interpolate between elements in array

Question

I am still trying to find a solution to my problem described here: matplotlib: assign color to a radius. I tried it first with contourplot but I think it is a better solution when I try to plot circles on the surface of the disk and assign colors to them. Therefore I have an array:

arr = np.array([[ 114.28, 14],
            [ 128.57, 16],
            [ 142.85,19],
            [ 157.13,20],
            [ 171.41,21],
            [ 185.69,22],
            [ 199.97,24],
            [ 214.25,27],
            [ 228.53,29],
            [ 242.81,30],
            [ 257.09,31],
            [ 271.37,34],
            [ 288.65,35],
            [ 299.93,36],
            [ 300,38]])

I would like to extend this array to an array with about 300 elements (depends on the radius of the disk. If the radius would be e.g. 500, I want to have an array with 500 elements)by interpolating between the values of the array linearly. I need an interpolation of both columns. I found this article: Interpolate between elements in an array of floats but I don't understand the code as they are talking about milliseconds and LED's... Thanks in advance !

Answer 1

IIUC, I think that you can just use np.interp to interpolate your points. From the documentations, np.interp is used for:

One-dimensional linear interpolation.

Which sounds just about like what you're after.

So you can create an array of 300 evenly spaced points from your minimum x value to your maximum x value using np.linspace:

new_x = np.linspace(min(arr[:,0]), max(arr[:,0]), num=300)

And then interpolate your new y values:

new_y = np.interp(new_x, arr[:,0], arr[:,1])

To illustrate graphically:

# Show the original 15 points:
plt.scatter(arr[:,0], arr[:,1], label='original', zorder=10)

# Show the interpolated 300 points:
plt.scatter(new_x, new_y, label='interpolated', s=0.5)

plt.legend()

plt.show()

Edit Based on your comment, to interpolate exactly 20 points between each datapoint in your array, you can create your new x axis by iterating through your array and applying linspace to get 20 points between each consecutive x value. However, this will yield 280 points, because you will be creating 20 points between 15 of your datapoints, leading to 20*(15-1) new datapoints:

new_x = np.concatenate([np.linspace(arr[i,0],arr[i+1,0], num=20)
                        for i in range(len(arr)-1)])

new_y = np.interp(new_x, arr[:,0], arr[:,1])


# Show the original 15 points:
plt.scatter(arr[:,0], arr[:,1], label='original', zorder=10)

# Show the interpolated 280 points:
plt.scatter(new_x, new_y, label='interpolated', s=0.5)

plt.legend()

plt.show()