def face_normals_and_jacobians(cls, vertices, affine_map):
"""Compute the normals and face jacobians of the unit element
transformed according to `affine_map'.
Returns a pair of lists [normals], [jacobians].
"""
from hedge._internal import tetrahedron_fj_and_normal
from hedge.tools import sign
return tetrahedron_fj_and_normal(sign(affine_map.jacobian()),
cls.face_vertex_numbers, vertices)
def face_normals_and_jacobians(cls, vertices, affine_map):
"""Compute the normals and face jacobians of the unit element
transformed according to `affine_map'.
Returns a pair of lists [normals], [jacobians].
"""
from hedge._internal import tetrahedron_fj_and_normal
from hedge.tools import sign
return tetrahedron_fj_and_normal(
sign(affine_map.jacobian()),
cls.face_vertex_numbers,
vertices)
def face_normals_and_jacobians(vertices, affine_map):
"""Compute the normals and face jacobians of the unit element
transformed according to `affine_map'.
Returns a pair of lists [normals], [jacobians].
"""
from hedge.tools import sign
m = affine_map.matrix
orient = sign(affine_map.jacobian())
face1 = m[:, 1] - m[:, 0]
raw_normals = [
orient*numpy.array([m[1, 0], -m[0, 0]]),
orient*numpy.array([face1[1], -face1[0]]),
orient*numpy.array([-m[1, 1], m[0, 1]]),
]
face_lengths = [numpy.linalg.norm(fn) for fn in raw_normals]
return [n/fl for n, fl in zip(raw_normals, face_lengths)], \
face_lengths
def face_normals_and_jacobians(vertices, affine_map):
"""Compute the normals and face jacobians of the unit element
transformed according to `affine_map'.
Returns a pair of lists [normals], [jacobians].
"""
from hedge.tools import sign
m = affine_map.matrix
orient = sign(affine_map.jacobian())
face1 = m[:, 1] - m[:, 0]
raw_normals = [
orient * numpy.array([m[1, 0], -m[0, 0]]),
orient * numpy.array([face1[1], -face1[0]]),
orient * numpy.array([-m[1, 1], m[0, 1]]),
]
face_lengths = [numpy.linalg.norm(fn) for fn in raw_normals]
return [n/fl for n, fl in zip(raw_normals, face_lengths)], \
face_lengths
