def test_hex_collision_3d(delta):
hex_1 = np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0],
[0, 0, 1], [1, 0, 1], [0, 1, 1], [1, 1, 1]],
dtype=np.float64)
P0 = np.array([1.5 + delta, 1.5 + delta, 0.5], dtype=np.float64)
P1 = np.array([2, 2, 1], dtype=np.float64)
P2 = np.array([2, 1.25, 0.25], dtype=np.float64)
P3 = P1 + P2 - P0
quad_1 = np.array([P0, P1, P2, P3], dtype=np.float64)
n = (np.cross(quad_1[1] - quad_1[0], quad_1[2] - quad_1[0])
/ np.linalg.norm(
np.cross(quad_1[1] - quad_1[0],
quad_1[2] - quad_1[0])))
quad_2 = quad_1 + n
hex_2 = np.zeros((8, 3), dtype=np.float64)
hex_2[:4, :] = quad_1
hex_2[4:, :] = quad_2
actual_distance = np.linalg.norm(
np.array([1, 1, P0[2]], dtype=np.float64) - hex_2[0])
distance = np.linalg.norm(compute_distance_gjk(hex_1, hex_2))
if P0[0] < 1:
assert(np.isclose(distance, 0, atol=1e-15))
else:
print("Computed distance ", distance,
"Actual distance ", actual_distance)
assert(np.isclose(distance, actual_distance, atol=1e-15))
def test_cube_distance(delta, scale):
cubes = [scale * np.array([[-1, -1, -1], [1, -1, -1], [-1, 1, -1], [1, 1, -1],
[-1, -1, 1], [1, -1, 1], [-1, 1, 1], [1, 1, 1]],
dtype=np.float64)]
# Rotate cube 45 degrees around z, so that an edge faces along x-axis (vertical)
r = R.from_euler('z', 45, degrees=True)
cubes.append(r.apply(cubes[0]))
# Rotate cube around y, so that a corner faces along the x-axis
r = R.from_euler('y', np.arctan2(1.0, np.sqrt(2)))
cubes.append(r.apply(cubes[1]))
# Rotate cube 45 degrees around y, so that an edge faces along x-axis (horizontal)
r = R.from_euler('y', 45, degrees=True)
cubes.append(r.apply(cubes[0]))
# Rotate scene through an arbitrary angle
r = R.from_euler('xyz', [22, 13, -47], degrees=True)
for c0 in range(4):
for c1 in range(4):
dx = cubes[c0][:, 0].max() - cubes[c1][:, 0].min()
cube0 = cubes[c0]
# Separate cubes along x-axis by distance delta
cube1 = cubes[c1] + np.array([dx + delta, 0, 0])
c0rot = r.apply(cube0)
c1rot = r.apply(cube1)
distance = np.linalg.norm(compute_distance_gjk(c0rot, c1rot))
print(distance, delta)
assert(np.isclose(distance, delta))
def test_line_point_distance(delta):
line = np.array([[0.1, 0.2, 0.3], [0.5, 0.8, 0.7]], dtype=np.float64)
point_on_line = line[0] + 0.27 * (line[1] - line[0])
normal = np.cross(line[0], line[1])
point = point_on_line + delta * normal
distance = np.linalg.norm(compute_distance_gjk(line, point))
actual_distance = distance_point_to_line_3D(line[0], line[1], point)
assert(np.isclose(distance, actual_distance, atol=1e-15))
def test_tetra_collision_3d(delta):
tetra_1 = np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1]], dtype=np.float64)
tetra_2 = np.array([[0, 0, -3], [1, 0, -3], [0, 1, -3], [0.5, 0.3, -delta]], dtype=np.float64)
actual_distance = distance_point_to_plane_3D(tetra_1[0], tetra_1[1], tetra_1[2], tetra_2[3])
distance = np.linalg.norm(compute_distance_gjk(tetra_1, tetra_2))
if delta < 0:
assert(np.isclose(distance, 0, atol=1e-15))
else:
assert(np.isclose(distance, actual_distance, atol=1e-15))
def test_quad_distance2d(delta):
quad_1 = np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0]], dtype=np.float64)
quad_2 = np.array([[0, 1 + delta, 0], [2, 2, 0], [2, 4, 0], [4, 4, 0]], dtype=np.float64)
P1 = quad_1[2]
P2 = quad_1[3]
point = quad_2[0]
actual_distance = distance_point_to_line_3D(P1, P2, point)
distance = np.linalg.norm(compute_distance_gjk(quad_1, quad_2))
assert(np.isclose(distance, actual_distance, atol=1e-15))
def test_tri_distance(delta):
tri_1 = np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0]], dtype=np.float64)
tri_2 = np.array([[1, delta, 0], [3, 1.2, 0], [1, 1, 0]], dtype=np.float64)
P1 = tri_1[2]
P2 = tri_1[1]
point = tri_2[0]
actual_distance = distance_point_to_line_3D(P1, P2, point)
distance = np.linalg.norm(compute_distance_gjk(tri_1, tri_2))
assert(np.isclose(distance, actual_distance, atol=1e-15))
def test_line_line_distance(delta):
line = np.array([[-0.5, -0.7, -0.3], [1, 2, 3]], dtype=np.float64)
point_on_line = line[0] + 0.38 * (line[1] - line[0])
normal = np.cross(line[0], line[1])
point = point_on_line + delta * normal
line_2 = np.array([point, [2, 5, 6]], dtype=np.float64)
distance = np.linalg.norm(compute_distance_gjk(line, line_2))
actual_distance = distance_point_to_line_3D(line[0], line[1], line_2[0])
assert(np.isclose(distance, actual_distance, atol=1e-15))
def test_tetra_distance_3d(delta):
tetra_1 = np.array([[0, 0, 0.2], [1, 0, 0.1], [0, 1, 0.3],
[0, 0, 1]], dtype=np.float64)
tetra_2 = np.array([[0, 0, -3], [1, 0, -3], [0, 1, -3],
[0.5, 0.3, -delta]], dtype=np.float64)
actual_distance = distance_point_to_plane_3D(tetra_1[0], tetra_1[1],
tetra_1[2], tetra_2[3])
distance = np.linalg.norm(compute_distance_gjk(tetra_1, tetra_2))
print("Computed distance ", distance, "Actual distance ", actual_distance)
assert(np.isclose(distance, actual_distance, atol=1e-15))
