###############
# Authored by Weisheng Jiang
# Book 4  |  From Basic Arithmetic to Machine Learning
# Published and copyrighted by Tsinghua University Press
# Beijing, China, 2022
###############

# Bk4_Ch8_02.py

import matplotlib.pyplot as plt 
import numpy as np

def plot_shape(X,copy = False):
    if copy:
        fill_color = np.array([255,236,255])/255
        edge_color = np.array([255,0,0])/255
    else:
        fill_color = np.array([219,238,243])/255
        edge_color = np.array([0,153,255])/255
    
    plt.fill(X[:,0], X[:,1],
             color = fill_color,
             edgecolor = edge_color)
    
    plt.plot(X[:,0], X[:,1],marker = 'x',
             markeredgecolor = edge_color*0.5,
             linestyle = 'None') 

X = np.array([[1,1],
              [0,-1],
              [-1,-1],
              [-1,1]]) + np.array([3,3])

# visualizations

thetas = np.linspace(30, 330, num=11)

for theta in thetas:
    
    fig, ax = plt.subplots()
    
    theta = theta/180*np.pi;
    # rotation
    R = np.array([[np.cos(theta),  np.sin(theta)],
                  [-np.sin(theta), np.cos(theta)]])
    
    Z = X@R;
    plot_shape(Z,True) # plot copy
    
    plot_shape(X)      # plot original
    
    # Decorations
    ax.grid(linestyle='--', linewidth=0.25, color=[0.5,0.5,0.5])
    plt.axis('equal')
    plt.axis('square')
    plt.axhline(y=0, color='k', linewidth = 0.25)
    plt.axvline(x=0, color='k', linewidth = 0.25)
    plt.xticks(np.arange(-5, 6))
    plt.yticks(np.arange(-5, 6))
    ax.set_xlim(-5,5)
    ax.set_ylim(-5,5)
    ax.spines['top'].set_visible(False)
    ax.spines['right'].set_visible(False)
    ax.spines['bottom'].set_visible(False)
    ax.spines['left'].set_visible(False)
    plt.xlabel('$x_1$')
    plt.ylabel('$x_2$')