from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
import numpy as np

def plot_implicit(fn, bbox=(-2.5,2.5)):
    ''' create a plot of an implicit function
    fn  ...implicit function (plot where fn==0)
    bbox ..the x,y,and z limits of plotted interval'''
    xmin, xmax, ymin, ymax, zmin, zmax = bbox*3
    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')
    A = np.linspace(xmin, xmax, 100) # resolution of the contour
    B = np.linspace(xmin, xmax, 15) # number of slices
    A1,A2 = np.meshgrid(A,A) # grid on which the contour is plotted

    for z in B: # plot contours in the XY plane
        X,Y = A1,A2
        Z = fn(X,Y,z)
        cset = ax.contour(X, Y, Z+z, [z], zdir='z')
        # [z] defines the only level to plot for this contour for this value of z

    for y in B: # plot contours in the XZ plane
        X,Z = A1,A2
        Y = fn(X,y,Z)
        cset = ax.contour(X, Y+y, Z, [y], zdir='y')

    for x in B: # plot contours in the YZ plane
        Y,Z = A1,A2
        X = fn(x,Y,Z)
        cset = ax.contour(X+x, Y, Z, [x], zdir='x')

    # must set plot limits because the contour will likely extend
    # way beyond the displayed level.  Otherwise matplotlib extends the plot limits
    # to encompass all values in the contour.
    ax.set_zlim3d(zmin,zmax)
    ax.set_xlim3d(xmin,xmax)
    ax.set_ylim3d(ymin,ymax)

    plt.show()

def goursat_tangle(x,y,z):
    a,b,c = 0.0,-5.0,11.8
    return x**4+y**4+z**4+a*(x**2+y**2+z**2)**2+b*(x**2+y**2+z**2)+c

plot_implicit(goursat_tangle)

def hyp_part1(x,y,z):
    return -(x**2) - (y**2) + (z**2) - 1

plot_implicit(hyp_part1, bbox=(-100.,100.))

def sphere(x,y,z):
    return x**2 + y**2 + z**2 - 2.0**2

def translate(fn,x,y,z):
    return lambda a,b,c: fn(x-a,y-b,z-c)

def union(*fns):
    return lambda x,y,z: np.min(
        [fn(x,y,z) for fn in fns], 0)

def intersect(*fns):
    return lambda x,y,z: np.max(
        [fn(x,y,z) for fn in fns], 0)

def subtract(fn1, fn2):
    return intersect(fn1, lambda *args:-fn2(*args))

plot_implicit(union(sphere,translate(sphere, 1.,1.,1.)), (-2.,3.))

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)

import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d import Axes3D

def hyp_part1(x,y,z):
    return -(x**2) - (y**2) + (z**2) - 1

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

x_range = np.arange(-100,100,10)
y_range = np.arange(-100,100,10)
X,Y = np.meshgrid(x_range,y_range)
A = np.linspace(-100, 100, 15)

A1,A2 = np.meshgrid(A,A)

for z in A:
    X,Y = A1, A2
    Z = hyp_part1(X,Y,z)
    ax.contour(X, Y, Z+z, [z], zdir='z')

for y in A:
    X,Z= A1, A2
    Y = hyp_part1(X,y,Z)
    ax.contour(X, Y+y, Z, [y], zdir='y')

for x in A:
    Y,Z = A1, A2
    X = hyp_part1(x,Y,Z)
    ax.contour(X+x, Y, Z, [x], zdir='x')

ax.set_zlim3d(-100,100)
ax.set_xlim3d(-100,100)
ax.set_ylim3d(-100,100)