def test_rotate(self):
q = Quaternion.from_axis_angle(numpy.array([0, 1, 0]), math.pi / 2.0)
v = q.rotate((1, 0, 0))
self.assertAlmostEqual(0, v[0])
self.assertAlmostEqual(0, v[1])
self.assertAlmostEqual(-1, v[2])
def test_rotate(self):
q = Quaternion.from_axis_angle(numpy.array([0, 1, 0]), math.pi / 2.0)
v = q.rotate((1, 0, 0))
self.assertAlmostEqual( 0, v[0])
self.assertAlmostEqual( 0, v[1])
self.assertAlmostEqual(-1, v[2])
def test_from_axis_angle(self):
theta = math.pi / 5.0
c = math.cos(theta / 2.0)
s = math.sin(theta / 2.0)
q = Quaternion.from_axis_angle(numpy.array([1, -1, 1]), theta)
self.assertAlmostEqual(c, q.w)
self.assertAlmostEqual(s * math.sqrt(1.0 / 3.0), q.x)
self.assertAlmostEqual(-s * math.sqrt(1.0 / 3.0), q.y)
self.assertAlmostEqual(s * math.sqrt(1.0 / 3.0), q.z)
def test_from_axis_angle(self):
theta = math.pi / 5.0
c = math.cos(theta / 2.0)
s = math.sin(theta / 2.0)
q = Quaternion.from_axis_angle(numpy.array([1, -1, 1]), theta)
self.assertAlmostEqual( c, q.w)
self.assertAlmostEqual( s * math.sqrt(1.0 / 3.0), q.x)
self.assertAlmostEqual(-s * math.sqrt(1.0 / 3.0), q.y)
self.assertAlmostEqual( s * math.sqrt(1.0 / 3.0), q.z)
def setUp(self):
self.a = Quaternion(1, 0, 1, 0)
self.b = Quaternion(1, 1, 0, 0)
self.c = Quaternion(0, 1, 0, 1)
class TestQuaternion(unittest.TestCase):
def setUp(self):
self.a = Quaternion(1, 0, 1, 0)
self.b = Quaternion(1, 1, 0, 0)
self.c = Quaternion(0, 1, 0, 1)
def test_iadd(self):
self.a += self.c
self.b += self.c
self.assertEqual(Quaternion(1, 1, 1, 1), self.a)
self.assertEqual(Quaternion(1, 2, 0, 1), self.b)
def test_isub(self):
self.a -= self.c
self.b -= self.c
self.assertEqual(Quaternion(1, -1, 1, -1), self.a)
self.assertEqual(Quaternion(1, 0, 0, -1), self.b)
def test_imul(self):
ua = numpy.float32(self.a.w)
ub = numpy.float32(self.b.w)
va = numpy.array([self.a.x, self.a.y, self.a.z])
vb = numpy.array([self.b.x, self.b.y, self.b.z])
u = ua * ub - numpy.dot(va, vb)
v = ua * vb + ub * va + numpy.cross(va, vb)
self.a *= self.b
self.assertAlmostEqual(self.a.w, u)
self.assertAlmostEqual(self.a.x, v[0])
self.assertAlmostEqual(self.a.y, v[1])
self.assertAlmostEqual(self.a.z, v[2])
def test_add(self):
self.assertEqual(Quaternion(1, 1, 1, 1), self.a + self.c)
self.assertEqual(Quaternion(1, 2, 0, 1), self.b + self.c)
def test_sub(self):
self.assertEqual(Quaternion(1, -1, 1, -1), self.a - self.c)
self.assertEqual(Quaternion(1, 0, 0, -1), self.b - self.c)
def test_mul(self):
ua = numpy.float32(self.a.w)
ub = numpy.float32(self.b.w)
va = numpy.array([self.a.x, self.a.y, self.a.z])
vb = numpy.array([self.b.x, self.b.y, self.b.z])
u = ua * ub - numpy.dot(va, vb)
v = ua * vb + ub * va + numpy.cross(va, vb)
r = self.a * self.b
self.assertAlmostEqual(r.w, u)
self.assertAlmostEqual(r.x, v[0])
self.assertAlmostEqual(r.y, v[1])
self.assertAlmostEqual(r.z, v[2])
def test_eq(self):
self.assertTrue(Quaternion(1, 2, 3, 4), Quaternion(1, 2, 3, 4))
def test_ne(self):
self.assertTrue(Quaternion(1, 2, 3, 4), Quaternion(0, 2, 3, 4))
def test_length(self):
