def test__compute_valid_bad_degree(self):
from bezier.hazmat import helpers
degree = 4
num_nodes = ((degree + 1) * (degree + 2)) // 2
nodes = np.zeros((2, num_nodes), order="F")
triangle = self._make_one(nodes, degree=degree)
with self.assertRaises(helpers.UnsupportedDegree) as exc_info:
triangle._compute_valid()
self.assertEqual(exc_info.exception.degree, degree)
self.assertEqual(exc_info.exception.supported, (1, 2, 3))
def test__compute_valid_linear(self):
# Positively signed Jacobian (i.e. edges have inward normals).
nodes = self.UNIT_TRIANGLE
triangle = self._make_one(nodes, 1)
self.assertTrue(triangle._compute_valid())
# Change the nodes from counterclockwise to clockwise, so the
# Jacobian becomes negatively signed.
nodes = np.asfortranarray(nodes[:, (1, 0, 2)])
triangle = self._make_one(nodes, 1, copy=False)
self.assertFalse(triangle._compute_valid())
# Collinear.
nodes = np.asfortranarray([[0.0, 1.0, 2.0], [0.0, 2.0, 4.0]])
triangle = self._make_one(nodes, 1, copy=False)
self.assertFalse(triangle._compute_valid())
def test__compute_valid_quadratic(self):
# Positively signed Jacobian (i.e. edges have inward normals).
nodes = np.asfortranarray([
[0.0, 0.5, 1.0, 0.1875, 0.625, 0.0],
[0.0, -0.1875, 0.0, 0.5, 0.625, 1.0],
])
triangle = self._make_one(nodes, 2, copy=False)
self.assertTrue(triangle._compute_valid())
# Change the nodes from counterclockwise to clockwise, so the
# Jacobian becomes negatively signed.
nodes = np.asfortranarray(nodes[:, (2, 1, 0, 4, 3, 5)])
triangle = self._make_one(nodes, 2, copy=False)
self.assertFalse(triangle._compute_valid())
# Mixed sign Jacobian: B(L1, L2, L3) = [L1^2 + L2^2, L2^2 + L3^2]
nodes = np.asfortranarray([[1.0, 0.0, 1.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 1.0, 0.0, 0.0, 1.0]])
triangle = self._make_one(nodes, 2, copy=False)
self.assertFalse(triangle._compute_valid())
def test__compute_valid_cubic(self):
# Positively signed Jacobian (i.e. edges have inward normals).
nodes = np.asfortranarray([
[0.0, 1.0, 2.0, 3.0, 0.0, 1.0, 2.25, 0.0, 1.25, 0.0],
[0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.25, 2.0, 2.25, 3.0],
])
triangle = self._make_one(nodes, 3, copy=False)
self.assertTrue(triangle._compute_valid())
# Change the nodes from counterclockwise to clockwise, so the
# Jacobian becomes negatively signed.
nodes = np.asfortranarray(nodes[:, (3, 2, 1, 0, 6, 5, 4, 8, 7, 9)])
triangle = self._make_one(nodes, 3, copy=False)
self.assertFalse(triangle._compute_valid())
# Mixed sign Jacobian: B(L1, L2, L3) = [L1^3 + L2^3, L2^3 + L3^3]
nodes = np.asfortranarray([
[1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0],
])
triangle = self._make_one(nodes, 3, copy=False)
self.assertFalse(triangle._compute_valid())
def test__compute_valid_bad_dimension(self):
nodes = np.zeros((3, 6), order="F")
triangle = self._make_one(nodes, 2)
with self.assertRaises(NotImplementedError):
triangle._compute_valid()