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import matplotlib.pyplot as plt
import numpy as np
class billiard_circle():
    def __init__(self,x_0,y_0,vx_0,vy_0,N,dt):
        self.x_0 = x_0
        self.y_0 = y_0
        self.vx_0 = vx_0
        self.vy_0 = vy_0
        self.N = N
        self.dt = dt
    def motion_calculate(self):
        self.x = []
        self.y = []
        self.vx = []
        self.vy = []
        self.t = [0]
        self.x.append(self.x_0)
        self.y.append(self.y_0)
        self.vx.append(self.vx_0)
        self.vy.append(self.vy_0)
        for i in range(1,self.N):
            self.x.append(self.x[i - 1] + self.vx[i - 1]*self.dt)
            self.y.append(self.y[i - 1] + self.vy[i - 1]*self.dt)
            self.vx.append(self.vx[i - 1])
            self.vy.append(self.vy[i - 1])
            if (np.sqrt( self.x[i]**2+self.y[i]**2 ) > 1.0):
                self.x[i],self.y[i] = self.correct('np.sqrt(x**2+(y)**2) < 1.0',self.x[i - 1], self.y[i - 1], self.vx[i - 1], self.vy[i - 1])
                self.vx[i],self.vy[i] = self.reflect(self.x[i],self.y[i],self.vx[i - 1], self.vy[i - 1])
            self.t.append(self.t[i - 1] + self.dt)
        return self.x, self.y
        
    def correct(self,condition,x,y,vx,vy):
        vx_c = vx/100.0
        vy_c = vy/100.0
        while eval(condition):
            x = x + vx_c*self.dt
            y = y + vy_c*self.dt
        return x-vx_c*self.dt,y-vy_c*self.dt    
    def reflect(self,x,y,vx,vy):
        module = np.sqrt(x**2+y**2)  ### normalization
        x = x/module
        y = y/module
        v = np.sqrt(vx**2+vy**2)
        cos1 = (vx*x+vy*y)/v
        cos2 = (vx*y-vy*x)/v
        vt = -v*cos1
        vc = v*cos2 
        vx_n = vt*x+vc*y
        vy_n = vt*y-vc*x
        return vx_n,vy_n
    def phase_plot(self):
        plt.figure(figsize = (8,8))
        record_x = []
        record_vx = []
        for i in range(len(self.x)):
            if (abs(self.y[i] - 0)<0.001):
                record_vx.append(self.vx[i])
                record_x.append(self.x[i])
        plt.xlabel('x')
        plt.ylabel(r'$v_x$')
        plt.plot(record_x,record_vx,'r.')
        #plt.savefig('chapter3_3.31_phasey=0.png', dpi= 144)
        plt.show()
A=billiard_circle(0.2,0,1,0.6,150000,0.01)
A.motion_calculate()
A.phase_plot()