def bbox_volume(coords, angles=(0., 0.)):
"""
Compute the volume of bouding box of a cloud of points
for a given rotation of the cloud of points
Needs the rotation angles (rotation angle along x, rotation angle along y)
and the coordinates (3D array) of the cloud of points
"""
angles = np.array(angles)
# cloud of points rotation
coords_rot = bf.rotate_aggregate(coords, angles=angles)
# calculation of the side
_min = coords_rot.min(axis=0)
_max = coords_rot.max(axis=0)
lengths = np.sqrt((_max - _min)**2)
volume = lengths[0] * lengths[1] * lengths[2]
return volume
def included_ellipsoid_optim(coord, tol=1e-13, quiet=True):
"""
Compute the largest included ellidpsoid of a cloud of points
Needs the required precision (tol)
and the coordinates (3D array) of the cloud of points
"""
# finding optimal bounding box
bbox_res = bbox.bbox_optim(coord)
if quiet is False:
plot.bbox_plot(coord, bbox_res)
# rotation of the cloud of points in the main direction of the bbox
coord = bf.rotate_aggregate(coord, angles=bbox_res['angles'])
# initial a, b, c
a = (np.sqrt((max(coord[:, 0]) - min(coord[:, 0]))**2)) / 2.
b = (np.sqrt((max(coord[:, 1]) - min(coord[:, 1]))**2)) / 2.
c = (np.sqrt((max(coord[:, 2]) - min(coord[:, 2]))**2)) / 2.
a_before = 0.
b_before = 0.
c_before = 0.
volume_before = 0.
volume = 4. / 3. * np.pi * a * b * c
test = 'false'
point_inside = 'true'
while abs(volume - volume_before) > tol:
volume_before = volume
# test if points inside the bounded ellipsoid
for i in range(len(coord)):
if (coord[i, 0]**2 / a**2 + coord[i, 1]**2 / b**2 +
coord[i, 2]**2 / c**2) < 1:
point_inside = 'true'
#print('x =', coord[i, 0], 'y =', coord[i, 1], 'z =', coord[i, 2])
break
else:
point_inside = 'false'
if point_inside == 'true':
a1 = a_before
b1 = b_before
c1 = c_before
a_before = a
b_before = b
c_before = c
a = a - abs(a1 - a) / 2.
b = b - abs(b1 - b) / 2.
c = c - abs(c1 - c) / 2.
test = 'true'
elif point_inside == 'false' and test == 'true':
a1 = a_before
b1 = b_before
c1 = c_before
a_before = a
b_before = b
c_before = c
a = a + abs(a1 - a) / 2.
b = b + abs(b1 - b) / 2.
c = c + abs(c1 - c) / 2.
else:
print(
'error, the bbox did not work:'
' bbox does not not touch the extrema of the cloud of points')
break
volume = 4. / 3. * np.pi * a * b * c
if (quiet is False):
print('volume =', volume)
print('a = ', a, 'b = ', b, 'c = ', c)
plot.fit_ellipsoid_plot(coord, a, b, c, 10000)
return {'volume': volume, 'a': a, 'b': b, 'c': c, 'bbox': bbox_res}
def bounding_ellipsoid_optim(coord, tol=1e-3, quiet=True):
"""
Compute the smallest bounding ellidpsoid of a cloud of points
Needs the required precision (tol)
and the coordinates (3D array) of the cloud of points
"""
# finding optimal bounding box
bbox_res = bbox.bbox_optim(coord)
if quiet is False:
plot.bbox_plot(coord, bbox_res)
# rotation of the cloud of points in the main direction of the bbox
coord = bf.rotate_aggregate(coord, angles=bbox_res['angles'])
# plot.bbox_plot(coord, 0., 0., 2)
# initial a, b, c
a = np.sqrt((max(coord[:, 0]) - min(coord[:, 0]))**2) / 2.
b = np.sqrt((max(coord[:, 1]) - min(coord[:, 1]))**2) / 2.
c = np.sqrt((max(coord[:, 2]) - min(coord[:, 2]))**2) / 2.
volume_before = 0.
volume = 4. / 3. * np.pi * a * b * c
while abs(volume - volume_before) > tol:
volume_before = volume
# test if points outside the bounded ellipsoid
for i in range(len(coord)):
if (coord[i, 0]**2 / a**2 + coord[i, 1]**2 / b**2 +
coord[i, 2]**2 / c**2) > 1:
point_outside = 'true'
break
else:
point_outside = 'false'
if point_outside == 'true':
a_before = a
b_before = b
c_before = c
a = a * 2
b = b * 2
c = c * 2
elif point_outside == 'false':
a1 = a_before
b1 = b_before
c1 = c_before
a_before = a
b_before = b
c_before = c
a = a - abs(a1 - a) / 2.
b = b - abs(b1 - b) / 2.
c = c - abs(c1 - c) / 2.
volume = 4. / 3. * np.pi * a * b * c
"""
print(point_outside)
print('before =', volume_before)
"""
if (quiet is False):
print('volume =', volume)
print('a = ', a, 'b = ', b, 'c = ', c)
plot.fit_ellipsoid_plot(coord, a, b, c, 10000)
return {'volume': volume, 'a': a, 'b': b, 'c': c, 'bbox': bbox_res}
import basic_functions as bf
import matplotlib.pyplot as plt
ellipsoid = {'a': 100, 'b': 50, 'c': 30}
aggregate = tie.ellipsoid_test_image(ellipsoid,
npoints=10000,
noise_amplitude=10.,
angles=(np.pi / 7., np.pi / 6.))
fig = plot.scatter_plot(aggregate)
bb.bbox_volume(aggregate)
bbox = bb.bbox_optim(aggregate)
print(bbox)
fig = plot.bbox_plot(aggregate, bbox)
rotated_aggregate = bf.rotate_aggregate(aggregate, angles=bbox['angles'])
rotated_bbox = bb.compute_bbox(rotated_aggregate)
fig = plot.bbox_plot(rotated_aggregate, rotated_bbox)
ellipsoid = be.bounding_ellipsoid_optim(aggregate)
plot.fit_ellipsoid_plot(rotated_aggregate, ellipsoid)
ellipsoid = {'a': 100, 'b': 50, 'c': 30}
aggregate = tie.ellipsoid_test_image(ellipsoid,
npoints=10000,
noise_amplitude=30.,
angles=(np.pi / 7., np.pi / 6.))
plot.scatter_plot(aggregate)
ellipsoid = be.bounding_ellipsoid_optim(aggregate, 1e-3)
rotated_aggregate = bf.rotate_aggregate(aggregate,