Interpolating 3d data at a single point in space (Python 2.7) - python-2.7

Question

I have a point cloud in 4 dimensions, where each point in the cloud has a location and a value (x,y,z,Value). In addition, I have a 'special' point, S0, within the 3d point cloud; I've used this example to find the closest 10 points in the cloud, relative to S0. Now, I have a numpy array for each of the 10 closest points and their values. How can I interpolate these 10 points, to find the interpolated value at point S0? Example code is shown below:
import numpy as np
import matplotlib.pyplot as plt
numpoints = 20
linexs = 320
lineys = 40
linezs = 60
linexe = 20
lineye = 20
lineze = 0
# Create vectors of points
xpts = np.linspace(linexs, linexe, numpoints)
ypts = np.linspace(lineys, lineye, numpoints)
zpts = np.linspace(linezs, lineze, numpoints)
lin = np.dstack((xpts,ypts,zpts))
# Image line of points
fig = plt.figure()
ax = fig.add_subplot(211, projection='3d')
ax.set_xlim(0,365); ax.set_ylim(-85, 85); ax.set_zlim(0, 100)
ax.plot_wireframe(xpts, ypts, zpts)
ax.view_init(elev=12, azim=78)
def randrange(n, vmin, vmax):
return (vmax - vmin)*np.random.rand(n) + vmin
n = 10
for n in range(21):
xs = randrange(n, 0, 350)
ys = randrange(n, -75, 75)
zs = randrange(n, 0, 100)
ax.scatter(xs, ys, zs)
dat = np.dstack((xs,ys,zs))
ax.set_xlabel('X Label')
ax.set_xlim(0,350)
ax.set_ylabel('Y Label')
ax.set_ylim(-75,75)
ax.set_zlabel('Z Label')
ax.set_zlim(0,100)
ax = fig.add_subplot(212, projection='3d')
ax.set_xlim(0,365); ax.set_ylim(-85, 85); ax.set_zlim(0, 100)
ax.plot_wireframe(xpts,ypts,zpts)
ax.view_init(elev=12, azim=78)
plt.show()
dist = []
# Calculate distance from first point to all other points in cloud
for l in range(len(xpts)):
aaa = lin[0][0]-dat
dist.append(np.sqrt(aaa[0][l][0]**2+aaa[0][l][1]**2+aaa[0][l][2]**2))
full = np.dstack((dat,dist))
aaa = full[0][full[0][:,3].argsort()]
print(aaa[0:10])

Answer 1

A basic example. Note that the meshgrid is not needed for the interpolation, but only to make a fast ufunc to generate an example function A=f(x,y,z), here A=x+y+z.
from scipy.interpolate import interpn
import numpy as np
#make up a regular 3d grid
X=np.linspace(-5,5,11)
Y=np.linspace(-5,5,11)
Z=np.linspace(-5,5,11)
xv,yv,zv = np.meshgrid(X,Y,Z)
# make up a function
# see http://docs.scipy.org/doc/numpy/reference/ufuncs.html
A = np.add(xv,np.add(yv,zv))
#this one is easy enough for us to know what to expect at (.5,.5,.5)
# usage : interpn(points, values, xi, method='linear', bounds_error=True, fill_value=nan)
interpn((X,Y,Z),A,[0.5,0.5,0.5])
Output:
array([ 1.5])
If you pass in an array of points of interest, it will give you multiple answers.