Interpolation Exercise 1

In [23]:
%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np

In [24]:
from scipy.interpolate import interp1d

2D trajectory interpolation

The file trajectory.npz contains 3 Numpy arrays that describe a 2d trajectory of a particle as a function of time:

  • t which has discrete values of time t[i].
  • x which has values of the x position at those times: x[i] = x(t[i]).
  • x which has values of the y position at those times: y[i] = y(t[i]).

Load those arrays into this notebook and save them as variables x, y and t:

In [25]:
with np.load('trajectory.npz') as data:
    t = data['t']
    x = data['x']
    y = data['y']

In [26]:
assert isinstance(x, np.ndarray) and len(x)==40
assert isinstance(y, np.ndarray) and len(y)==40
assert isinstance(t, np.ndarray) and len(t)==40

Use these arrays to create interpolated functions $x(t)$ and $y(t)$. Then use those functions to create the following arrays:

  • newt which has 200 points between $\{t_{min},t_{max}\}$.
  • newx which has the interpolated values of $x(t)$ at those times.
  • newy which has the interpolated values of $y(t)$ at those times.

In [27]:
newt = np.linspace(t.min(),t.max(),200)
fx = interp1d(t,x,kind = 'cubic')
fy = interp1d(t,y,kind = 'cubic')
newx = fx(newt)
newy = fy(newt)

In [28]:
assert newt[0]==t.min()
assert newt[-1]==t.max()
assert len(newt)==200
assert len(newx)==200
assert len(newy)==200

Make a parametric plot of $\{x(t),y(t)\}$ that shows the interpolated values and the original points:

  • For the interpolated points, use a solid line.
  • For the original points, use circles of a different color and no line.
  • Customize you plot to make it effective and beautiful.

In [33]:
plot = plt.gca()
plt.xlabel('Horizontal Distance')
plt.ylabel('Verital Distance')
plt.plot(x,y,'bo',color = 'g');

In [ ]:
assert True # leave this to grade the trajectory plot