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

# # Simple Way to Draw a Curve

# In[1]:


import numpy as np
import pandas as pd

from lets_plot import *
LetsPlot.setup_html()


# In[2]:


BG_CLR = '#253494'
EC_CLR = '#ffffcc'


# In[3]:


# Curve parametrized equation
def ec_eq(*, a=0, b=0):
    return lambda x, y: y ** 2 - x ** 3 - a * x - b


# In[4]:


def level(X, Y, *, eq, c=1):
    level_map = lambda z: np.exp(-c * np.abs(z))
    return level_map(eq(X, Y))


# In[5]:


dx, dy = 1.0 / 30.0, 1.0 / 10.0

x = np.arange(-3, 3, dx)
y = np.arange(-3, 3, dy)
X, Y = np.meshgrid(x, y)
curve_eq = ec_eq(a=-1, b=0)
Z = level(X, Y, eq=curve_eq, c=10)

df = pd.DataFrame(dict(x=X.reshape(-1), y=Y.reshape(-1), z=Z.reshape(-1)))


# In[6]:


theme_layer = scale_color_gradient(low=BG_CLR, high=EC_CLR) + scale_fill_gradient(low=BG_CLR, high=EC_CLR) + \
    xlim(df.x.min(), df.x.max()) + ylim(df.y.min(), df.y.max()) + ggsize(600, 450) + \
    theme_void() + theme(panel_background=element_rect(color=BG_CLR, fill=BG_CLR))


# In[7]:


ggplot() + \
    geom_point(aes(x='x', y='y', color='z'), data=df[df.z > 0.5].sort_values(by='z')) + \
    coord_fixed() + theme_layer + \
    ggtitle('Elliptic Curve by Points')


# In[8]:


ggplot() + \
    geom_bin2d(aes(x='x', y='y', fill='z'), data=df, stat='identity', color=BG_CLR) + \
    theme_layer + \
    ggtitle('Elliptic Curve by 2D-Bins')


# In[9]:


ggplot() + \
    geom_tile(aes(x='x', y='y', fill='z'), data=df, color=BG_CLR) + \
    theme_layer + \
    ggtitle('Elliptic Curve by Tiles')


# In[10]:


ggplot() + \
    geom_raster(aes(x='x', y='y', fill='z'), data=df) + \
    theme_layer + \
    ggtitle('Elliptic Curve by Raster')


# In[11]:


ggplot() + \
    geom_contour(aes(x='x', y='y', z='z', color='..level..'), data=df, bins=4) + \
    theme_layer + \
    ggtitle('Elliptic Curve by Contours')


# In[12]:


ggplot() + \
    geom_contourf(aes(x='x', y='y', z='z', fill='..level..'), data=df, binwidth=.3) + \
    theme_layer + \
    ggtitle('Elliptic Curve by Filled Contours')