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

# # Periodic Spline
# 
# This notebook replicates spec_splinep.m as an Jupyter/IPython notebook

# In[3]:


get_ipython().run_line_magic('matplotlib', 'inline')
import matplotlib.pyplot as plt
import numpy as np
import sys; sys.path.append('..')
from conformalmapping import *


# In[5]:


# Python Syntax for complex numbers is uses j rather than i
pts = [
 0.5896  + 1.2486j,
 -0.1426 + 1.5954j,
 -0.9133 + 1.1561j,
 -0.8465 + 0.3536j,
 -1.1116 - 0.2398j, 
 -1.2695 - 0.9643j,
 -0.5660 - 1.1075j,
 0.2013 - 0.7552j,
 0.8362 - 0.9634j,
 1.5838 - 0.7013j,
 1.3141 + 0.4008j,
 0.8474 + 0.7291j
]

# This looks slightly different to the matlab - we'll use a classmethod 
# constructor rather than trying to combine all the overloads into one
# place. This makes testing a little easier, and it makes coverage testing
# a lot easier.
s = Splinep.from_complex_list(pts)
print s


# In[6]:


ts = np.linspace(0.0, 1.0, 201)
ps = s.point(ts)
plt.plot(ps.real, ps.imag)
plt.plot(s.zpts.real, s.zpts.imag, 'r.')
plt.gca().set_aspect('equal')


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