Interpolate in 3D space using numpy

Question

I was wondering if there is a function to interpolate in 3D space. Say for example i have a matrix with x,y,z coordinates. Is there a way i can interpolate and calculate the z coordinate for a given x and y. For example:

A=[1,3,5,
   2,3,4
   4,4,8
   3,4,5]

And i need to calculate the z coordinate when x=3 y=3,5

Answer 1

Yes, scipy.interpolate provides functions for interpolation on precomputed grids as well as objects that expose __call(x)__ function to compute values on demand

Consider the following example

import numpy as np
from scipy import interpolate

A=[1,3,5,
   2,3,4,
   4,4,8,
   3,4,5]
xs = A[0::3]
ys = A[1::3]
zs = A[2::3]

points=np.zeros((len(xs),2))
values=np.zeros((len(xs)))
points[:,0] = xs
points[:,1] = ys
values[:] = zs

interpolator = interpolate.CloughTocher2DInterpolator(points,values)
z = interpolator(3,3.5)
print(z)

This code should output the value

5.489419430226453

It first converts the input list of n*3 values into three numpy arrays xs, ys, and zs. And then creates the interpolator object using the points and values arrays created at the previous stage.