def test_angle_3points_half_pi():
orig = (0.0, 0.0, 0.0)
vec1 = (1.0, 0.0, 0.0)
vec2 = (0.0, 2.0, 0.0)
nt.eq_(mm.angle_3points(orig, vec1, vec2), pi / 2.0)
vec2 = (0.0, 0.0, 3.0)
nt.eq_(mm.angle_3points(orig, vec1, vec2), pi / 2.0)
vec2 = (0.0, 0.0, -3.0)
nt.eq_(mm.angle_3points(orig, vec1, vec2), pi / 2.0)
vec1 = (0.0, 4.0, 0.0)
nt.eq_(mm.angle_3points(orig, vec1, vec2), pi / 2.0)
def test_angle_3points_half_pi():
orig = (0.0, 0.0, 0.0)
vec1 = (1.0, 0.0, 0.0)
vec2 = (0.0, 2.0, 0.0)
assert mm.angle_3points(orig, vec1, vec2) == pi / 2.0
vec2 = (0.0, 0.0, 3.0)
assert mm.angle_3points(orig, vec1, vec2) == pi / 2.0
vec2 = (0.0, 0.0, -3.0)
assert mm.angle_3points(orig, vec1, vec2) == pi / 2.0
vec1 = (0.0, 4.0, 0.0)
assert mm.angle_3points(orig, vec1, vec2) == pi / 2.0
def local_bifurcation_angle(bif_point):
"""Return the opening angle between two out-going sections in a bifurcation point.
We first ensure that the input point has only two children.
The bifurcation angle is defined as the angle between the first non-zero
length segments of a bifurcation point.
"""
def skip_0_length(sec):
"""Return the first point with non-zero distance to first point."""
p0 = sec[0]
cur = sec[1]
for i, p in enumerate(sec[1:]):
if not np.all(p[:COLS.R] == p0[:COLS.R]):
cur = sec[i + 1]
break
return cur
_raise_if_not_bifurcation(bif_point)
ch0, ch1 = (skip_0_length(bif_point.children[0].points),
skip_0_length(bif_point.children[1].points))
return morphmath.angle_3points(bif_point.points[-1], ch0, ch1)
def test_angle_3points_three_quarter_pi():
orig = (0.0, 0.0, 0.0)
vec1 = (1.0, 0.0, 0.0)
vec2 = (-2.0, 2.0, 0.0)
nt.assert_equal(mm.angle_3points(orig, vec1, vec2), 3 * pi / 4.0)
vec2 = (-3.0, 3.0, 0.0)
nt.assert_equal(mm.angle_3points(orig, vec1, vec2), 3* pi / 4.0)
vec2 = (-3.0, -3.0, 0.0)
nt.assert_equal(mm.angle_3points(orig, vec1, vec2), 3 * pi / 4.0)
vec2 = (-3.0, 0.0, 3.0)
nt.assert_equal(mm.angle_3points(orig, vec1, vec2), 3 * pi / 4.0)
vec2 = (-3.0, 0.0, -3.0)
nt.assert_equal(mm.angle_3points(orig, vec1, vec2), 3 * pi / 4.0)
def test_angle_3points_three_quarter_pi():
orig = (0.0, 0.0, 0.0)
vec1 = (1.0, 0.0, 0.0)
vec2 = (-2.0, 2.0, 0.0)
assert mm.angle_3points(orig, vec1, vec2) == 3 * pi / 4.0
vec2 = (-3.0, 3.0, 0.0)
assert mm.angle_3points(orig, vec1, vec2) == 3 * pi / 4.0
vec2 = (-3.0, -3.0, 0.0)
assert mm.angle_3points(orig, vec1, vec2) == 3 * pi / 4.0
vec2 = (-3.0, 0.0, 3.0)
assert mm.angle_3points(orig, vec1, vec2) == 3 * pi / 4.0
vec2 = (-3.0, 0.0, -3.0)
assert mm.angle_3points(orig, vec1, vec2) == 3 * pi / 4.0
def remote_bifurcation_angle(bif_point):
'''Return the opening angle between two out-going sections
in a bifurcation point
The angle is defined as between the bifurcation point and the
last points in the out-going sections.
'''
return morphmath.angle_3points(bif_point.points[-1],
bif_point.children[0].points[-1],
bif_point.children[1].points[-1])
def remote_bifurcation_angle(bif_point):
'''Return the opening angle between two out-going sections
in a bifurcation point
The angle is defined as between the bifurcation point and the
last points in the out-going sections.
'''
return morphmath.angle_3points(bif_point.points[-1],
bif_point.children[0].points[-1],
bif_point.children[1].points[-1])
def remote_bifurcation_angle(bif_point):
"""Return the opening angle between two out-going sections in a bifurcation point.
We first ensure that the input point has only two children.
The angle is defined as between the bifurcation point and the
last points in the out-going sections.
