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

import sympy

import matplotlib.path as path

from math import pi, cos, sin, 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]





points = []

while len(points) < 10:

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

    if new_p not in points:

        points.append(new_p)



print(points)



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:

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

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

    k = k + 1



points = np.array(points)



plt.grid()

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



# 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]



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

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



ax = sqrt(c)  # radius on the x-axis

by = sqrt(a)  # radius on the y-axis

t_rot = 0 # 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(u + Ell_rot[0, :], v + Ell_rot[1, :], 'darkorange')  # rotated ellipse

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

# plt.show()

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