import numpy linalg import numpy random from matplotlib import pyplot

  • Anonymous
  • Python
  • 22 Jan 2020 
  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
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 convex(p):

    hull = ConvexHull(p)

    return len(hull.simplices) == len(p)





def empty_poligon(p, points):

    p = np.array(p)

    hull = ConvexHull(p)

    hull = np.array([np.array([p[i][0], p[i][1]]) for i in hull.vertices])



    for i in points:

        if i not in p:

            if inPolygon(i[0], i[1], hull[:, 0], hull[:, 1]):

                print(i)

    #         return False

    # return True

    return False





def inPolygon(x, y, xp, yp):

    c = 0

    for i in range( len(xp)):

        if (((yp[i] <= y and y < yp[i - 1]) or (yp[i - 1] <= y and y < yp[i])) and \

                (x > (xp[i - 1] - xp[i]) * (y - yp[i]) / (yp[i - 1] - yp[i]) + xp[i])): c = 1 - c





    return c





points = []

while len(points) < 8:

    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)):

                    if convex([points[i1], points[i2], points[i3], points[i4], points[i5]]):

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

                        if empty_poligon([points[i1], points[i2], points[i3], points[i4], points[i5]], 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))
← newer dump
older dump →