import numpy as np
import matplotlib.pyplot as plt
from math import pi
import math

# HACKISH WARNING: this version internally uses 0 to 2 for the sine wave x axis, but labels it 0 to 2pi
# This is so the two graphs can be the same size. I couldn't work out how to otherwise within pyplot.
# (Actually only wanted the height of the two graphs to be the same, and was originally aiming to have the second x axis with the same scale as the first, which would have made it 3.14x longer.)

def addLines(quad, color):
	incr = 1.0/1000.0
	start = quad/2.0
	end = start + 0.5 + incr
	x = np.arange(start, end, incr)
	lines = plt.plot(x, np.sin(pi*x), '')
	plt.setp(lines, color=color, linewidth=2.5, solid_capstyle='butt', solid_joinstyle='miter')


def addPolar(quad, color):
	incr = pi/1000.0
	start = quad*pi/2.0
	end = start + pi/2.0 + incr
	x = np.arange(start, end, incr)
	lines = plt.plot(np.cos(x), np.sin(x), '')
	plt.setp(lines, color=color, linewidth=2.0, solid_capstyle='butt', solid_joinstyle='miter')
		
def addTicks():
	start = 0 # in pi
	end = 3 # in pi
	tickPoints = []
	tickNames = []
	done = [] # in units of pi
	#denoms = [1, 2, 4, 8] # show more
	denoms = [1, 2]
	for denom in denoms:
		for numer in range(denom * start, denom * end):
			val = (numer+0.0)/(denom+0.0)
			if val not in done:
				#tickPoints.append(val * pi) # this is preferred
				tickPoints.append(val) # dodgy hack to help make the graph square. 
				done.append(val)
				
				pich = u'\u03C0'
				strTop = str(numer) + pich
				if numer == 0:
					strTop = "0"
				elif numer == 1:
					strTop = pich
				

				if denom == 1:
					tickNames.append(strTop)
				else:
					tickNames.append(strTop + "/" + str(denom))
	
	plt.xticks(tickPoints, tickNames)	

	
def drawSine():
	addLines(-1, 'yellow')
	addLines(0, 'brown')
	addLines(1, 'r')
	addLines(2, 'orange')
	addLines(3, 'yellow')
	addLines(4, 'brown')

	addTicks()
	slack = .1
	plt.axis('scaled')
	plt.xlim(-slack, 2.0 + slack)
	plt.ylim(-1.1, 1.1)
	plt.grid(True)
	
	plt.xlabel('$x$')
	plt.ylabel('$y$')
	plt.title(r'$y = \sin x$')

	plt.text( .25,  0, 'I', family='serif', fontsize=26, ha='center', va='center')
	plt.text(.75,  0, 'II', family='serif', fontsize=26, ha='center', va='center')
	plt.text(1.25, 0, 'III', family='serif', fontsize=26, ha='center', va='center')
	plt.text( 1.75, 0, 'IV', family='serif', fontsize=26, ha='center', va='center')

def drawUnitCircle():
	addPolar(0, 'brown')
	addPolar(1, 'r')
	addPolar(2, 'orange')
	addPolar(3, 'yellow')

	edge = 1.1
	plt.axis('scaled')
	plt.axis([-edge, edge, -edge, edge])
	plt.grid(True)

	plt.xlabel('$x$')
	plt.ylabel('$y$')
	plt.title(r'$x^2 + y^2 = 1$')
	
	lo = .85 #label offset
	plt.text( lo,  lo, 'I', family='serif', fontsize=26, ha='center', va='center')
	plt.text(-lo,  lo, 'II', family='serif', fontsize=26, ha='center', va='center')
	plt.text(-lo, -lo, 'III', family='serif', fontsize=26, ha='center', va='center')
	plt.text( lo, -lo, 'IV', family='serif', fontsize=26, ha='center', va='center')

def twoInOne():	
	plt.subplot(121)
	drawUnitCircle()
	plt.subplot(122)
	drawSine()

twoInOne()
plt.savefig("Sine_quads_01_Pengo.svg")

plt.show()