"""
_raise_if_not_bifurcation(bif_point)
return morphmath.angle_3points(bif_point.points[-1],
bif_point.children[0].points[-1],
bif_point.children[1].points[-1])
def remote_bifurcation_angle(bif_point):
'''Return the opening angle between two out-going sections
in a bifurcation point
We first ensure that the input point has only two children.
The angle is defined as between the bifurcation point and the
last points in the out-going sections.
'''
assert len(bif_point.children) == 2, 'A bifurcation point must have exactly 2 children'
return morphmath.angle_3points(bif_point.points[-1],
bif_point.children[0].points[-1],
bif_point.children[1].points[-1])
def local_bifurcation_angle(bifurcation_point):
'''Return the opening angle between two out-going segments
in a bifurcation point
The bifurcation angle is defined as the angle between the first non-zero
length segments of a bifurcation point.
'''
def _skip_0_length(p, c):
'''Return the first child c with non-zero distance to parent p'''
while np.all(p.value[:COLS.R] == c.value[:COLS.R])\
and not tr.is_leaf(c) and not tr.is_forking_point(c):
c = c.children[0]
return c
ch = (_skip_0_length(bifurcation_point, bifurcation_point.children[0]),
_skip_0_length(bifurcation_point, bifurcation_point.children[1]))
return mm.angle_3points(bifurcation_point.value,
ch[0].value, ch[1].value)
def local_bifurcation_angle(bif_point):
'''Return the opening angle between two out-going sections
in a bifurcation point
The bifurcation angle is defined as the angle between the first non-zero
length segments of a bifurcation point.
'''
def skip_0_length(sec):
'''Return the first point with non-zero distance to first point'''
p0 = sec[0]
cur = sec[1]
for i, p in enumerate(sec[1:]):
if not np.all(p[:COLS.R] == p0[:COLS.R]):
cur = sec[i + 1]
break
return cur
ch = (skip_0_length(bif_point.children[0].points),
skip_0_length(bif_point.children[1].points))
return mm.angle_3points(bif_point.points[-1], ch[0], ch[1])
def local_bifurcation_angle(bif_point):
'''Return the opening angle between two out-going sections
in a bifurcation point
The bifurcation angle is defined as the angle between the first non-zero
length segments of a bifurcation point.
'''
def skip_0_length(sec):
'''Return the first point with non-zero distance to first point'''
p0 = sec[0]
cur = sec[1]
for i, p in enumerate(sec[1:]):
if not np.all(p[:COLS.R] == p0[:COLS.R]):
cur = sec[i + 1]
break
return cur
ch0, ch1 = (skip_0_length(bif_point.children[0].points),
skip_0_length(bif_point.children[1].points))
return morphmath.angle_3points(bif_point.points[-1], ch0, ch1)
def meander_angle(triplet):
'''Return the angle between a triplet of consecutive points'''
return mm.angle_3points(triplet[1], triplet[0], triplet[2])
def test_angle_3points_opposing_returns_pi():
orig = (0.0, 0.0, 0.0)
vec1 = (1.0, 1.0, 1.0)
vec2 = (-2.0, -2.0, -2.0)
angle = mm.angle_3points(orig, vec1, vec2)
assert angle == pi
def test_angle_3points_equal_points_returns_zero():
orig = (0.0, 1.0, 0.0)
vec1 = (1.0, 0.0, 0.0)
vec2 = (0.0, 1.0, 0.0)
a = mm.angle_3points(orig, vec1, vec2)
nt.assert_equal(a, 0.0)
def test_angle_3points_equal_points_returns_zero():
orig = (0.0, 1.0, 0.0)
vec1 = (1.0, 0.0, 0.0)
vec2 = (0.0, 1.0, 0.0)
a = mm.angle_3points(orig, vec1, vec2)
assert a == 0.0
def test_angle_3points_opposing_returns_pi():
orig = (0.0, 0.0, 0.0)
vec1 = (1.0, 1.0, 1.0)
vec2 = (-2.0, -2.0, -2.0)
angle=mm.angle_3points(orig, vec1, vec2)
nt.assert_equal(angle, pi)
def test_angle_3points_collinear_returns_zero():
orig = (0.0, 0.0, 0.0)
vec1 = (1.0, 1.0, 1.0)
vec2 = (2.0, 2.0, 2.0)
angle = mm.angle_3points(orig, vec1, vec2)
assert angle == 0.0
def test_angle_3points_collinear_returns_zero():
orig = (0.0, 0.0, 0.0)
vec1 = (1.0, 1.0, 1.0)
vec2 = (2.0, 2.0, 2.0)
angle=mm.angle_3points(orig, vec1, vec2)
nt.assert_equal(angle, 0.0)
def section_meander_angles(section):
'''Inter-segment opening angles in a section'''
p = section.points
return [
mm.angle_3points(p[i - 1], p[i - 2], p[i]) for i in range(2, len(p))
]
def section_meander_angles(section):
'''Inter-segment opening angles in a section'''
p = section.points
return [mm.angle_3points(p[i - 1], p[i - 2], p[i])
for i in range(2, len(p))]