def test__compute_valid_bad_degree(self):
from bezier import _helpers
degree = 4
num_nodes = ((degree + 1) * (degree + 2)) // 2
nodes = np.zeros((2, num_nodes), order="F")
surface = self._make_one(nodes, degree=degree)
with self.assertRaises(_helpers.UnsupportedDegree) as exc_info:
surface._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
surface = self._make_one(nodes, 1)
self.assertTrue(surface._compute_valid())
# Change the nodes from counterclockwise to clockwise, so the
# Jacobian becomes negatively signed.
nodes = np.asfortranarray(nodes[:, (1, 0, 2)])
surface = self._make_one(nodes, 1, _copy=False)
self.assertFalse(surface._compute_valid())
# Collinear.
nodes = np.asfortranarray([[0.0, 1.0, 2.0], [0.0, 2.0, 4.0]])
surface = self._make_one(nodes, 1, _copy=False)
self.assertFalse(surface._compute_valid())
def test__compute_valid_invalid_linear(self):
nodes = np.asfortranarray([
[0.0, 0.0, 0.0],
[1.0, 2.0, 2.0],
[2.0, 4.0, 4.0],
])
surface = self._make_one(nodes, 1)
self.assertFalse(surface._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],
])
surface = self._make_one(nodes, 2, _copy=False)
self.assertTrue(surface._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)])
surface = self._make_one(nodes, 2, _copy=False)
self.assertFalse(surface._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]])
surface = self._make_one(nodes, 2, _copy=False)
self.assertFalse(surface._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],
])
surface = self._make_one(nodes, 3, _copy=False)
self.assertTrue(surface._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)])
surface = self._make_one(nodes, 3, _copy=False)
self.assertFalse(surface._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],
])
surface = self._make_one(nodes, 3, _copy=False)
self.assertFalse(surface._compute_valid())
def test__compute_valid_quadratic_valid(self):
nodes = np.asfortranarray([
[0.0, 0.0],
[0.5, -0.1875],
[1.0, 0.0],
[0.1875, 0.5],
[0.625, 0.625],
[0.0, 1.0],
])
surface = self._make_one(nodes, 2)
self.assertTrue(surface._compute_valid())
def test__compute_valid_quadratic_invalid(self):
# B(L1, L2, L3) = [L1^2 + L2^2, L2^2 + L3^2]
nodes = np.asfortranarray([
[1.0, 0.0],
[0.0, 0.0],
[1.0, 1.0],
[0.0, 0.0],
[0.0, 0.0],
[0.0, 1.0],
])
surface = self._make_one(nodes, 2)
self.assertFalse(surface._compute_valid())
def test__compute_valid_cubic_valid(self):
nodes = np.asfortranarray([
[0.0, 0.0],
[1.0, 0.0],
[2.0, 0.0],
[3.0, 0.0],
[0.0, 1.0],
[1.0, 1.0],
[2.25, 1.25],
[0.0, 2.0],
[1.25, 2.25],
[0.0, 3.0],
])
surface = self._make_one(nodes, 3)
self.assertTrue(surface._compute_valid())
def test__compute_valid_cubic_invalid(self):
# B(L1, L2, L3) = [L1^3 + L2^3, L2^3 + L3^3]
nodes = np.asfortranarray([
[1.0, 0.0],
[0.0, 0.0],
[0.0, 0.0],
[1.0, 1.0],
[0.0, 0.0],
[0.0, 0.0],
[0.0, 0.0],
[0.0, 0.0],
[0.0, 0.0],
[0.0, 1.0],
])
surface = self._make_one(nodes, 3)
self.assertFalse(surface._compute_valid())
def test__compute_valid_bad_dimension(self):
nodes = np.zeros((3, 6), order="F")
surface = self._make_one(nodes, 2)
with self.assertRaises(NotImplementedError):
surface._compute_valid()
def test__compute_valid_bad_degree(self):
nodes = np.zeros((15, 2), order='F')
surface = self._make_one(nodes, 4)
with self.assertRaises(NotImplementedError):
surface._compute_valid()
def test__compute_valid_valid_linear(self):
surface = self._make_one(self.UNIT_TRIANGLE, 1)
self.assertTrue(surface._compute_valid())
