import numpy linalg import numpy random from matplotlib import pyplot

  • Anonymous
  • Python
  • 23 Jan 2020 
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import numpy.linalg

import numpy.random

from matplotlib import pyplot as plt

import numpy as np

from scipy.spatial import ConvexHull

from sympy import *

import matplotlib.path as path





def calculate_b_c(p):

    A = [[p[0][0] * p[0][1], p[0][1] * p[0][1], p[0][0], p[0][1], 1],

         [p[1][0] * p[1][1], p[1][1] * p[1][1], p[1][0], p[1][1], 1],

         [p[2][0] * p[2][1], p[2][1] * p[2][1], p[2][0], p[2][1], 1],

         [p[3][0] * p[3][1], p[3][1] * p[3][1], p[3][0], p[3][1], 1],

         [p[4][0] * p[4][1], p[4][1] * p[4][1], p[4][0], p[4][1], 1]]



    B = [[p[0][0] * p[0][0], p[0][1] * p[0][1], p[0][0], p[0][1], 1],

         [p[1][0] * p[1][0], p[1][1] * p[1][1], p[1][0], p[1][1], 1],

         [p[2][0] * p[2][0], p[2][1] * p[2][1], p[2][0], p[2][1], 1],

         [p[3][0] * p[3][0], p[3][1] * p[3][1], p[3][0], p[3][1], 1],

         [p[4][0] * p[4][0], p[4][1] * p[4][1], p[4][0], p[4][1], 1]]



    C = [[p[0][0] * p[0][0], p[0][0] * p[0][1], p[0][0], p[0][1], 1],

         [p[1][0] * p[1][0], p[1][0] * p[1][1], p[1][0], p[1][1], 1],

         [p[2][0] * p[2][0], p[2][0] * p[2][1], p[2][0], p[2][1], 1],

         [p[3][0] * p[3][0], p[3][0] * p[3][1], p[3][0], p[3][1], 1],

         [p[4][0] * p[4][0], p[4][0] * p[4][1], p[4][0], p[4][1], 1]]



    D = [[p[0][0] * p[0][0], p[0][0] * p[0][1], p[0][1] * p[0][1], p[0][1], 1],

         [p[1][0] * p[1][0], p[1][0] * p[1][1], p[1][1] * p[1][1], p[1][1], 1],

         [p[2][0] * p[2][0], p[2][0] * p[2][1], p[2][1] * p[2][1], p[2][1], 1],

         [p[3][0] * p[3][0], p[3][0] * p[3][1], p[3][1] * p[3][1], p[3][1], 1],

         [p[4][0] * p[4][0], p[4][0] * p[4][1], p[4][1] * p[4][1], p[4][1], 1]]



    E = [[p[0][0] * p[0][0], p[0][0] * p[0][1], p[0][1] * p[0][1], p[0][0], 1],

         [p[1][0] * p[1][0], p[1][0] * p[1][1], p[1][1] * p[1][1], p[1][0], 1],

         [p[2][0] * p[2][0], p[2][0] * p[2][1], p[2][1] * p[2][1], p[2][0], 1],

         [p[3][0] * p[3][0], p[3][0] * p[3][1], p[3][1] * p[3][1], p[3][0], 1],

         [p[4][0] * p[4][0], p[4][0] * p[4][1], p[4][1] * p[4][1], p[4][0], 1]]



    F = [[p[0][0] * p[0][0], p[0][0] * p[0][1], p[0][1] * p[0][1], p[0][0], p[0][1]],

         [p[1][0] * p[1][0], p[1][0] * p[1][1], p[1][1] * p[1][1], p[1][0], p[1][1]],

         [p[2][0] * p[2][0], p[2][0] * p[2][1], p[2][1] * p[2][1], p[2][0], p[2][1]],

         [p[3][0] * p[3][0], p[3][0] * p[3][1], p[3][1] * p[3][1], p[3][0], p[3][1]],

         [p[4][0] * p[4][0], p[4][0] * p[4][1], p[4][1] * p[4][1], p[4][0], p[4][1]]]



    a = numpy.linalg.det(A)

    b = (-1) * numpy.linalg.det(B)

    c = numpy.linalg.det(C)

    d = (-1) * numpy.linalg.det(D)

    e = numpy.linalg.det(E)

    f = (-1) * numpy.linalg.det(F)



    return a, b, c, d, e, f



def in_ellipse(p, koef):

    x = p[0]

    y = p[1]

    d = koef[0] * x**2 + koef[1]*x*y + koef[2]*y**2 + koef[3]*x + koef[4]*y + koef[5] 

    if d < 0:

        return True

    else:

        return False



def rotate(A,B,C):

  return (B[0]-A[0])*(C[1]-B[1])-(B[1]-A[1])*(C[0]-B[0])





def jarvismarch(A):

  n = len(A)

  P = range(n)

  for i in range(1,n):

    if A[P[i]][0]<A[P[0]][0]: 

      P[i], P[0] = P[0], P[i]  

  H = [P[0]]

  del P[0]

  P.append(H[0])

  while True:

    right = 0

    for i in range(1,len(P)):

      if rotate(A[H[-1]],A[P[right]],A[P[i]])<0:

        right = i

    if P[right]==H[0]: 

      break

    else:

      H.append(P[right])

      del P[right]

  H = [A[H[i]] for i in range(len(H))]  

  return np.array(H)      





def empty_poligon(p, points):

     bbPath = path.Path(p)

     new_p = [[i[0],i[1]] for i in p]

     for i in points:

        if [i[0],i[1]] not in new_p: 

            if bbPath.contains_point(i, radius=0.0):

                return False

            else:

                a,b,c,d,e,f = calculate_b_c(p)

                if in_ellipse(i, [ a,b,c,d,e,f]):

                    return False

                

     return True





points = []

while len(points) < 10:

    new_p = [numpy.random.randint(-5, 5), numpy.random.randint(-5, 5)]

    if new_p not in points:

        points.append(new_p)

points = np.array(points)

print(points)

    



k = 0

for i in points:

    plt.plot(i[0], i[1], '.')

    plt.annotate(str("%d" % k), [i[0], i[1]])

    k = k + 1



plt.grid()

plt.plot(points[:, 0], points[:, 1], 'o')

plt.show()

#plt.savefig('/home/kate/Рабочий стол/Figure_1.png')



for i1 in range(len(points)):

    for i2 in range(i1 + 1, len(points)):

        for i3 in range(i2 + 1, len(points)):

            for i4 in range(i3 + 1, len(points)):

                for i5 in range(i4 + 1, len(points)):

                    conv = jarvismarch([points[i1], points[i2], points[i3], points[i4], points[i5]])

                    

                    if (len(conv) == 5):

                         if empty_poligon(conv, points):

                             print(i1, i2, i3, i4, i5)



a, b, c, d, e, f = calculate_b_c(points)



# print(a, b, c, d, e, f)

# x = symbols('x')

# y = symbols('y')

# plot_implicit(Eq(a * x ** 2 + b * x * y + c * y ** 2 + d * x + e * y + f))
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