def is_seg1_overlapping_with_seg2(seg1, seg2):
'''Checks if a segment is in proximity of another one upstream'''
# get the coordinates of seg2 (from the origin)
s1 = coords(seg2[0])
s2 = coords(seg2[1])
# vector of the center of seg2 (from the origin)
C = 0.5 * (s1 + s2)
# endpoint of seg1 (from the origin)
P = coords(seg1[1])
# vector from the center C of seg2 to the endpoint P of seg1
CP = P - C
# vector of seg2
S1S2 = s2 - s1
# projection of CP upon seg2
prj = mm.vector_projection(CP, S1S2)
# check if the distance of the orthogonal complement of CP projection on S1S2
# (vertical distance from P to seg2) is smaller than the sum of the radii. (overlap)
# If not exit early, because there is no way that backtracking can feasible
if not is_seg2_within_seg1_radius(np.linalg.norm(CP - prj), seg1, seg2):
return False
# projection lies within the length of the cylinder. Check if the distance between
# the center C of seg2 and the projection of the end point of seg1, P is smaller than
# half of the others length plus a 5% tolerance
return np.linalg.norm(prj) < 0.55 * np.linalg.norm(S1S2)
def test_vector_projection_collinear():
v1 = np.array([1., 2., 3.])
v2 = np.array([4., 8., 12.])
res = mm.vector_projection(v1, v2)
assert np.allclose(res, v1)
def test_vector_projection_perpendicular():
v1 = np.array([2., 0., 0.])
v2 = np.array([0., 3., 0.])
res = mm.vector_projection(v1, v2)
assert np.allclose(res, (0., 0., 0.))
def is_seg1_overlapping_with_seg2(seg1, seg2):
'''Checks if a segment is in proximity of another one upstream'''
# get the coordinates of seg2 (from the origin)
s1 = coords(seg2[0])
s2 = coords(seg2[1])
# vector of the center of seg2 (from the origin)
C = 0.5 * (s1 + s2)
# endpoint of seg1 (from the origin)
P = coords(seg1[1])
# vector from the center C of seg2 to the endpoint P of seg1
CP = P - C
# vector of seg2
S1S2 = s2 - s1
# projection of CP upon seg2
prj = mm.vector_projection(CP, S1S2)
# check if the distance of the orthogonal complement of CP projection on S1S2
# (vertical distance from P to seg2) is smaller than the sum of the radii. (overlap)
# If not exit early, because there is no way that backtracking can feasible
if not is_seg2_within_seg1_radius(np.linalg.norm(CP - prj), seg1,
seg2):
return False
# projection lies within the length of the cylinder. Check if the distance between
# the center C of seg2 and the projection of the end point of seg1, P is smaller than
# half of the others length plus a 5% tolerance
return np.linalg.norm(prj) < 0.55 * np.linalg.norm(S1S2)
def test_vector_projection_perpendicular():
v1 = np.array([2., 0., 0.])
v2 = np.array([0., 3., 0.])
res = mm.vector_projection(v1, v2)
nt.assert_true(np.allclose(res, (0.,0.,0.)))
def test_vector_projection_collinear():
v1 = np.array([1., 2., 3.])
v2 = np.array([4., 8., 12.])
res = mm.vector_projection(v1, v2)
nt.assert_true(np.allclose(res, v1))
def test_vector_projection():
v1 = np.array([4., 1., 0.])
v2 = np.array([2., 3., 0.])
res = mm.vector_projection(v1, v2)
nt.assert_true(
np.allclose(res, (1.6923076923076923, 2.5384615384615383, 0.)))
def test_vector_projection():
v1 = np.array([4., 1., 0.])
v2 = np.array([2., 3., 0.])
res = mm.vector_projection(v1, v2)
nt.assert_true(np.allclose(res, (1.6923076923076923, 2.5384615384615383, 0.)))
