How to plot a line with matplotlib which is given in linear algebra form?

Question

This is a trivial problem but I run into it again and again and I am sure there is a elegant solution, which I would like to use.

I do math with numpy and would like to plot lines that are results of linear algebra calculations. These lines come in the form

So I would would like to "outsource" the job of finding the start end endpoint of my line to a clever sipplet of python code, so that my resulting line gets drawn into my 3D plot, honoring the existing dimensions of the plot. E.g. if I plotted a 3D parabel from x = -2 to 2 and z = -3 to 3, and I wanted to draw a line , it would figure out that it would need to start at (-2,1,-2) and end at (2,1,2).

How could that work?

mathfux · Accepted Answer · 2020-10-22 17:34:39Z

3

At first, it's important to define projection parameter. At second, you need to work with different shapes of P, v and z in order to obtain X, Y, Z parameters that corresponds to coordinates of plot method:

import matplotlib.pyplot as plt
import numpy as np

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

P = np.array([1,1,1]).reshape(-1,1)
v = np.array([1,0,1]).reshape(-1,1)
z = np.linspace(-3,3,100)
X, Y, Z = P + v*z

ax.plot(X, Y, Z)
plt.show()

Per comments

reshape(-1, 1) adds an extra dimension which is required for broadcasting (you can also read a nice tutorial on this topic). It is also a substitute of reshape(3, 1). Simple case (arr1 = v; arr2 = np.linspace(-3,3,11)) can be visualized like so:

Ending points of a curve g = (1, 1, 1) + z * (1, 0, 1) are at the bounds of interval of z, namely:

g1 = (1, 1, 1) + (-3) * (1, 0, 1) = (-2, 1, -2)
g2 = (1, 1, 1) + 3 * (1, 0, 1) = (4, 1, 4)

Note that z = 1 is needed to get ending point = (2,1,2)

edited Oct 22, 2020 at 17:34

answered Oct 21, 2020 at 22:09

mathfux

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2 Comments

Andreas Schuldei Over a year ago

can you please explain what the reshape(-1,1) does? And what about the -3,3 range? That is obviously manual (which is not a major issue). But that is just a rough guess of the range we might be in, right?

mathfux Over a year ago

@AndreasSchuldei Look at my update.In general, you can solve some equations to find a range required like in my example. One more to mention, np.linspace(-3,3,2) is enough because we need only two points to define a segment.

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