#!/usr/bin/python from numpy import array,linalg from scipy import optimize import sys,math def thirdPoint(a): xdiff=a[1][0]-a[0][0] ydiff=a[1][1]-a[0][1] return [a[1][0]-ydiff,a[1][1]+xdiff] #Least squares method with scipy.optimize def fit_func(orig_parameter): def f(parameter, xdata, ydata): # ydata = final * interminv * xdata old_theta = orig_parameter[2]*math.pi/180 a = parameter[0] b = parameter[1] new_theta = parameter[2]*math.pi/180 # transform x intermidiate = array([[math.cos(old_theta),-math.sin(old_theta),orig_parameter[0]],[math.sin(old_theta),math.cos(old_theta),orig_parameter[1]],[0,0,1]]) final = array([[math.cos(new_theta),-math.sin(new_theta),a],[math.sin(new_theta),math.cos(new_theta),b],[0,0,1]]) res = [] resultdata = [] for (x,y) in zip(xdata,ydata): r = intermidiate.dot(linalg.inv(final).dot([x[0],x[1],1])) resultdata.append((r[0],r[1])) res.append(math.hypot(y[0]-r[0],y[1]-r[1])) return res return f N=2 orig_parameter = list(map(float,sys.stdin.readline().split())) xdata = [list(map(float,sys.stdin.readline().split())) for _ in range(N)] ydata = [list(map(float,sys.stdin.readline().split())) for _ in range(N)] result0 = optimize.leastsq(fit_func(orig_parameter),orig_parameter,args=(xdata+[thirdPoint(xdata)],ydata+[thirdPoint(ydata)])) result = optimize.least_squares(fit_func(orig_parameter),result0[0],args=(xdata+[thirdPoint(xdata)],ydata+[thirdPoint(ydata)]),method='trf') print(' '.join('%.12f'%e for e in result.x)) print(result)