def test_maps_the_perimeter_to_itself(self):
# Make a rectangle, with enough support points to get a decent approximation
perimeter = np.array([
[-2, -1],
[-2, -0.9],
[-2, -0.8],
[-2, -0.7],
[-2, -0.5],
[-2, 0],
[-2, 1],
[0, 1],
[1, 1],
[1, 0],
[1, -1],
[0, -1],
]) + np.array([[-10, 5]])
warp_coords = poly.warp_to_circle(perimeter, perimeter, i_max=200, r_max=-1)
# Warp perimeter should always be (almost) on the unit circle
warp_r = np.sqrt(warp_coords[:, 0]**2 + warp_coords[:, 1]**2)
np.testing.assert_almost_equal(warp_r, np.ones_like(warp_r), decimal=2)
# Inverse should project exactly back to the perimeter
inv_warp_coords = poly.inv_warp_to_circle(warp_coords, perimeter, i_max=200)
np.testing.assert_almost_equal(inv_warp_coords, perimeter, decimal=4)
def test_can_warp_and_inv_warp_beyond_the_edge(self):
# Make a circle with radius 5
theta = np.linspace(0, 2*np.pi, 50)
perimeter = np.stack([np.cos(theta) * 5 + 2.0, np.sin(theta)*5 - 1.0], axis=1)
# Ray along x == -y
coords = np.array([
[0, 0],
[1, -1],
[2, -2],
[3, -3],
[4, -4],
[5, -5],
[6, -6],
[7, -7],
[8, -8],
[9, -9],
[10, -10],
]) + np.array([
[2.0, -1.0],
])
warp_coords = poly.warp_to_circle(coords, perimeter, i_max=200, r_max=-1)
# Warping in this case is just centering and scaling by 5
exp_warp_coords = (coords - np.array([[2.0, -1.0]])) / 5
np.testing.assert_almost_equal(warp_coords, exp_warp_coords, decimal=4)
inv_warp_coords = poly.inv_warp_to_circle(warp_coords, perimeter, i_max=200)
np.testing.assert_almost_equal(coords, inv_warp_coords, decimal=4)
def test_warp_inv_warp_oversampled_square(self):
# Make a square, with enough support points to get a decent approximation
perimeter = np.array([
[-1, -1],
[-1, -0.9],
[-1, -0.8],
[-1, -0.7],
[-1, -0.5],
[-1, 0],
[-1, 1],
[0, 1],
[1, 1],
[1, 0],
[1, -1],
[0, -1],
])
assert perimeter.shape[1] == 2
# Make an X inside the square
coords = np.array([
[-1, -1],
[-0.5, -0.5],
[0, 0],
[0.5, 0.5],
[1, 1],
[-0.5, 0.5],
[-1, 1],
[0.5, -0.5],
[1, -1],
])
warp_coords = poly.warp_to_circle(coords, perimeter, i_max=200)
inv_warp_coords = poly.inv_warp_to_circle(warp_coords, perimeter, i_max=200)
np.testing.assert_almost_equal(coords, inv_warp_coords)
def test_project_circle_onto_circle(self):
theta = np.arange(0, 2*np.pi, np.pi/100)
perimeter = np.stack([2*np.cos(theta), 2*np.sin(theta)], axis=1)
coords = np.random.rand(100, 2) * 4 - 2
coords = coords[(coords[:, 0]**2 + coords[:, 1]**2) < 4]
warp_coords = poly.warp_to_circle(coords, perimeter)
np.testing.assert_almost_equal(warp_coords, coords/2)
def test_project_square_onto_circle_oversampled(self):
# Make a square, with enough support points to get a decent approximation
perimeter = np.array([
[-1, -1],
[-1, -0.9],
[-1, -0.8],
[-1, -0.7],
[-1, -0.5],
[-1, 0],
[-1, 1],
[0, 1],
[1, 1],
[1, 0],
[1, -1],
[0, -1],
])
assert perimeter.shape[1] == 2
# Make an X inside the square
coords = np.array([
[-1, -1],
[-0.5, -0.5],
[0, 0],
[0.5, 0.5],
[1, 1],
[-0.5, 0.5],
[-1, 1],
[0.5, -0.5],
[1, -1],
])
warp_coords = poly.warp_to_circle(coords, perimeter, i_max=200)
# Projects to a smaller X inside the circle
exp_coords = np.array([
[-0.70710678, -0.70710678],
[-0.35355339, -0.35355339],
[0.0, 0.0],
[0.35355339, 0.35355339],
[0.70710678, 0.70710678],
[-0.35355339, 0.35355339],
[-0.70710678, 0.70710678],
[0.35355339, -0.35355339],
[0.70710678, -0.70710678],
])
np.testing.assert_almost_equal(warp_coords, exp_coords)