我的目标是使用python插值3D向量场
import numpy as np
import matplotlib.pyplot as plt
# For interpolation
from scipy.interpolate import RegularGridInterpolator
#%% VECTOR FIELD
xx, yy, zz = np.meshgrid(np.arange(-0.8, 1, 0.2),
np.arange(-0.8, 1, 0.2),
np.arange(-0.8, 1, 0.8))
uu = np.sin(np.pi * xx) * np.cos(np.pi * yy) * np.cos(np.pi * zz)
vv = -np.cos(np.pi * xx) * np.sin(np.pi * yy) * np.cos(np.pi * zz)
ww = (np.sqrt(2.0 / 3.0) * np.cos(np.pi * xx) * np.cos(np.pi * yy) *
np.sin(np.pi * zz))
# Ravel -> make 1D lists
x = np.ravel(xx)
y = np.ravel(yy)
z = np.ravel(zz)
u = np.ravel(uu)
v = np.ravel(vv)
w = np.ravel(ww)
#%% INTERPOLATION FUNCTION
def interpolate_field(x,y,z,u,v,w,new_points):
x = np.unique(x)
y = np.unique(y)
z = np.unique(z)
u = np.reshape(u, (len(x), len(y), len(z)))
v = np.reshape(u, (len(x), len(y), len(z)))
w = np.reshape(u, (len(x), len(y), len(z)))
u_int_f = RegularGridInterpolator((x, y, z), u)
v_int_f = RegularGridInterpolator((x, y, z), v)
w_int_f = RegularGridInterpolator((x, y, z), w)
u_int = u_int_f(new_points)
v_int = v_int_f(new_points)
w_int = w_int_f(new_points)
return u_int, v_int, w_int
#%% EVALUATE INTERPOLATION FUNCTION
new_grid = np.meshgrid(
np.linspace(np.min(x), np.max(x), 20),
np.linspace(np.min(y), np.max(y), 20),
np.linspace(np.min(z), np.max(z), 3)
, indexing="xy")
# create list of new_points
new_points = np.vstack(list(map(np.ravel, new_grid))).T
# get vector field values at new points
uint, vint, wint = interpolate_field(x,y,z,u,v,w,new_points)
new_points = np.array(new_points)
xn = new_points[:,0]
yn = new_points[:,1]
zn = new_points[:,2]
# PLOT
fig = plt.figure(dpi=300)
ax = fig.gca(projection='3d')
ax.quiver(xn, yn, zn, uint, vint, wint, length=0.1)
plt.show()
正如您所看到的,插值函数出现了一些问题,因为生成的矢量图根本没有显示与原始图相同的行为。我非常感谢你帮助我理解我做错了什么
下面是一种使用
RegularGridInterpolator
的方法:生成的绘图如下所示:
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