#!/usr/bin/env python
# coding: utf-8

# Just a toy to evaluate the Chmutov surface.
# 
# See: [this website](http://mrhonner.com/archives/14859) for more.
# 
# The equation of the surface is: $2[x^2(3-4x^2)^2 + y^2(3-4y^2)^2 + z^2(3-4z^2)^2] = 3$
# 
# The matplotlib plotting routine comes from [here](http://stackoverflow.com/questions/4680525/plotting-implicit-equations-in-3d).
# 

# In[1]:


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()


# In[2]:


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)


# In[3]:


def chmutov_surface(x,y,z):
    return 2.*((x**2)*(3.-4.*(x**2))**2 + (y**2)*(3.-4.*(y**2))**2 + (z**2)*(3.-4.*(z**2))**2)-3.


# In[6]:


plot_implicit(chmutov_surface,bbox=(-1.1,1.1))


# In[ ]: