def test_extend_to_y(self):
""" extend a line given by two points to desired y-coordinate """
p1 = f.vector(0, 0, 0)
p2 = f.vector(1, 1, 0)
y = 5
self.assert_np_equal(f.extend_to_y(p1, p2, y), f.vector(y, y, 0))
def test_arbitrary_rotation_axis(self):
""" rotation of a point around arbitrary axis """
point = f.vector(1, 0, 0)
origin = f.vector(0, 0, 0)
axis = f.vector(1, 1, 0)
self.assert_np_almost_equal(
f.arbitrary_rotation(point, axis, np.pi, origin),
f.vector(0, 1, 0))
def test_arbitrary_rotation_point(self):
""" rotation of a point from another origin """
point = f.vector(0, 2, 0)
origin = f.vector(0, 1, 0)
axis = f.vector(0, 0, 1)
self.assert_np_equal(
f.arbitrary_rotation(point, axis, -np.pi / 2, origin),
f.vector(1, 1, 0))
def test_angle_between(self):
""" angle between two vectors """
v1 = f.vector(0, 0, 1)
v2 = f.vector(0, 2, 0)
self.assertEqual(f.angle_between(v1, v2), np.pi / 2)
self.assertEqual(f.angle_between(v1, v1), 0)
v1 = f.vector(1, 0, 0)
v2 = f.vector(1, 1, 0)
self.assertAlmostEqual(f.angle_between(v1, v2), np.pi / 4)
def test_curve_length(self):
""" length of a curve given by a list of points """
curve = np.array([
f.vector(0, 0, 0),
f.vector(1, 0, 0),
f.vector(1, 1, 0),
f.vector(1, 2, 0),
f.vector(0, 2, 0),
])
self.assertAlmostEqual(c.curve_length(curve), 4)
def test_xy_line_intersection(self):
""" intersection of two lines in xy-plane """
# line 1
p1 = f.vector(0, 0, 0)
p2 = f.vector(1, 1, 0)
# line 2
p3 = f.vector(1, 0, 0)
p4 = f.vector(0, 1, 0)
self.assert_np_equal(f.xy_line_intersection(p1, p2, p3, p4),
f.vector(0.5, 0.5, 0))
def test_to_cartesian_point(self):
""" polar point to xyz """
# polar point
p = np.array([1, np.pi / 2, 2])
# cartesian versions
# axis: z
self.assert_np_almost_equal(f.to_cartesian(p, axis='z'),
f.vector(0, 1, 2))
self.assert_np_almost_equal(f.to_cartesian(p, axis='x'),
f.vector(2, 0, 1))
self.assert_np_almost_equal(f.to_cartesian(p, axis='x', direction=-1),
f.vector(2, 0, -1))
def test_rotate(self):
""" simple rotation around a coordinate system axis """
v = f.vector(1, 0, 0)
r = f.rotate(v, np.pi / 2, axis='x')
self.assertAlmostEqual(f.angle_between(r, v), 0)
r = f.rotate(v, np.pi / 4, axis='y')
self.assertAlmostEqual(f.angle_between(r, v), np.pi / 4)
def test_to_cartesian_curve(self):
""" f.to_cartesian() for a list of points """
# polar points
points = [
f.vector(1, 0, 0),
f.vector(1, np.pi / 2, 1),
f.vector(2, 0, 1)
]
self.assert_np_almost_equal(
c.to_cartesian(points),
np.array([f.vector(1, 0, 0),
f.vector(0, 1, 1),
f.vector(2, 0, 1)]))
def test_to_polar_x_axis(self):
""" cartesian coordinate system to polar c.s., rotation around x-axis """
cartesian = f.vector(5, 2, 2)
polar = f.vector(8**0.5, np.pi / 4, 5)
self.assert_np_almost_equal(polar, f.to_polar(cartesian, axis='x'))
def test_rotate_exception(self):
""" an exception must be raised if axis is anything but x, y, or z """
with self.assertRaises(ValueError):
f.rotate(f.vector(0, 0, 1), np.pi / 2, 'a')
def test_unit_vector(self):
""" scale vector to magnitude 1 """
vector = f.vector(3, 5, 7)
unit_vector = vector / np.linalg.norm(vector)
self.assert_np_equal(unit_vector, f.unit_vector(vector))