import numpy linalg import numpy random from matplotlib import pyplot

  • Anonymous
  • Python
  • 03 Mar 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

import sympy

import matplotlib.path as path

from math import pi, cos, sin, atan, asin, fabs, sqrt





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):

    if koef[0] * p[0] ** 2 + koef[1] * p[0] * p[1] + koef[2] * p[1] ** 2 + koef[3] * p[0] + koef[4] * p[1] + koef[

        5] < 0:

        return True

    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 = [i for i in 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 H





def empty_ellipse(p, points):

    bbPath = path.Path(p)

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

    for i in points:

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

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

                return False

            else:

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

                    return False

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





def equation(a, b, c):

    discriminant = b ** 2 - 4 * a * c

    if discriminant < 0:

        print('Корней нет')

        return None

    elif discriminant == 0:

        x = -b / (2 * a)

        return x

    else:

        x1 = (-b + discriminant ** 0.5) / (2 * a)

        x2 = (-b - discriminant ** 0.5) / (2 * a)

        return max(abs(x1), abs(x2))







points = []

while len(points) < 7:

    new_p = [numpy.random.randint(-10, 10), numpy.random.randint(-10, 10)]

    if new_p not in points:

        points.append(new_p)



print(points)

# points = [[-5, -3], [-4, 4], [2, 9], [-1, 8], [1, -4], [3, 4], [7, 4]]

empty_ellipses = []

ee = []



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):

                        flag = empty_ellipse(conv, points)

                        if flag:

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

                            empty_ellipses.append(flag)

                            ee.append([points[i1], points[i2], points[i3], points[i4], points[i5]])



k = 0

for i in points:

    if i in ee[0]:

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

    else:

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

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

    k = k + 1



points = np.array(points)



plt.grid()

plt.axis([-11, 11, -11, 11], 'equal')

plt.gca().set_aspect("equal")



# x = sympy.symbols('x')

# y = sympy.symbols('y')

# p0 = sympy.plot_implicit(sympy.Eq(empty_ellipses[0][0] * x*x + empty_ellipses[0][1] * x * y + empty_ellipses[0][2] * y*y + empty_ellipses[0][3] * x + empty_ellipses[0][4] * y + empty_ellipses[0][5]), show=False)

# for i in empty_ellipses:

#    p0.extend(sympy.plot_implicit(sympy.Eq(i[0] * (x ** 2) + i[1] * x * y + i[2] * (y ** 2) + i[3] * x + i[4] * y + i[5]), show=False))

# p0.show()





a = empty_ellipses[0][0]

b = empty_ellipses[0][1]

c = empty_ellipses[0][2]

d = empty_ellipses[0][3]

e = empty_ellipses[0][4]

f = empty_ellipses[0][5]



matrix = np.mat([[c, b/2], [b/2, a]])

print (matrix)

w, ww = np.linalg.eig(matrix)

print(ww)

ww = np.squeeze(np.asarray(ww))



y0 = (d * b - 2 * a * e) / (4 * a * c - b * b)  # y-position of the center

x0 = -(e + 2 * c * y0) / b  # x-position of the center



k = ww[0][1] / ww[0][0]

k1 = ww[1][1] / ww[1][0]



xrange = [-10, 0, 10]

yrange = [y0 + k * (_x - x0) for _x in xrange]

plt.plot(xrange, yrange)

yrange = [y0 + k1 * (_x - x0) for _x in xrange]

plt.plot(xrange, yrange)

# plt.plot([ww[0][0]+x0, x0, ww[1][0]+x0], [ww[0][1]+y0, y0, ww[1][1]+y0])



#

# _A = a + b * k + c * k * k

# _B = b * y0 - b * k * x0 - 2 * c * k * x0 + 2 * k * c * y0 + d + e * k

# _C = c * y0 * y0 + c * k * k * x0 * x0 - 2 * k * c * y0 * x0 + e * y0 - e * k * x0 + f

#

# print(_A, _B, _C)

#

# point_a = equation(_A, _B, _C)

# point_b = point_a * k + y0

#

# plt.plot(point_a, point_b, 'yo')

# ax = sqrt((point_a - x0) ** 2 + (point_b - y0) ** 2)

#

# _A = a + b * k1 + c * k1 * k1

# _B = b * y0 - b * k1 * x0 - 2 * c * k1 * x0 + 2 * k1 * c * y0 + d + e * k1

# _C = c * y0 * y0 + c * k1 * k1 * x0 * x0 - 2 * k1 * c * y0 * x0 + e * y0 - e * k1 * x0 + f

#

# print(_A, _B, _C)

#

# point_a = equation(_A, _B, _C)

# point_b = point_a * k1 + y0

#

# plt.plot(point_a, point_b, 'yo')

#

# by = sqrt((point_a - x0) ** 2 + (point_b - y0) ** 2)

#

# # radius on the x-axis

# # radius on the y-axis

#

# t_rot = atan(k)  # rotation angle

#

# t = np.linspace(0, 2 * pi, 100)

# Ell = np.array([ax * np.cos(t), by * np.sin(t)])

# R_rot = np.array([[cos(t_rot), -sin(t_rot)], [sin(t_rot), cos(t_rot)]])

# # 2-D rotation matrix

#

# Ell_rot = np.zeros((2, Ell.shape[1]))

# for i in range(Ell.shape[1]):

#     Ell_rot[:, i] = np.dot(R_rot, Ell[:, i])

#

# plt.plot(x0 + Ell_rot[0, :], y0 + Ell_rot[1, :], 'darkorange')  # rotated ellipse

# plt.grid(color='lightgray', linestyle='--')

# # plt.show()

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

# x = sympy.symbols('x')

# y = sympy.symbols('y')

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