Python: How to resample a 3d curve given by points as spline in equal distances?

Question

Allow me to separate this to increasing difficulty questions:

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1.

I have some 1d curve, given as a (n,) point array.

I would like to have it re-sampled k times, and have the results come from a cubic spline that passes through all points.

This can be done with interp1d

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2. The curve is given at non-same-interval samples as an array of shape (n, 2) where (:, 0) represents the sample time, and (:, 1) represent the sample values.

I want to re-sample the curve at k same-time-intervals.

How can this be done?

I thought i could do t_sampler = interp1d(np.arange(0,k),arr[:, 0]) for the time, then interp1d(t_sampler(np.arange(0,k)), arr[:, 1])

Am I missing something with this?

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3.

How can I re-sample the curve at equal distance intervals? (question 2 was equal time intervals)

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4.

What if the curve is 3d given by an array of shape (n, 4) , where (:,0) are the (non uniform) sampling times, and the rest are the locations sampled?

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Sorry for many-questionsin-single-question, they seemed too similar to open a new question for every one.

Answer 1

Partial answer; for 1 and 2 I would do this:

from scipy.interpolate import interp1d
import numpy as np

# dummy data
x = np.arange(-100,100,10)
y = x**2 + np.random.normal(0,1, len(x))

# interpolate:
f = interp1d(x,y, kind='cubic')

# resample at k intervals, with k = 100:
k = 100
# generate x axis:
xnew = np.linspace(np.min(x), np.max(x), k)

# call f on xnew to sample y values:
ynew = f(xnew)

plt.scatter(x,y)
plt.plot(xnew, ynew)