How do I plot trajectory from points whose coordinates are known to me at several time instants?

Question

I have the coordinates of say 10 points at different time levels and I wish to join those coordinates to make it look like a trajectory?

def euler_method(points, x_dot, y_dot, x1, x2, time_step, n_steps):
    n_points = len(points[:, 0])
    point_trajectory = np.zeros((n_points, 2, n_steps))
    for i in range(0, n_steps):
        point_trajectory[:, :, i] = points
        f1 = sp.lambdify((x1, x2), x_dot, "numpy")
        f2 = sp.lambdify((x1, x2), y_dot, "numpy")
        u = f1(points[:, [0]], points[:, [1]])
        v = f2(points[:, [0]], points[:, [1]])                  
        points_new_x = points[:, [0]] + u*time_step
        points_new_y = points[:, [1]] + v*time_step
        points = np.hstack((points_new_x, points_new_y))
     return point_trajectory

def plot_trajectory(points_at_diff_time) - Is what I want to create

I am not able to think how to represent it. Please suggest how to do it, preferably in matplotlib.

EDIT: Something like this - moving points with different coordinates at different times.

Not clear what you're asking. Perhaps you can draw a picture and inline it in your question. — John Zwinck, Aug 07 '16 at 17:12
Do you have a parametric form for the trajectory? E.g., is it the trajectory of a cannonball? — Ami Tavory, Aug 07 '16 at 17:28
The particles are fluid particles, and I have the numerical representation available through Euler integration, which in turn indeed comes from parametrization. — Manish, Aug 07 '16 at 17:31

score 1 · Accepted Answer · edited May 23 '17 at 12:14

1

import numpy as np
import matplotlib.pyplot as plt

# make fake data to test with
pt = np.zeros((6, 2, 3)) # 6 points, (x,y), 3 timesteps
pt[:,0] = [-2,-1,1] # x=time, same for all

# set y values
pt[0,1] = [3,4,4.5]
pt[1,1] = [2,2.9,3.4]
pt[2,1] = [1,1.9,2.4]
pt[3,1] = [0,0.6,1.0]
pt[4,1] = [-1.5,-1.6,-1.6]
pt[5,1] = [-2.8,-3.7,-3.8]

# now plot: x and y are 2D
x = pt[:,0].T
y = pt[:,1].T

plt.plot(x, y)
plt.show()

If you want to smooth the lines, see here: https://stackoverflow.com/a/5284038/4323

edited May 23 '17 at 12:14

Community

1
1

answered Aug 07 '16 at 17:46

John Zwinck

239,568
38
324
436

This method was elegant and really fulfilled the purpose. Can you please explain the general idea behind this approach? Does it always take each row independently when you plot a matrix wrt to a matrix? – Manish Aug 08 '16 at 04:34

How do I plot trajectory from points whose coordinates are known to me at several time instants?

1 Answers1