Plotting implicit equations in 3d

Question

I\'d like to plot implicit equation F(x,y,z) = 0 in 3D. Is it possible in Matplotlib?

Answer 1

As far as I know, it is not possible. You have to solve this equation numerically by yourself. Using scipy.optimize is a good idea. The simplest case is that you know the range of the surface that you want to plot, and just make a regular grid in x and y, and try to solve equation F(xi,yi,z)=0 for z, giving a starting point of z. Following is a very dirty code that might help you

from scipy import *
from scipy import optimize

xrange = (0,1)
yrange = (0,1)
density = 100
startz = 1

def F(x,y,z):
    return x**2+y**2+z**2-10

x = linspace(xrange[0],xrange[1],density)
y = linspace(yrange[0],yrange[1],density)

points = []
for xi in x:
    for yi in y:
        g = lambda z:F(xi,yi,z)
        res = optimize.fsolve(g, startz, full_output=1)
        if res[2] == 1:
            zi = res[0]
            points.append([xi,yi,zi])

points = array(points)