def test_create(self):
v = Vector3()
self.assertTrue(np.array_equal(v, [0.,0.,0.]))
self.assertEqual(v.shape, self._shape)
v = Vector3([1.,2.,3.])
self.assertTrue(np.array_equal(v, [1.,2.,3.]))
self.assertEqual(v.shape, self._shape)
v = Vector3(Vector3())
self.assertTrue(np.array_equal(v, [0.,0.,0.]))
self.assertEqual(v.shape, self._shape)
v4 = [1., 2., 3., 4.]
result = vector3.create_from_vector4(v4)
v, w = result
np.testing.assert_almost_equal(v, [1.,2.,3.], decimal=5)
np.testing.assert_almost_equal(w, 4., decimal=5)
v4 = Vector4([1., 2., 3., 4.])
result = vector3.create_from_vector4(v4)
v, w = result
np.testing.assert_almost_equal(v, [1.,2.,3.], decimal=5)
np.testing.assert_almost_equal(w, 4., decimal=5)
m = Matrix44.from_translation([1.,2.,3.])
v = Vector3.from_matrix44_translation(m)
self.assertTrue(np.array_equal(v, [1.,2.,3.]))
m = Matrix44.from_translation([1.,2.,3.])
v = Vector3(m)
self.assertTrue(np.array_equal(v, [1.,2.,3.]))
def test_create(self):
v = Vector3()
self.assertTrue(np.array_equal(v, [0.,0.,0.]))
self.assertEqual(v.shape, self._shape)
v = Vector3([1.,2.,3.])
self.assertTrue(np.array_equal(v, [1.,2.,3.]))
self.assertEqual(v.shape, self._shape)
v = Vector3(Vector3())
self.assertTrue(np.array_equal(v, [0.,0.,0.]))
self.assertEqual(v.shape, self._shape)
v4 = [1., 2., 3., 4.]
result = vector3.create_from_vector4(v4)
v, w = result
np.testing.assert_almost_equal(v, [1.,2.,3.], decimal=5)
np.testing.assert_almost_equal(w, 4., decimal=5)
v4 = Vector4([1., 2., 3., 4.])
result = vector3.create_from_vector4(v4)
v, w = result
np.testing.assert_almost_equal(v, [1.,2.,3.], decimal=5)
np.testing.assert_almost_equal(w, 4., decimal=5)
m = Matrix44.from_translation([1.,2.,3.])
v = Vector3.from_matrix44_translation(m)
self.assertTrue(np.array_equal(v, [1.,2.,3.]))
m = Matrix44.from_translation([1.,2.,3.])
v = Vector3(m)
self.assertTrue(np.array_equal(v, [1.,2.,3.]))
def apply_to_vector( quat, vec ):
"""Rotates a vector by a quaternion.
:param numpy.array quat: The quaternion.
:param numpy.array vec: The vector.
:rtype: numpy.array
:return: The vector rotated by the quaternion.
.. seealso:: http://content.gpwiki.org/index.php/OpenGL:Tutorials:Using_Quaternions_to_represent_rotation
"""
def apply( quat, vec3 ):
"""
v = numpy.array( vec )
return v + 2.0 * vector.cross(
quat[:-1],
vector.cross( quat[:-1], v ) + (quat[-1] * v)
)
"""
length = vector.length( vec3 )
vec3 = vector.normalise( vec3 )
# use the vector to create a new quaternion
# this is basically the vector3 to vector4 conversion with W = 0
vec_quat = numpy.array( [ vec3[ 0 ], vec3[ 1 ], vec3[ 2 ], 0.0 ] )
# quat * vec * quat^-1
result = cross( quat, cross( vec_quat, conjugate( quat ) ) )
return result[ :-1 ] * length
if vec.size == 3:
# convert to vector4
# ignore w component
return apply( quat, vec )
elif vec.size == 4:
vec3 = vector3.create_from_vector4( vec )
vec3 = apply( quat, vec3 )
return vector4.create_from_vector3( vec3 )
else:
raise ValueError( "Vector size unsupported" )
def test_create_from_vector4(self):
v4 = [1., 2., 3., 4.]
result = vector3.create_from_vector4(v4)
v, w = result
np.testing.assert_almost_equal(v, [1., 2., 3.], decimal=5)
np.testing.assert_almost_equal(w, 4., decimal=5)
def test_create_from_vector4(self):
v4 = [1., 2., 3., 4.]
result = vector3.create_from_vector4(v4)
v, w = result
np.testing.assert_almost_equal(v, [1.,2.,3.], decimal=5)
np.testing.assert_almost_equal(w, 4., decimal=5)