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

# ## Strips on sphere ##

# In[1]:


import numpy as np


# We generate a sphere from 12 strips. The basic strip is parameterized and discretized below:

# In[12]:


theta=np.linspace(0, 5*np.pi/36, 30)  #5pi/36=25 degrees
phi=np.linspace(-np.pi/2, np.pi/2, 100)
theta, phi=np.meshgrid(theta, phi)
x=np.cos(theta)*np.cos(phi)
y=np.sin(theta)*np.cos(phi)
z=np.sin(phi)


# This strip is rotated about Oz, with integer multiple of $\pi/6$ radians. Since z-rotation  does not change z values, we define only a planar rotation of `alpha` radians:

# In[13]:


def Rot(alpha):
    return np.array([[np.cos(alpha), -np.sin(alpha)], [np.sin(alpha), np.cos(alpha)]])


# Instead of applying this rotation successively to each point in the basic strip, we make use of the numpy function `einsum` (Einstein summation), and rotate simultaneously   all points with coordinates in  two equally shaped meshgrids (x,y, in our case): 

# In[14]:


def rotate_z_mesh(x, y, alpha):
    return np.einsum('ji, mni -> jmn', Rot(alpha), np.dstack([x, y]))


# The colorscale to plot the sphere's strips:

# In[15]:


cofee_green=[[0.0,u'#543005'],
[0.1,u'#8c510a'],
[0.2, u'#bf812d'],
[0.3, u'#dfc27d'],
[0.4, u'#f6e8c3'],
[0.5, u'#f5f5f5'],
[0.6, u'#c7eae5'],
[0.7, u'#80cdc1'],
[0.8, u'#35978f'],
[0.9, u'#01665e'],
[1.0, u'#003c30']]


# In[16]:


import plotly.plotly as py
import plotly.tools as tls
from plotly.graph_objs import *


# In[17]:


def make_trace(x,y,z, colsc):# this function creates the trace for each strip on sphere
    return Surface(
        x=x,
        y=y,
        z=z,
        colorscale=colsc,         
        name=''            
    )


# In[18]:


dt=[make_trace(x,y,z, cofee_green)]#initial strip
for k in range(1,12):
    rez=rotate_z_mesh(x, y, k*np.pi/6)
    dt+=[make_trace(rez[0], rez[1], z, cofee_green)]


# In[19]:


data=Data(dt)


# In[20]:


axis = dict(
showbackground=True, 
backgroundcolor='rgb(20, 20, 20)', 
gridcolor='rgb(75, 75, 75)',      
zerolinecolor='rgb(75, 75, 75)'
    )

layout = Layout(
         title='Strips on sphere', 
         width=800,
         height=800,
         scene=Scene(  
         xaxis=XAxis(axis),
         yaxis=YAxis(axis), 
         zaxis=ZAxis(axis), 
        )
        )
        
fig = Figure(data=data, layout=layout)
py.sign_in('empet', 'my_api_key')
py.plot(fig, filename='spherical-strips')


# [https://plot.ly/~empet/4759](https://plot.ly/~empet/4759)

# In[31]:


from IPython.core.display import HTML
def  css_styling():
    styles = open("./custom.css", "r").read()
    return HTML(styles)
css_styling()