def test_L_intersection(self):
p_1 = np.zeros(3)
p_2 = np.random.rand(3)
p_3 = np.random.rand(3)
p_i = basics.segments_intersect_3d(p_1, p_2, p_2, p_3)
assert np.allclose(p_i, p_2.reshape((-1, 1)))
def test_equal_lines_segments_not_overlapping(self):
p_1 = np.ones(3)
p_2 = 0 * p_1
p_3 = 2 * p_1
p_4 = 3 * p_1
p_int = basics.segments_intersect_3d(p_1, p_2, p_3, p_4)
assert p_int is None
def test_lines_cross_segments_not(self):
p_1 = np.array([-1, 0, -1])
p_2 = np.array([0, 0, 0])
p_3 = np.array([1, -1, 1])
p_4 = np.array([1, 1, 1])
p_i = basics.segments_intersect_3d(p_1, p_2, p_3, p_4)
assert p_i is None
def test_parallel_lines(self):
p_1 = np.zeros(3)
p_2 = np.array([1, 0, 0])
p_3 = np.array([0, 1, 0])
p_4 = np.array([1, 1, 0])
p_i = basics.segments_intersect_3d(p_1, p_2, p_3, p_4)
assert p_i is None
def test_intersection_origin(self):
# 3D lines cross in the origin
p_1 = np.array([0, -1, -1])
p_2 = np.array([0, 1, 1])
p_3 = np.array([-1, 0, 1])
p_4 = np.array([1, 0, -1])
p_i = basics.segments_intersect_3d(p_1, p_2, p_3, p_4)
assert np.allclose(p_i, np.zeros(3))
def test_argument_order_arbitrary(self):
# Order of input arguments should be arbitrary
p_1 = np.array([0, -1, -1])
p_2 = np.array([0, 1, 1])
p_3 = np.array([-1, 0, 1])
p_4 = np.array([1, 0, -1])
p_known = np.zeros(3)
p_i_1 = basics.segments_intersect_3d(p_1, p_2, p_3, p_4)
p_i_2 = basics.segments_intersect_3d(p_2, p_1, p_3, p_4)
p_i_3 = basics.segments_intersect_3d(p_1, p_2, p_4, p_3)
p_i_4 = basics.segments_intersect_3d(p_2, p_1, p_4, p_3)
assert np.allclose(p_i_1, p_known)
assert np.allclose(p_i_2, p_known)
assert np.allclose(p_i_3, p_known)
assert np.allclose(p_i_4, p_known)
def test_constant_y_axis(self):
p_1 = np.array([1, 0, -1])
p_2 = np.array([1, 0, 1])
p_3 = np.array([1.5, 0, 0])
p_4 = np.array([0, 0, 1.5])
p_int = basics.segments_intersect_3d(p_1, p_2, p_3, p_4)
p_known = np.array([1, 0, 0.5]).reshape((-1, 1))
assert np.min(np.sum(np.abs(p_int - p_known), axis=0)) < 1e-8
def test_both_aligned_with_axis(self):
# Both lines are aligned an axis,
p_1 = np.array([-1, -1, 0])
p_2 = np.array([-1, 1, 0])
p_3 = np.array([-1, 0, -1])
p_4 = np.array([-1, 0, 1])
p_int = basics.segments_intersect_3d(p_1, p_2, p_3, p_4)
p_known = np.array([-1, 0, 0]).reshape((-1, 1))
assert np.allclose(p_int, p_known)
def test_pass_in_z_coord(self):
# The (x,y) coordinates gives intersection in origin, but z coordinates
# do not match
p_1 = np.array([-1, -1, -1])
p_2 = np.array([1, 1, -1])
p_3 = np.array([1, -1, 1])
p_4 = np.array([-1, 1, 1])
p_i = basics.segments_intersect_3d(p_1, p_2, p_3, p_4)
assert p_i is None
def test_segments_aligned_with_axis(self):
p_1 = np.array([0, 1, 1])
p_2 = 3 * p_1
p_3 = 0 * p_1
p_4 = 2 * p_1
p_int = basics.segments_intersect_3d(p_1, p_2, p_3, p_4)
p_known_1 = p_1.reshape((-1, 1))
p_known_2 = p_4.reshape((-1, 1))
assert np.min(np.sum(np.abs(p_int - p_known_1), axis=0)) < 1e-8
assert np.min(np.sum(np.abs(p_int - p_known_2), axis=0)) < 1e-8
def test_random_incline(self):
p_1 = np.random.rand(3)
p_2 = 3 * p_1
p_3 = 0 * p_1
p_4 = 2 * p_1
p_int = basics.segments_intersect_3d(p_1, p_2, p_3, p_4)
p_known_1 = p_1.reshape((-1, 1))
p_known_2 = p_4.reshape((-1, 1))
assert np.min(np.sum(np.abs(p_int - p_known_1), axis=0)) < 1e-8
assert np.min(np.sum(np.abs(p_int - p_known_2), axis=0)) < 1e-8
def test_segments_partly_overlap(self):
p_1 = np.ones(3)
p_2 = 3 * p_1
p_3 = 0 * p_1
p_4 = 2 * p_1
p_int = basics.segments_intersect_3d(p_1, p_2, p_3, p_4)
p_known_1 = p_1.reshape((-1, 1))
p_known_2 = p_4.reshape((-1, 1))
assert np.min(np.sum(np.abs(p_int - p_known_1), axis=0)) < 1e-8
assert np.min(np.sum(np.abs(p_int - p_known_2), axis=0)) < 1e-8
def test_segment_fully_overlapped(self):
# One line is fully covered by another
p_1 = np.ones(3)
p_2 = 2 * p_1
p_3 = 0 * p_1
p_4 = 3 * p_1
p_int = basics.segments_intersect_3d(p_1, p_2, p_3, p_4)
p_known_1 = p_1.reshape((-1, 1))
p_known_2 = p_2.reshape((-1, 1))
assert np.min(np.sum(np.abs(p_int - p_known_1), axis=0)) < 1e-8
assert np.min(np.sum(np.abs(p_int - p_known_2), axis=0)) < 1e-8
def test_segments_overlap_input_order(self):
# Test the order of inputs
p_1 = np.ones(3)
p_2 = 2 * p_1
p_3 = 0 * p_1
p_4 = 3 * p_1
p_int_1 = basics.segments_intersect_3d(p_1, p_2, p_3, p_4)
p_int_2 = basics.segments_intersect_3d(p_2, p_1, p_3, p_4)
p_int_3 = basics.segments_intersect_3d(p_1, p_2, p_4, p_3)
p_int_4 = basics.segments_intersect_3d(p_2, p_1, p_4, p_3)
p_known_1 = p_1.reshape((-1, 1))
p_known_2 = p_2.reshape((-1, 1))
assert np.min(np.sum(np.abs(p_int_1 - p_known_1), axis=0)) < 1e-8
assert np.min(np.sum(np.abs(p_int_1 - p_known_2), axis=0)) < 1e-8
assert np.min(np.sum(np.abs(p_int_2 - p_known_1), axis=0)) < 1e-8
assert np.min(np.sum(np.abs(p_int_2 - p_known_2), axis=0)) < 1e-8
assert np.min(np.sum(np.abs(p_int_3 - p_known_1), axis=0)) < 1e-8
assert np.min(np.sum(np.abs(p_int_3 - p_known_2), axis=0)) < 1e-8
assert np.min(np.sum(np.abs(p_int_4 - p_known_1), axis=0)) < 1e-8
assert np.min(np.sum(np.abs(p_int_4 - p_known_2), axis=0)) < 1e-8