Best practices

I am working to practice on some simple parameterized curve given by:

import numpy as np
import matplotlib.pyplot as plt

fig, ax = plt.subplots(figsize=(6, 3))

t = np.linspace(-4, 4, 100)

x = t
y = t**3 - 9*t 

ax.plot(x, y, label="curve")
ax.legend()

plt.show()

original

My problem: I would like to construct and show for some points on the plot:

  • the unit tangent vector T
  • the unit normal vector N, pointing towards the "concavity" (is it the right word?) of the curve

What I would like to have is depicted for 2 arbitrary points on the plot below (artificially constructed):

wanted

How could I have this, in a "pythonic" way? I am just aware that np.gradient gives the derivatives, such as:

dydx = np.gradient(y, x)

But I have no practice in using it and don't know how to plot unit vectors and, of course, normal vectors...

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4 Replies 4

julaine
•

I don't know of a matplotlib-builtin way to do this and I don't think there is. Numerical differentiation can be tricky and is out-of-scope for matplotlib.

You could calculate the slope of T as the derivative of your function and from that, draw the arrows yourself with matplotlib.

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lastchance
•

The unit tangent vector can be calculated by normalising successive differences (or centred differences if you want a higher-order method). The unit normal can then be computed by rotating 90 degrees. You can draw the arrows with, e.g., ax.annotate.

However …

You will have major problems with this if your aspect ratio is different from 1 (as in your plot). Although the arrows that you have drawn for T and N look 90 degrees apart that would not be the case if you used equal x and y ranges.

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