self.assertAlmostEqual(math.sqrt(2.0), self.a.length, places=6)
self.assertAlmostEqual(math.sqrt(2.0), self.b.length, places=6)
self.assertAlmostEqual(math.sqrt(2.0), self.c.length, places=6)
def test_normalize(self):
self.assertTrue(self.a.length > 1.0)
self.assertTrue(self.b.length > 1.0)
self.assertTrue(self.c.length > 1.0)
self.assertAlmostEqual(1.0, self.a.normalized().length, places=6)
self.assertAlmostEqual(1.0, self.b.normalized().length, places=6)
self.assertAlmostEqual(1.0, self.c.normalized().length, places=6)
def test_inverted(self):
self.assertEqual(self.a, self.a.inverted().inverted())
self.assertAlmostEqual(0.5, self.a.inverted().w)
self.assertAlmostEqual(0.0, self.a.inverted().x)
self.assertAlmostEqual(-0.5, self.a.inverted().y)
self.assertAlmostEqual(0.0, self.a.inverted().z)
self.assertTrue(self.a is not self.a.inverted().inverted())
def test_from_axis_angle(self):
theta = math.pi / 5.0
c = math.cos(theta / 2.0)
s = math.sin(theta / 2.0)
q = Quaternion.from_axis_angle(numpy.array([1, -1, 1]), theta)
self.assertAlmostEqual(c, q.w)
self.assertAlmostEqual(s * math.sqrt(1.0 / 3.0), q.x)
self.assertAlmostEqual(-s * math.sqrt(1.0 / 3.0), q.y)
self.assertAlmostEqual(s * math.sqrt(1.0 / 3.0), q.z)
def test_rotate(self):
q = Quaternion.from_axis_angle(numpy.array([0, 1, 0]), math.pi / 2.0)
v = q.rotate((1, 0, 0))
self.assertAlmostEqual(0, v[0])
self.assertAlmostEqual(0, v[1])
self.assertAlmostEqual(-1, v[2])
def test_conjugated(self):
self.assertEqual(Quaternion(1, 0, -1, 0), self.a.conjugated())
self.assertEqual(Quaternion(1, -1, 0, 0), self.b.conjugated())
self.assertEqual(Quaternion(0, -1, 0, -1), self.c.conjugated())
def test_ne(self):
self.assertTrue(Quaternion(1, 2, 3, 4), Quaternion(0, 2, 3, 4))
def test_sub(self):
self.assertEqual(Quaternion(1, -1, 1, -1), self.a - self.c)
self.assertEqual(Quaternion(1, 0, 0, -1), self.b - self.c)
def test_add(self):
self.assertEqual(Quaternion(1, 1, 1, 1), self.a + self.c)
self.assertEqual(Quaternion(1, 2, 0, 1), self.b + self.c)
def test_isub(self):
self.a -= self.c
self.b -= self.c
self.assertEqual(Quaternion(1, -1, 1, -1), self.a)
self.assertEqual(Quaternion(1, 0, 0, -1), self.b)
def test_iadd(self):
self.a += self.c
self.b += self.c
self.assertEqual(Quaternion(1, 1, 1, 1), self.a)
self.assertEqual(Quaternion(1, 2, 0, 1), self.b)
def test_conjugated(self):
self.assertEqual(Quaternion(1, 0, -1, 0), self.a.conjugated())
self.assertEqual(Quaternion(1, -1, 0, 0), self.b.conjugated())
self.assertEqual(Quaternion(0, -1, 0, -1), self.c.conjugated())
def setUp(self):
self.a = Quaternion(1,0,1,0)
self.b = Quaternion(1,1,0,0)
self.c = Quaternion(0,1,0,1)
class TestQuaternion(unittest.TestCase):
def setUp(self):
self.a = Quaternion(1,0,1,0)
self.b = Quaternion(1,1,0,0)
self.c = Quaternion(0,1,0,1)
def test_iadd(self):
self.a += self.c
self.b += self.c
self.assertEqual(Quaternion(1,1,1,1), self.a)
self.assertEqual(Quaternion(1,2,0,1), self.b)
def test_isub(self):
self.a -= self.c
self.b -= self.c
