'''
Curves(sin(x), circle, abs,cuspidal cubic, cycloid)
Programmed by Ching-Shoei Chiang
'''
from math import *
from visual import *
#from visual.text import *

# http://linuxgazette.net/144/john.html
scene.width = 2.5 * scene.height

#1 draw 3 axis.
xaxis = arrow(pos=(0,0), axis=(1,0), shaftwidth=0.01, color=color.red)
yaxis = arrow(pos=(0,0), axis=(0,1), shaftwidth=0.01, color=color.green)

# Work only for capital letters. It will print * for other letters
#xtex = label(pos=(1,0), text='X', xoffset = 3, box=false,  line=false, color=color.red, height=0.08, width=0.08, justify='center')
#ytex = label(pos=(0,1), text='Y', yoffset = 3, box=false, line=false, color=color.green, height=0.06, width=0.06, justify='center')

# Curve in 2D
#1 繪製一個方形
#square = curve(pos = [(0,0), (0,1), (1,1), (1,0), (0,0)], radius=0.01)

#2 繪製點(非曲線)，並設定不同的粗筆，繪製一個方形的四的端點
#square = points(pos = [(0,0), (0,1), (1,1), (1,0), (0,0)], radius=0.05, color=color.white)

#3 函數
#eqn = "sin(x)"
#x = arange(0, 6.28+0.1, 0.1)
#curve( x=x, y=eval(eqn) )

#4 參數式 x(t)=cos(t), y(t)=sin(t)
#t=arange(0,2*pi+0.1, 0.1)
#curve(x=cos(t), y=sin(t), red=cos(t), green=sin(t), blue=0.2, radius=0.03)

#5 參數式 x(t)=t, y(t)=|t| and 函數(y = |x|)
#t = arange(-1,1.1,0.1)
#curve(x=t, y=abs(t))

#6 參數式x(t)=t**2, y(t)=t**3, t in R
#test different value of maxno, and step
#step = 0.01
#maxno = 3
#t=arange(-maxno, maxno+step, step)
#curve(x=t**2, y=t**3, radius=0.05)

#7 參數式 x(t)=t**3-4*t, y(t)=t**2-4, t in R
# Do it by student. Is this function a 1-1 function?

#8
# Cycloid. 此指令需要在未畫軸線之前，讓scene.width = 2.5 * scene.height指令可執行
# t[0]==0 is the first drawing point for the circle

#t=arange(0,2*pi+0.1, 0.1)
#curve(pos=[(-1,0),(2*pi+1,0)], color=color.blue)
#L=curve(color=color.yellow)
#for deltat in arange(0, 2*pi+0.1, 0.1):
#    curve(x=deltat-sin(t+deltat), y=1-cos(t+deltat), red=t/(2*pi), green=t/(2*pi), blue=t/(2*pi), radius=0.01)
#curve(x=t-sin(t), y=1-cos(t), color=color.green)

#9 Tractrix (方法同#5)
t = arange(0.1,pi,0.1)
curve(x=cos(t)+log(tan(t/2)), y=sin(t))