I'm creating a Spark linear algebra library but wanted to plot a few graphs to get an idea of what's going on. These are the tools I tried.

__Sympy__

Sympy looked good as it allowed implicit functions. For instance, you can write:

from sympy import symbols

from sympy.plotting import plot3d

x, y = symbols('x y')

p = plot3d((x/2) + y, (x, -5, 5), (y, -5, 5))

The problem was that "SymPy uses Matplotlib behind the scenes to draw the graphs" [1] and Matplotlib has some issues in the z-order while rendering.

So, although SymPy gives you a lot more than just plotting, I moved on to...

__Mayavi__

... which renders things beautifully.

Until I tried to do something clever.

First, I had to update pip. Then, with, I tried:

from mayavi import mlab

.

.

mlab.options.backend = 'envisage'

which gave me:

ImportError: No module named envisage.ui.workbench.api

And after some googling, it looked like I needed to mess around with all sorts of libraries so I was a coward and gave up quickly.

__Jzy3d__

It turns out that there is a perfectly good Java library called Jzy3d which is quite mature.

Given:

v

_{1}= [8, -2, 2]

v

_{2}= [4, 2, 4]

I wanted to plot these vectors, the surface on which they lie and the shortest distance between this plane and [5, -5, 2] (this exercise can be found in Philip Klein's excellent "Coding the Matrix").

First, I had to convert this information to something Jzy3d can handle - which looks like this:

Mapper plane = new Mapper() {

@Override

public double f(double x, double y) {

return (x + (2 * y)) / 2;

}

};

_{1}+ t v

_{2}where s and t are any real numbers. Turning this information into parametric equations is easy:

x = 8s + 4t

y = -2s + 2t

z = 2s + 4t

and solving these simultaneous equations gives us the implicit function:

x + 2y - 2z = 0

or

z = (x + (2 * y)) / 2

which is the equation we find in our Java code above.

Finding the normal to an implicit function is simply the coefficients, that is [1, 2, -2]. At the point the normal meets [5, -5, 2] (which we'll call b) is the point where u b =s v

_{1}+ t v

_{2}. Once again, convert to parametric equations and then solve the simultaneous equations and you'll find t=-0.5 and s=1. This will give the point [6, -3, 0] and Jzy3d renders it like this:

where the red line is the normal, the green line is the point and the blue line is the closest point on the surface.

The rendering can be a bit jagged and I need to look at adding arrows to the vectors but so far, this seems to be the easiest plotting library to use.

[1] Doing Math with Python (No Starch Press)

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