def _calcFaceTangents(self):
faceVertexCoord = numerix.array(
numerix.take(self.vertexCoords, self.faceVertexIDs[0], axis=1))
tmp = self._faceCenters - faceVertexCoord
faceTangents1 = tmp / numerix.sqrtDot(tmp, tmp)
tmp = numerix.cross(faceTangents1, self.faceNormals, axis=0)
faceTangents2 = tmp / numerix.sqrtDot(tmp, tmp)
return faceTangents1, faceTangents2
def _calcFaceTangents(self):
faceVertexCoord = numerix.array(numerix.take(self.vertexCoords,
self.faceVertexIDs[0],
axis=1))
tmp = self.faceCenters - faceVertexCoord
self.faceTangents1 = tmp / numerix.sqrtDot(tmp, tmp)
tmp = numerix.cross(self.faceTangents1, self.faceNormals, axis=0)
self.faceTangents2 = tmp / numerix.sqrtDot(tmp, tmp)
def _calcFaceTangents(self):
tmp = numerix.array((-self.faceNormals[1], self.faceNormals[0]))
## copy required to get internal memory ordering correct for inlining.
tmp = tmp.copy()
mag = numerix.sqrtDot(tmp, tmp)
self.faceTangents1 = tmp / mag
self.faceTangents2 = numerix.zeros(self.faceTangents1.shape, 'd')
def _calcTangent1(self): norm = self.normal mag = numerix.sqrtDot(norm,norm) ## mag = numerix.sqrt(norm[0]**2 + norm[1]**2) tan1 = numerix.array((-norm[1],norm[0])) ## tan1 = PhysicalField(value = (-norm[1],norm[0])) return tan1/mag
def _calcCellDistance(self):
"""Calculate the distance between adjacent `Cell` centers.
If the Face is on a boundary and has only one bordering Cell,
the distance is from the Cell center to the Face center.
"""
if len(self.cellsID) == 2:
vec = self.cellCenters[0] - self.cellCenters[1]
else:
vec = self.center - self.cellCenters[0]
return numerix.sqrtDot(vec, vec)
def _calcNormal(self): """Normal is perpendicular to vector between vertices. """ tangent = self.vertices[1].getCoordinates() - self.vertices[0].getCoordinates() norm = numerix.array([-tangent[1],tangent[0]]) ## norm = PhysicalField(value = [-tangent[1],tangent[0]]) norm /= numerix.sqrtDot(norm,norm) ## we calculate the orientation after we know the normal ## norm *= self.orientation return norm
def _calcFaceAreas(self):
faceVertexIDs = MA.filled(self.faceVertexIDs, -1)
substitute = numerix.repeat(faceVertexIDs[numerix.newaxis, 0],
faceVertexIDs.shape[0], axis=0)
faceVertexIDs = numerix.where(MA.getmaskarray(self.faceVertexIDs), substitute, faceVertexIDs)
faceVertexCoords = numerix.take(self.vertexCoords, faceVertexIDs, axis=1)
faceOrigins = numerix.repeat(faceVertexCoords[:,0], faceVertexIDs.shape[0], axis=0)
faceOrigins = numerix.reshape(faceOrigins, MA.shape(faceVertexCoords))
faceVertexCoords = faceVertexCoords - faceOrigins
left = range(faceVertexIDs.shape[0])
right = left[1:] + [left[0]]
cross = numerix.sum(numerix.cross(faceVertexCoords, numerix.take(faceVertexCoords, right, 1), axis=0), 1)
self.faceAreas = numerix.sqrtDot(cross, cross) / 2.
