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
import matplotlib.path as path
from math import pi, cos, sin, atan, asin, fabs, sqrt
def ellipse_by_5_points(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 = -numpy.linalg.det(B)
c = numpy.linalg.det(C)
d = -numpy.linalg.det(D)
e = numpy.linalg.det(E)
f = -numpy.linalg.det(F)
return [a, b, c, d, e, f]
def in_ellipse(p, k):
if k[0] * p[0] ** 2 + k[1] * p[0] * p[1] + k[2] * p[1] ** 2 + k[3] * p[0] + k[4] * p[1] + k[5] < 0:
return True
return False
def empty_ellipse(k, points,used_points):
for i in points:
if i not in used_points and in_ellipse(i, k):
return False
return True
def empty_ellipses_into_5_points(points):
empty_ellipses = []
e_numbers = []
for p1 in range(len(p)):
for p2 in range(p1 + 1, len(p)):
for p3 in range(p2 + 1, len(p)):
for p4 in range(p3 + 1, len(p)):
for p5 in range(p4 + 1, len(p)):
if points_for_ellipse([p[p1], p[p2], p[p3], p[p4], p[p5]]):
k = ellipse_by_5_points([points[p1], points[p2], points[p3], points[p4], points[p5]])
draw_ellipse(k)
if empty_ellipse(k, points, [p[p1], p[p2], p[p3], p[p4], p[p5]]):
print(p1, p2, p3, p4, p5)
empty_ellipses.append(k)
e_numbers.append([p1, p2, p3, p4, p5])
return empty_ellipses, e_numbers
def draw_ellipse(ellipse):
a = ellipse[0]
b = ellipse[1]
c = ellipse[2]
d = ellipse[3]
e = ellipse[4]
f = ellipse[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)]])
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
# return [b / (2 * a), c / a]
def create_points(N):
points = []
while len(points) < N:
new_p = [numpy.random.randint(-10, 10), numpy.random.randint(-10, 10)]
if new_p not in points:
points.append(new_p)
return points
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))]
for i in range(len(H)):
if angle_180(H[i - 2], H[i - 1], H[i]):
return None
return H
def angle_180(a, b, c):
A = [a[0] - b[0], a[1] - b[1]]
B = [c[0] - b[0], c[1] - b[1]]
skal = A[0] * B[0] + A[1] * B[1]
d_A = A[0] * A[0] + A[1] * A[1]
d_B = B[0] * B[0] + B[1] * B[1]
if skal / (d_A * d_B) == -1:
return True
else:
return False
def points_for_ellipse(p):
conv = jarvismarch(p)
if (conv is not None and len(conv) == 5):
for i in range(len(p)):
return True
else:
return False
# p = create_points(6)
# print(p)
p = [[0, -1], [1, 7], [-9, -5], [1, -10], [4, -7], [5, 2]]
empty_ellipses, e_numbers = empty_ellipses_into_5_points(p)
print(e_numbers)
k = 0
for i in p:
plt.plot(i[0], i[1], 'bo')
plt.annotate(str("%d" % k), [i[0], i[1]])
k = k + 1
plt.grid()
plt.axis([-11, 11, -11, 11], 'equal')
plt.gca().set_aspect("equal")
plt.show()
# for ellipse in empty_ellipses:
# draw_ellipse(ellipse)
# plt.grid(color='lightgray', linestyle='--')
# plt.savefig('/home/kate/Рабочий стол/Figure_1.png')