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I have a number of height values across a grid, specified in a series of lists:

[3, 1, -2, -3, -3] # x = 0m 
[2, -7, -14, -30, -39] # x = 10m
[46, 22, 5, -2, -8] # x = 20m

The example above shows a 40m x 20m grid in the form 

[x=0y=0, x=0y=10...][x=10y=0, x=10y=10...] etc.

I need to calculate the height at a specific x,y coordinate. I have looked at various interpolate functions and example but can't make any sense out of them - please help!

An example would be the height at x = 5m, y = 5m in teh grid above, which would be in the middle of the values 3, 1 2 and -7 (-1ish?)

Thanks

tp503
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  • Is it what you need? https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.interpolate.interp2d.html –  Jan 03 '19 at 12:34
  • You may want to check [this post](https://stackoverflow.com/questions/37872171/how-can-i-perform-two-dimensional-interpolation-using-scipy) – Cedric Zoppolo Jan 03 '19 at 17:49

3 Answers3

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You can use scipy.interpolate.interp2d. The code below should do the job:

import numpy as np
from scipy.interpolate import interp2d

# Original data (e.g. measurements)
a = [3, 1, -2, -3, -3]
b = [2, -7, -14, -30, -39]
c = [46, 22, 5, -2, -8]

x = [0, 10, 20]             # x-coordinates
y = [0, 10, 20, 30, 40]     # y-coordinates

# Organise data in matrix
z = np.vstack([a, b, c]).T

# Create interpolation function
f_z = interp2d(x, y, z)

# Desired x/y values
x_interp = 5
y_interp = 5

# Collect interpolated z-value
z_interp = f_z(x_interp, y_interp)
print(z_interp)  # (result: [-0.25])
MPA
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Solution: Transform into 2D array

import numpy as np

a = [3, 1, -2, -3, -3] # x = 0m 
b = [2, -7, -14, -30, -39] # x = 10m
c = [46, 22, 5, -2, -8] # x = 20m

all_lists = [a,b,c]


grid = np.vstack(all_lists) # Edit: thanks @jochen for better code

>>print(grid.shape)
(3, 5)

Now you can access grid via x,y coordinates

grid[1,1] and etc

Based on this, you can create logic.

If x = 5, y = 5, then you can create square corners indexes by this:

indexes: x/5 +0, x/5+1, y/5,y/5+1 ---> by combining them you get [0,0],[0,1],[1,0],[1,1]

At the end you just feed grid with those indexes

SUM = grid[0,0] + grid[0,1] + grid[1,0] + grid[1,1]
Martin
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  • The construction of your grid is unnecessary complex. It could be `grid = np.vstack([a, b, c])` Your code actually constructs and allocates memory for 3 grids, discarding the first two. – jochen Jan 03 '19 at 14:10
  • thanks. I tried vstack and it just extended array, but with your code, it does it better – Martin Jan 03 '19 at 14:46
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You can achieve this with interpolate.gridddata function from scipy.

With below code you can get the any interpolation you want from your grid.

import itertools
import numpy as np
from scipy.interpolate import griddata

dataX0 = [3, 1, -2, -3, -3] # x = 0m
dataX10 = [2, -7, -14, -30, -39] # x = 10m
dataX20 = [46, 22, 5, -2, -8] # x = 20m
data = dataX0 + dataX10 + dataX20
points = list(itertools.product(range(0,30,10),range(0,50,10)))

outputPoint = (5,5)
outputValue = griddata(points=points,values=data, xi=outputPoint, method="cubic")
print outputValue

The example above give you the interpolation at ouputPoint (5,5). And the output would give:

>>> 
-2.78976054957
Cedric Zoppolo
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  • You may want to check [this post](https://stackoverflow.com/questions/37872171/how-can-i-perform-two-dimensional-interpolation-using-scipy) – Cedric Zoppolo Jan 03 '19 at 15:01
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    The post you linked applies to most answers given here. Perhaps you could add it as a comment to the original question, so that it is more likely to get noticed by other readers? – MPA Jan 03 '19 at 15:19