def test_distance_point_grad(self):
# Test gradient with respect to each projected point, leaving the
# polyline fixed.
# Move pts along simple polyline and compare gradients.
# Points are a bit tunes, because at discontinuous points, the numerical
# gradient jumps to far for the tested precision, although the plots are
# perfectly ok
pl = Polyline([[0, 0], [1, 0.8], [1.1, 1.9]])
test_eps = 1e-2 # Max allowed deviation, chose suitable for num grad
npts = 1000
# Test x gradient
ys = [-1, 2]
x = np.linspace(-1, 2, npts)
for yi in ys:
y = yi + np.zeros_like(x)
pts = np.vstack((x, y)).T
dists, _, _, proj_vecs = pl.get_dist_to_line(pts)
# Gradients are simply the normalized negative projection vectors
_norm = np.linalg.norm(proj_vecs,
axis=1).reshape(len(proj_vecs), 1)
gradients = -proj_vecs / _norm
# Directional gradient along x
num_grad = np.gradient(dists, x)
grad = np.dot(gradients, [1, 0])
assert np.allclose(num_grad, grad, atol=test_eps)
# Test y gradient
xs = [-1, 2]
y = np.linspace(-1, 1.5, npts)
for xi in xs:
x = xi + np.zeros_like(y)
pts = np.vstack((x, y)).T
dists, dists_grad, _, proj_vecs = pl.get_dist_to_line(pts)
# Gradients are simply the normalized negative projection vectors
_norm = np.linalg.norm(proj_vecs,
axis=1).reshape(len(proj_vecs), 1)
gradients = -proj_vecs / _norm
# Directional gradient along x
num_grad = np.gradient(dists, y)
grad = np.dot(gradients, [0, 1])
assert np.allclose(num_grad, grad, atol=test_eps)
return
def test_distance(self):
v = [[1, 3], [3, 5], [6, 2], [2, 2]]
pl = Polyline(v)
# Test values are chosen to yield simple distances and vectors and were
# calculated by hand apriori
pts = [[1, 2], [1.5, 5.5], [3, 6], [3.5, 3.5], [5.5, 3.5], [4, 1],
[2, 2.5]]
dists, _, proj_to, proj_vecs = pl.get_dist_to_line(pts)
# Should show from pt to closest part of the polyline
proj_vecs_exp = [[0, 1], [1, -1], [0, -1], [0.5, 0.5], [-0.5, -0.5],
[0, 1], [0, -0.5]]
dists_exp = [1., sqrt(2.), 1., sqrt(2.) / 2., sqrt(2.) / 2., 1., 0.5]
# id < 0: Onto segment with -id-1, else onto vertex with id
# Last point projects exactly orthogonally to end of segment, thus -3
proj_to_exp = [0, -1, 1, -2, -2, -3, -3]
for i, (pvexp, dexp,
ptexp) in enumerate(zip(proj_vecs_exp, dists_exp,
proj_to_exp)):
assert proj_vecs[i, 0] == approx(pvexp[0])
assert proj_vecs[i, 1] == approx(pvexp[1])
assert dists[i] == approx(dexp)
assert proj_to[i] == ptexp
return