self.assertEqual(Quaternion(1,-1,1,-1), self.a)
self.assertEqual(Quaternion(1,0,0,-1), self.b)
def test_imul(self):
ua = numpy.float32(self.a.w)
ub = numpy.float32(self.b.w)
va = numpy.array([self.a.x, self.a.y, self.a.z])
vb = numpy.array([self.b.x, self.b.y, self.b.z])
u = ua * ub - numpy.dot(va, vb)
v = ua * vb + ub * va + numpy.cross(va, vb)
self.a *= self.b
self.assertAlmostEqual(self.a.w, u)
self.assertAlmostEqual(self.a.x, v[0])
self.assertAlmostEqual(self.a.y, v[1])
self.assertAlmostEqual(self.a.z, v[2])
def test_add(self):
self.assertEqual(Quaternion(1,1,1,1), self.a + self.c)
self.assertEqual(Quaternion(1,2,0,1), self.b + self.c)
def test_sub(self):
self.assertEqual(Quaternion(1,-1,1,-1), self.a - self.c)
self.assertEqual(Quaternion(1,0,0,-1), self.b - self.c)
def test_mul(self):
ua = numpy.float32(self.a.w)
ub = numpy.float32(self.b.w)
va = numpy.array([self.a.x, self.a.y, self.a.z])
vb = numpy.array([self.b.x, self.b.y, self.b.z])
u = ua * ub - numpy.dot(va, vb)
v = ua * vb + ub * va + numpy.cross(va, vb)
r = self.a * self.b
self.assertAlmostEqual(r.w, u)
self.assertAlmostEqual(r.x, v[0])
self.assertAlmostEqual(r.y, v[1])
self.assertAlmostEqual(r.z, v[2])
def test_eq(self):
self.assertTrue(Quaternion(1,2,3,4), Quaternion(1,2,3,4))
def test_ne(self):
self.assertTrue(Quaternion(1,2,3,4), Quaternion(0,2,3,4))
def test_length(self):
self.assertAlmostEqual(math.sqrt(2.0), self.a.length, places=6)
self.assertAlmostEqual(math.sqrt(2.0), self.b.length, places=6)
self.assertAlmostEqual(math.sqrt(2.0), self.c.length, places=6)
def test_normalize(self):
self.assertTrue(self.a.length > 1.0)
self.assertTrue(self.b.length > 1.0)
self.assertTrue(self.c.length > 1.0)
self.assertAlmostEqual(1.0, self.a.normalized().length, places=6)
self.assertAlmostEqual(1.0, self.b.normalized().length, places=6)
self.assertAlmostEqual(1.0, self.c.normalized().length, places=6)
def test_inverted(self):
self.assertEqual(self.a, self.a.inverted().inverted())
self.assertAlmostEqual( 0.5, self.a.inverted().w)
self.assertAlmostEqual( 0.0, self.a.inverted().x)
self.assertAlmostEqual(-0.5, self.a.inverted().y)
self.assertAlmostEqual( 0.0, self.a.inverted().z)
self.assertTrue(self.a is not self.a.inverted().inverted())
def test_from_axis_angle(self):
theta = math.pi / 5.0
c = math.cos(theta / 2.0)
s = math.sin(theta / 2.0)
q = Quaternion.from_axis_angle(numpy.array([1, -1, 1]), theta)
self.assertAlmostEqual( c, q.w)
self.assertAlmostEqual( s * math.sqrt(1.0 / 3.0), q.x)
self.assertAlmostEqual(-s * math.sqrt(1.0 / 3.0), q.y)
self.assertAlmostEqual( s * math.sqrt(1.0 / 3.0), q.z)
def test_rotate(self):
q = Quaternion.from_axis_angle(numpy.array([0, 1, 0]), math.pi / 2.0)
v = q.rotate((1, 0, 0))
self.assertAlmostEqual( 0, v[0])
self.assertAlmostEqual( 0, v[1])
self.assertAlmostEqual(-1, v[2])
def test_conjugated(self):
self.assertEqual(Quaternion(1, 0, -1, 0), self.a.conjugated())
self.assertEqual(Quaternion(1, -1, 0, 0), self.b.conjugated())
self.assertEqual(Quaternion(0, -1, 0, -1), self.c.conjugated())
