没有VTK的python中的3D数据的插值/子采样

Question

我想要做的是相当简单,但到目前为止我还没有找到一个简单的方法:

我有一个带有浮点值的3D直线网格(因此3个坐标轴-1D numpy数组 - 用于网格单元的中心,3D numpy数组具有相应的形状,每个单元格中心都有一个值),我想插值(或您可以将其整个数组称为子样本数据(例如,尺寸因子为5),并使用线性插值.我见过的所有方法都涉及2D,然后是1D插值或VTK技巧,而不是使用(可移植性).

有人会建议一种方法,相当于在3D阵列中同时取5x5x5单元,平均并返回每个方向5倍的阵列吗？

提前感谢您的任何建议

编辑: 这是数据的样子,'d'是表示3D网格细胞的3D数组.每个单元格都有一个标量浮点值(在我的情况下是压力),'x','y'和'z'是三个1D数组,包含每个单元格的单元格的空间坐标(参见形状以及'x'数组的方式)好像)

In [42]: x.shape
Out[42]: (181L,)

In [43]: y.shape
Out[43]: (181L,)

In [44]: z.shape
Out[44]: (421L,)

In [45]: d.shape
Out[45]: (181L, 181L, 421L)

In [46]: x
Out[46]: 
array([-0.410607  , -0.3927568 , -0.37780656, -0.36527296, -0.35475321,
       -0.34591168, -0.33846866, -0.33219107, -0.32688467, -0.3223876 ,
        ...
        0.34591168,  0.35475321,  0.36527296,  0.37780656,  0.3927568 ,
        0.410607  ])

我想做的是创建一个3D数组,让我们说一个90x90x210的形状(大约缩小2倍),首先从具有上述尺寸的阵列上的轴上对坐标进行二次采样,然后将3D数据"插值"到那个阵列.我不确定'插值'是否是正确的术语.下采样？平均？这是数据的2D切片:

Answer 1

以下是使用scipy.interpolate.griddata在不规则网格上进行3D插值的示例.

import numpy as np
import scipy.interpolate as interpolate
import matplotlib.pyplot as plt


def func(x, y, z):
    return x ** 2 + y ** 2 + z ** 2

# Nx, Ny, Nz = 181, 181, 421
Nx, Ny, Nz = 18, 18, 42

subsample = 2
Mx, My, Mz = Nx // subsample, Ny // subsample, Nz // subsample

# Define irregularly spaced arrays
x = np.random.random(Nx)
y = np.random.random(Ny)
z = np.random.random(Nz)

# Compute the matrix D of shape (Nx, Ny, Nz).
# D could be experimental data, but here I'll define it using func
# D[i,j,k] is associated with location (x[i], y[j], z[k])
X_irregular, Y_irregular, Z_irregular = (
    x[:, None, None], y[None, :, None], z[None, None, :])
D = func(X_irregular, Y_irregular, Z_irregular)

# Create a uniformly spaced grid
xi = np.linspace(x.min(), x.max(), Mx)
yi = np.linspace(y.min(), y.max(), My)
zi = np.linspace(y.min(), y.max(), Mz)
X_uniform, Y_uniform, Z_uniform = (
    xi[:, None, None], yi[None, :, None], zi[None, None, :])

# To use griddata, I need 1D-arrays for x, y, z of length 
# len(D.ravel()) = Nx*Ny*Nz.
# To do this, I broadcast up my *_irregular arrays to each be 
# of shape (Nx, Ny, Nz)
# and then use ravel() to make them 1D-arrays
X_irregular, Y_irregular, Z_irregular = np.broadcast_arrays(
    X_irregular, Y_irregular, Z_irregular)
D_interpolated = interpolate.griddata(
    (X_irregular.ravel(), Y_irregular.ravel(), Z_irregular.ravel()),
    D.ravel(),
    (X_uniform, Y_uniform, Z_uniform),
    method='linear')

print(D_interpolated.shape)
# (90, 90, 210)

# Make plots
fig, ax = plt.subplots(2)

# Choose a z value in the uniform z-grid
# Let's take the middle value
zindex = Mz // 2
z_crosssection = zi[zindex]

# Plot a cross-section of the raw irregularly spaced data
X_irr, Y_irr = np.meshgrid(sorted(x), sorted(y))
# find the value in the irregular z-grid closest to z_crosssection
z_near_cross = z[(np.abs(z - z_crosssection)).argmin()]
ax[0].contourf(X_irr, Y_irr, func(X_irr, Y_irr, z_near_cross))
ax[0].scatter(X_irr, Y_irr, c='white', s=20)   
ax[0].set_title('Cross-section of irregular data')
ax[0].set_xlim(x.min(), x.max())
ax[0].set_ylim(y.min(), y.max())

# Plot a cross-section of the Interpolated uniformly spaced data
X_unif, Y_unif = np.meshgrid(xi, yi)
ax[1].contourf(X_unif, Y_unif, D_interpolated[:, :, zindex])
ax[1].scatter(X_unif, Y_unif, c='white', s=20)
ax[1].set_title('Cross-section of downsampled and interpolated data')
ax[1].set_xlim(x.min(), x.max())
ax[1].set_ylim(y.min(), y.max())

plt.show()