How to interpolate scattered data with SciPy

Measurements collected along survey lines, sensor routes, or irregular experiment locations rarely align as a rectangular grid. SciPy can estimate a value at a new coordinate directly from those scattered samples while preserving their two-dimensional geometry.

The scipy.interpolate.griddata() function accepts point coordinates with shape (n, D), one sample value per point, and separate query coordinates. Linear interpolation triangulates the input with Qhull and evaluates a piecewise plane within each simplex; data already arranged on a regular grid belongs with RegularGridInterpolator instead.

Linear interpolation covers only the convex hull of the measured coordinates, so a query beyond that boundary returns NaN by default. The known plane in the sample data supplies exact inside-hull values, while the outside point confirms that missing coverage is detected rather than silently extrapolated.

1. Create scattered_data_interpolate.py with the scattered coordinate and value arrays.

   scattered_data_interpolate.py

   import numpy as np
   from scipy.interpolate import griddata
    
   np.set_printoptions(precision=2, suppress=True)
    
   points = np.array([
       [0.0, 0.0],
       [2.0, 0.0],
       [0.0, 2.0],
       [2.0, 2.0],
       [0.8, 0.6],
       [1.5, 1.2],
   ])
   values = 3 * points[:, 0] - 2 * points[:, 1] + 4

   The affine relation z = 3*x - 2*y + 4 gives each scattered point a known value that linear interpolation can reproduce inside the hull.

2. Append the query coordinates and linear interpolation call to scattered_data_interpolate.py.

   query_points = np.array([
       [0.5, 0.5],
       [1.25, 0.75],
       [1.8, 1.6],
       [2.4, 1.0],
   ])
   interpolated = griddata(points, values, query_points, method="linear")

   The first three query points lie inside the measured square. The fourth point lies beyond its right edge and should remain NaN.

3. Append the inside-hull and outside-hull verification to scattered_data_interpolate.py.

   expected = 3 * query_points[:3, 0] - 2 * query_points[:3, 1] + 4
   inside_match = np.allclose(interpolated[:3], expected)
   outside_is_nan = np.isnan(interpolated[3])
    
   print("query points:")
   print(query_points)
   print("interpolated:", interpolated)
   print("inside values verified:", inside_match)
   print("outside hull detected:", outside_is_nan)
    
   if not inside_match or not outside_is_nan:
       raise SystemExit("interpolation verification failed")

   np.allclose() checks the interpolated values against the known plane, and the final condition exits with an error if either boundary check fails.

4. Run scattered_data_interpolate.py to verify the interpolation result.

   $ python3 scattered_data_interpolate.py
   query points:
   [[0.5  0.5 ]
    [1.25 0.75]
    [1.8  1.6 ]
    [2.4  1.  ]]
   interpolated: [4.5  6.25 6.2   nan]
   inside values verified: True
   outside hull detected: True