi) for zi in zs]


fig = plt.figure(figsize=(16, 12))
ax = fig.add_subplot(111, projection='3d')
#for x_arr, y_arr, z_arr in zip(x, y, z):
#    ax.plot(x_arr, y_arr, z_arr)

X = np.array(x)
Y = np.array(y)
Z = np.array(z)
ax.plot_surface(X,Y,Z, cmap="RdYlBu")

plt.show()