def __init__(self, face_number, degree):
# Create quadrature rule on reference triangle
reference_triangle = reference_element.UFCTriangle()
reference_rule = make_quadrature(reference_triangle, degree)
ref_points = reference_rule.get_points()
ref_weights = reference_rule.get_weights()
# Get geometry information about the face of interest
reference_tet = reference_element.UFCTetrahedron()
face = reference_tet.get_topology()[2][face_number]
vertices = reference_tet.get_vertices_of_subcomplex(face)
# Use tet to map points and weights on the appropriate face
vertices = [numpy.array(list(vertex)) for vertex in vertices]
x0 = vertices[0]
J = numpy.matrix([vertices[1] - x0, vertices[2] - x0]).transpose()
x0 = numpy.matrix(x0).transpose()
# This is just a very numpyfied way of writing J*p + x0:
F = lambda p: \
numpy.array(J*numpy.matrix(p).transpose() + x0).flatten()
points = numpy.array([F(p) for p in ref_points])
# Map weights: multiply reference weights by sqrt(|J^T J|)
detJTJ = numpy.linalg.det(J.transpose() * J)
weights = numpy.sqrt(detJTJ) * ref_weights
# Initialize super class with new points and weights
QuadratureRule.__init__(self, reference_tet, points, weights)
self._reference_rule = reference_rule
self._J = J
def __init__(self, face_number, degree):
# Create quadrature rule on reference triangle
reference_triangle = reference_element.UFCTriangle()
reference_rule = make_quadrature(reference_triangle, degree)
ref_points = reference_rule.get_points()
ref_weights = reference_rule.get_weights()
# Get geometry information about the face of interest
reference_tet = reference_element.UFCTetrahedron()
face = reference_tet.get_topology()[2][face_number]
vertices = reference_tet.get_vertices_of_subcomplex(face)
# Use tet to map points and weights on the appropriate face
vertices = [np.array(list(vertex)) for vertex in vertices]
x0 = vertices[0]
J = np.vstack([vertices[1] - x0, vertices[2] - x0]).T
# This is just a very npfied way of writing J*p + x0:
points = np.einsum("ij,kj->ki", J, ref_points) + x0
# Map weights: multiply reference weights by sqrt(|J^T J|)
detJTJ = np.linalg.det(np.dot(J.T, J))
weights = np.sqrt(detJTJ) * ref_weights
# Initialize super class with new points and weights
QuadratureRule.__init__(self, reference_tet, points, weights)
self._reference_rule = reference_rule
self._J = J