def test_angle_gradient_diag(self):
# Middle index is moved on a fine grid to test analytical dx, dy
# components againt the numerical ones from finite differences
pl = Polyline([[-1.03, -1.03], [0, 0], [1.03, 1.03]])
idx = 1 # Movable vertex id (middle vertex to obtain mutliple angles)
test_eps = 1e-2 # Max allowed deviation, chose suitable for num grad
# Test on a diagonal between fixed vertices
x_pos = np.linspace(-2, 2, 501)
cos_angles, cos_angles_grad_x, cos_angles_grad_y = [], [], []
for xi in x_pos:
pl.replace_vertex(idx, [xi, -xi])
cos_ang, cos_ang_grad = pl.get_cos_angle_at_vertex(idx)
cos_angles.append(cos_ang)
cos_angles_grad_x.append(cos_ang_grad[0])
cos_angles_grad_y.append(cos_ang_grad[1])
# Test analytical against numerical gradients
cos_angles_grad = (np.array(cos_angles_grad_x) -
np.array(cos_angles_grad_y)) / sqrt(2)
num_grad = np.gradient(cos_angles, np.diff(x_pos)[0] * np.sqrt(2))
assert np.allclose(num_grad, cos_angles_grad, atol=test_eps)
return
def test_angle_gradient_dy(self):
# Middle index is moved on a fine grid to test analytical dy components
# againt the numerical ones from finite differences
pl = Polyline([[-1.03, -1.03], [0, 0], [1.03, 1.03]])
idx = 1 # Movable vertex id (middle vertex to obtain mutliple angles)
test_eps = 1e-2 # Max allowed deviation, chose suitable for num grad
x_pos = [1.5, 0.75, 0.25, 0., -0.25, -0.75, -1.5]
y_pos = np.linspace(-2, 2, 501)
for xi in x_pos:
cos_angles, cos_angles_grad_y = [], []
for yi in y_pos:
pl.replace_vertex(idx, [xi, yi])
cos_ang, cos_ang_grad = pl.get_cos_angle_at_vertex(idx)
cos_angles.append(cos_ang)
cos_angles_grad_y.append(cos_ang_grad[1])
# Test analytical against numerical gradients
num_grad_y = np.gradient(cos_angles, y_pos)
assert np.allclose(num_grad_y, cos_angles_grad_y, atol=test_eps)
return