def test_line_element_sphere():
"""
Integrate the equator curve of a unit sphere
and check it with the known value
"""
sphere = Sphere()
length = sphere.arc_length(Equator(), step=100)
np.testing.assert_almost_equal(length, 2 * math.pi, decimal=3)
def test_guass_map():
""" Compare different implementations
of the normal map
"""
sphere = Sphere()
uv = sphere.coordinates(10)
n1 = sphere.N(uv)
n2 = sphere.unit_normals(uv)
np.testing.assert_array_almost_equal(n1, n2)
def test_jacobian():
"""
Compare two implementations of the jacobian
"""
sphere = Sphere()
uv = sphere.coordinates(10)
jac1 = sphere.jacobian_matrix(uv)
jac2 = np.array(sphere.df(uv))
np.testing.assert_almost_equal(jac1, jac2)
def test_normals():
"""
On the unit sphere the points and normals are the same..
"""
sphere = Sphere()
uv = sphere.coordinates(10)
points = sphere.f(uv)
normals = sphere.unit_normals(uv)
valid_indicies = ~np.isnan(normals).any(axis=1)
np.testing.assert_almost_equal(np.abs(normals[valid_indicies]),
np.abs(points[valid_indicies]),
decimal=1)
def test_area_element_sphere():
"""
Integrate the area a unit sphere
and check it with the known value
"""
r = 2
area = Sphere(r).surface_area(step=50)
np.testing.assert_almost_equal(area, 4 * math.pi * r * r, decimal=1)
def test_gaussian_curvature_methods():
""" Test that methods of generating
K are equal
"""
n = 10
for surface in EllipsoidLatLon(), EllipsoidTriaxial(), Sphere(), Torus():
uv = surface.coordinates(n)
gc1 = surface.gaussian_curvature(uv)
gc2 = surface.gaussian_curvature2(uv)
gc3 = surface.gaussian_curvature3(uv)
np.testing.assert_array_almost_equal(gc1, gc2, decimal=2)
np.testing.assert_array_almost_equal(gc2, gc3, decimal=2)
def test_gauss_bonnet():
""" Test the theorum that total guassian curvature
of a closed surface equals 2*pi*euler characteristic
"""
SPHERE_EULER_CHARACTERISTIC = 2
TORUS_EULER_CHARACTERISTIC = 0
surface = Sphere(2)
total = surface.total_gaussian_curvature(500)
np.testing.assert_almost_equal(total,
2 * math.pi * SPHERE_EULER_CHARACTERISTIC,
decimal=1)
surface = EllipsoidLatLon()
total = surface.total_gaussian_curvature(500)
np.testing.assert_almost_equal(total,
2 * math.pi * SPHERE_EULER_CHARACTERISTIC,
decimal=1)
surface = Torus()
total = surface.total_gaussian_curvature(500)
np.testing.assert_almost_equal(total,
2 * math.pi * TORUS_EULER_CHARACTERISTIC,
decimal=1)