def test_superpose(self):
# create a few test sets with random data points, including degenerate
# situations. (e.g. one point, two points, linear points)
references = [ # a list of 2-tuples: (points, degenerate)
(numpy.random.normal(0, 5, (n, 3)), False) for n in xrange(4, 40)
] + [
#(numpy.array([[0,0,1]], float), True),
#(numpy.array([[0,0,0],[0,0,1]], float), True),
#(numpy.array([[0,0,0],[0,0,1],[0,0,2]], float), True),
#(numpy.array([[0,0,0],[0,0,1],[0,0,2],[0,0,4]], float), True),
#(numpy.random.normal(0, 5, (3, 3)), True)
]
# Do a random transformation on the points
randomized = []
for points, degenerate in references:
#points[:] -= points.mean(axis=0)
axis = random_unit(3)
angle = numpy.random.uniform(0, numpy.pi * 2)
transformation = Complete()
transformation.set_rotation_properties(angle, axis, False)
transformation.t[:] = numpy.random.normal(0, 5, 3)
randomized.append(
(numpy.array([transformation.vector_apply(p)
for p in points]), transformation))
for (ref_points, degenerate), (tr_points,
transf) in zip(references, randomized):
check_transf = superpose(ref_points, tr_points)
# check whether the rotation matrix is orthogonal
self.assertArraysAlmostEqual(
numpy.dot(check_transf.r, check_transf.r.transpose()),
numpy.identity(3, float), 1e-5)
# first check whether check_transf brings the tr_points back to the ref_points
check_points = numpy.dot(
tr_points, check_transf.r.transpose()) + check_transf.t
self.assertArraysAlmostEqual(ref_points,
check_points,
1e-5,
doabs=True)
if not degenerate:
# if the set of points is not degenerate, check whether transf and check_transf
# are each other inverses
tmp = Complete()
tmp.apply_before(transf)
tmp.apply_before(check_transf)
self.assertArraysAlmostEqual(
numpy.dot(transf.r, check_transf.r),
numpy.identity(3, float), 1e-5)
self.assertArrayAlmostZero(tmp.t, 1e-5)
# Add some distortion to the transformed points
randomized = []
for tr_points, transf in randomized:
tr_points[:] += numpy.random.normal(0, 1.0, len(tr_points))
# Do a blind test
for (ref_points, degenerate), (tr_points,
transf) in zip(references, randomized):
superpose(ref_points, tr_points)
def test_superpose(self):
# create a few test sets with random data points, including degenerate
# situations. (e.g. one point, two points, linear points)
references = [ # a list of 2-tuples: (points, degenerate)
(numpy.random.normal(0, 5, (n, 3)), False) for n in xrange(4, 40)
] + [
#(numpy.array([[0,0,1]], float), True),
#(numpy.array([[0,0,0],[0,0,1]], float), True),
#(numpy.array([[0,0,0],[0,0,1],[0,0,2]], float), True),
#(numpy.array([[0,0,0],[0,0,1],[0,0,2],[0,0,4]], float), True),
#(numpy.random.normal(0, 5, (3, 3)), True)
]
# Do a random transformation on the points
randomized = []
for points, degenerate in references:
#points[:] -= points.mean(axis=0)
axis = random_unit(3)
angle = numpy.random.uniform(0, numpy.pi*2)
transformation = Complete()
transformation.set_rotation_properties(angle, axis, False)
transformation.t[:] = numpy.random.normal(0, 5, 3)
randomized.append((
numpy.array([transformation.vector_apply(p) for p in points]),
transformation
))
for (ref_points, degenerate), (tr_points, transf) in zip(references, randomized):
check_transf = superpose(ref_points, tr_points)
# check whether the rotation matrix is orthogonal
self.assertArraysAlmostEqual(numpy.dot(check_transf.r, check_transf.r.transpose()), numpy.identity(3, float), 1e-5)
# first check whether check_transf brings the tr_points back to the ref_points
check_points = numpy.dot(tr_points, check_transf.r.transpose()) + check_transf.t
self.assertArraysAlmostEqual(ref_points, check_points, 1e-5, doabs=True)
if not degenerate:
# if the set of points is not degenerate, check whether transf and check_transf
# are each other inverses
tmp = Complete()
tmp.apply_before(transf)
tmp.apply_before(check_transf)
self.assertArraysAlmostEqual(numpy.dot(transf.r, check_transf.r), numpy.identity(3, float), 1e-5)
self.assertArrayAlmostZero(tmp.t, 1e-5)
# Add some distortion to the transformed points
randomized = []
for tr_points, transf in randomized:
tr_points[:] += numpy.random.normal(0, 1.0, len(tr_points))
# Do a blind test
for (ref_points, degenerate), (tr_points, transf) in zip(references, randomized):
superpose(ref_points, tr_points)
