import numpy linalg import numpy random from matplotlib import pyplot

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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([-21, 21, -21, 21], 'equal')
plt.gca().set_aspect("equal")
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]])
w, ww = np.linalg.eig(matrix)
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]
r_2 = a * x0 *x0 + b * x0 * y0 + c * y0 * y0 - f
delta_x = r_2/(a+b*k+c*k*k)
delta_y = k*k * delta_x
ax = sqrt(delta_x + delta_y)
delta_x = r_2/(a+b*k1+c*k1*k1)
delta_y = k1 *k1* delta_x
by = sqrt(delta_x + delta_y)
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()