def getMeshIntersections(self, line):
field, endpoints = line
# get Proteus mesh index for this field
field_id = self.fieldNames.index(field)
femFun = self.u[field_id]
mesh = femFun.femSpace.mesh
referenceElement = femFun.femSpace.elementMaps.referenceElement
if referenceElement.dim == 2 and referenceElement.nNodes == 3:
toPolyhedron = triangleVerticesToNormals
elif referenceElement.dim == 3 and referenceElement.nNodes == 4:
toPolyhedron = tetrahedronVerticesToNormals
else:
raise NotImplementedError(
"Unable to compute mesh intersections for this element type")
intersections = np.asarray(list(
getMeshIntersections(mesh, toPolyhedron, endpoints)),
dtype=np.double)
endpoints = np.asarray(endpoints, np.double)
length = norm(endpoints[1] - endpoints[0])
length_segments = [(old_div(norm(i[0] - endpoints[0]), length),
old_div(norm(i[1] - endpoints[0]), length), i)
for i in intersections]
segments = self.pruneDuplicateSegments(endpoints, length_segments)
return segments
def test_mesh_intersections(self):
"""
Test correctness of intersecting a line and a tetrahedral mesh.
"""
endpoints = np.asarray(((0, 0, 0), (1, 1, 1)))
mesh_type = namedtuple('mesh', 'nodeArray elementNodesArray')
nodeArray = np.asarray(([[0., 0., 0.], [0.5, 0., 0.], [1., 0., 0.],
[0., 0.5, 0.], [0.5, 0.5, 0.], [1., 0.5, 0.],
[0., 1., 0.], [0.5, 1., 0.], [1., 1., 0.],
[0., 0., 0.5], [0.5, 0., 0.5], [1., 0., 0.5],
[0., 0.5, 0.5], [0.5, 0.5, 0.5],
[1., 0.5, 0.5], [0., 1., 0.5], [0.5, 1., 0.5],
[1., 1., 0.5], [0., 0., 1.], [0.5, 0., 1.],
[1., 0., 1.], [0., 0.5, 1.], [0.5, 0.5, 1.],
[1., 0.5, 1.], [0., 1., 1.], [0.5, 1., 1.],
[1., 1., 1.]]))
elementNodesArray = np.asarray([[0, 1, 4, 13], [0, 1, 10, 13],
[0, 3, 4, 13], [0, 3, 12, 13],
[0, 9, 10, 13], [0, 9, 12, 13],
[1, 2, 5, 14], [1, 2, 11, 14],
[1, 4, 5, 14], [1, 4, 13, 14],
[1, 10, 11, 14], [1, 10, 13, 14],
[3, 4, 7, 16], [3, 4, 13, 16],
[3, 6, 7, 16], [3, 6, 15, 16],
[3, 12, 13, 16], [3, 12, 15, 16],
[4, 5, 8, 17], [4, 5, 14, 17],
[4, 7, 8, 17], [4, 7, 16, 17],
[4, 13, 14, 17], [4, 13, 16, 17],
[9, 10, 13, 22], [9, 10, 19, 22],
[9, 12, 13, 22], [9, 12, 21, 22],
[9, 18, 19, 22], [9, 18, 21, 22],
[10, 11, 14, 23], [10, 11, 20, 23],
[10, 13, 14, 23], [10, 13, 22, 23],
[10, 19, 20, 23], [10, 19, 22, 23],
[12, 13, 16, 25], [12, 13, 22, 25],
[12, 15, 16, 25], [12, 15, 24, 25],
[12, 21, 22, 25], [12, 21, 24, 25],
[13, 14, 17, 26], [13, 14, 23, 26],
[13, 16, 17, 26], [13, 16, 25, 26],
[13, 22, 23, 26], [13, 22, 25, 26]])
mesh = mesh_type(nodeArray=nodeArray,
elementNodesArray=elementNodesArray)
toPolyhedron = tetrahedronVerticesToNormals
eq_(getMeshIntersections(mesh, toPolyhedron, endpoints),
set([((0.5, 0.5, 0.5), (1, 1, 1)), ((0, 0, 0), (0.5, 0.5, 0.5))]))
def getMeshIntersections(self, line):
field, endpoints = line
# get Proteus mesh index for this field
field_id = self.fieldNames.index(field)
femFun = self.u[field_id]
mesh = femFun.femSpace.mesh
referenceElement = femFun.femSpace.elementMaps.referenceElement
if referenceElement.dim == 2 and referenceElement.nNodes == 3:
toPolyhedron = triangleVerticesToNormals
elif referenceElement.dim == 3 and referenceElement.nNodes == 4:
toPolyhedron = tetrahedronVerticesToNormals
else:
raise NotImplementedError("Unable to compute mesh intersections for this element type")
intersections = np.asarray(list(getMeshIntersections(mesh, toPolyhedron, endpoints)), dtype=np.double)
endpoints = np.asarray(endpoints, np.double)
length = norm(endpoints[1] - endpoints[0])
length_segments = [(old_div(norm(i[0]-endpoints[0]),length), old_div(norm(i[1]-endpoints[0]),length), i) for i in intersections]
segments = self.pruneDuplicateSegments(endpoints, length_segments)
return segments
def test_mesh_intersections(self):
"""
Test correctness of intersecting a line and a tetrahedral mesh.
"""
endpoints = np.asarray(((0, 0, 0), (1, 1, 1)))
mesh_type = namedtuple('mesh', 'nodeArray elementNodesArray')
nodeArray = np.asarray(([[ 0. , 0. , 0. ],
[ 0.5, 0. , 0. ],
[ 1. , 0. , 0. ],
[ 0. , 0.5, 0. ],
[ 0.5, 0.5, 0. ],
[ 1. , 0.5, 0. ],
[ 0. , 1. , 0. ],
[ 0.5, 1. , 0. ],
[ 1. , 1. , 0. ],
[ 0. , 0. , 0.5],
[ 0.5, 0. , 0.5],
[ 1. , 0. , 0.5],
[ 0. , 0.5, 0.5],
[ 0.5, 0.5, 0.5],
[ 1. , 0.5, 0.5],
[ 0. , 1. , 0.5],
[ 0.5, 1. , 0.5],
[ 1. , 1. , 0.5],
[ 0. , 0. , 1. ],
[ 0.5, 0. , 1. ],
[ 1. , 0. , 1. ],
[ 0. , 0.5, 1. ],
[ 0.5, 0.5, 1. ],
[ 1. , 0.5, 1. ],
[ 0. , 1. , 1. ],
[ 0.5, 1. , 1. ],
[ 1. , 1. , 1. ]]))
elementNodesArray = np.asarray([[ 0, 1, 4, 13],
[ 0, 1, 10, 13],
[ 0, 3, 4, 13],
[ 0, 3, 12, 13],
[ 0, 9, 10, 13],
[ 0, 9, 12, 13],
[ 1, 2, 5, 14],
[ 1, 2, 11, 14],
[ 1, 4, 5, 14],
[ 1, 4, 13, 14],
[ 1, 10, 11, 14],
[ 1, 10, 13, 14],
[ 3, 4, 7, 16],
[ 3, 4, 13, 16],
[ 3, 6, 7, 16],
[ 3, 6, 15, 16],
[ 3, 12, 13, 16],
[ 3, 12, 15, 16],
[ 4, 5, 8, 17],
[ 4, 5, 14, 17],
[ 4, 7, 8, 17],
[ 4, 7, 16, 17],
[ 4, 13, 14, 17],
[ 4, 13, 16, 17],
[ 9, 10, 13, 22],
[ 9, 10, 19, 22],
[ 9, 12, 13, 22],
[ 9, 12, 21, 22],
[ 9, 18, 19, 22],
[ 9, 18, 21, 22],
[10, 11, 14, 23],
[10, 11, 20, 23],
[10, 13, 14, 23],
[10, 13, 22, 23],
[10, 19, 20, 23],
[10, 19, 22, 23],
[12, 13, 16, 25],
[12, 13, 22, 25],
[12, 15, 16, 25],
[12, 15, 24, 25],
[12, 21, 22, 25],
[12, 21, 24, 25],
[13, 14, 17, 26],
[13, 14, 23, 26],
[13, 16, 17, 26],
[13, 16, 25, 26],
[13, 22, 23, 26],
[13, 22, 25, 26]])
mesh = mesh_type(nodeArray=nodeArray, elementNodesArray=elementNodesArray)
toPolyhedron = tetrahedronVerticesToNormals
eq_(getMeshIntersections(mesh, toPolyhedron, endpoints),
set([((0.5, 0.5, 0.5), (1, 1, 1)), ((0, 0, 0), (0.5, 0.5, 0.5))]))