def _rightHandOrientation(self):
faceVertexIDs = MA.filled(self.faceVertexIDs, 0)
faceVertexCoords = numerix.take(self.vertexCoords, faceVertexIDs, axis=1)
t1 = faceVertexCoords[:,1,:] - faceVertexCoords[:,0,:]
t2 = faceVertexCoords[:,2,:] - faceVertexCoords[:,1,:]
norm = numerix.cross(t1, t2, axis=0)
## reordering norm's internal memory for inlining
norm = norm.copy()
norm = norm / numerix.sqrtDot(norm, norm)
faceNormals = -norm
return 1 - 2 * (numerix.dot(faceNormals, self.cellDistanceVectors) < 0)
def _calcFaceAreas(self):
faceVertexIDs = MA.filled(self.faceVertexIDs, -1)
substitute = numerix.repeat(faceVertexIDs[numerix.newaxis, 0],
faceVertexIDs.shape[0], axis=0)
faceVertexIDs = numerix.where(MA.getmaskarray(self.faceVertexIDs),
substitute, faceVertexIDs)
faceVertexCoords = numerix.take(self.vertexCoords, faceVertexIDs, axis=1)
faceOrigins = numerix.repeat(faceVertexCoords[:,0], faceVertexIDs.shape[0], axis=0)
faceOrigins = numerix.reshape(faceOrigins, MA.shape(faceVertexCoords))
faceVertexCoords = faceVertexCoords - faceOrigins
left = range(faceVertexIDs.shape[0])
right = left[1:] + [left[0]]
cross = numerix.sum(numerix.cross(faceVertexCoords,
numerix.take(faceVertexCoords, right, 1),
axis=0),
1)
return numerix.sqrtDot(cross, cross) / 2.
def _calcNormal(self):
"""Calculate the unit normal vector.
Unit normal vector is calculated from cross-product of two
tangent vectors.
.. warning::
Doesn't work if t1 and t2 are colinear!
"""
t1 = self.vertices[1].getCoordinates() - self.vertices[0].getCoordinates()
t2 = self.vertices[2].getCoordinates() - self.vertices[1].getCoordinates()
norm = numerix.crossProd(t1, t2)
norm /= numerix.sqrtDot(norm, norm)
## we calculate the orientation after we know the normal
## norm *= self.orientation
return norm
def _calcFaceAreas(self):
faceVertexCoords = numerix.take(self.vertexCoords, self.faceVertexIDs, axis=1)
tangent = faceVertexCoords[:,1] - faceVertexCoords[:,0]
return numerix.sqrtDot(tangent, tangent)
def _calcFaceToCellDistance(self, id):
vec = self.center - self.cellCenters[id]
return numerix.sqrtDot(vec, vec)
def _getPointToCellDistances(self, point):
tmp = self.getCellCenters() - PhysicalField(point)
from fipy.tools import numerix
return numerix.sqrtDot(tmp, tmp)
def _getPointToCellDistances(self, point):
tmp = self.cellCenters - PhysicalField(point)
return numerix.sqrtDot(tmp, tmp)
def _calcFaceAreas(self):
faceVertexCoords = numerix.take(self.vertexCoords, self.faceVertexIDs, axis=1)
tangent = faceVertexCoords[:, 1] - faceVertexCoords[:, 0]
return numerix.sqrtDot(tangent, tangent)
def _getAddedMeshValues(self, other, resolution=1e-2):
"""Calculate the parameters to define a concatenation of `other` with `self`
Parameters
----------
other : ~fipy.meshes.mesh.Mesh
The `Mesh` to concatenate with `self`
resolution : float
How close vertices have to be (relative to the smallest
cell-to-cell distance in either mesh) to be considered the same
Returns
-------
dict
(`vertexCoords`, `faceVertexIDs`, `cellFaceIDs`) for the new mesh.
"""
selfc = self._concatenableMesh
otherc = other._concatenableMesh
selfNumFaces = selfc.faceVertexIDs.shape[-1]
selfNumVertices = selfc.vertexCoords.shape[-1]
otherNumFaces = otherc.faceVertexIDs.shape[-1]
otherNumVertices = otherc.vertexCoords.shape[-1]
## check dimensions
if(selfc.vertexCoords.shape[0] != otherc.vertexCoords.shape[0]):
raise MeshAdditionError("Dimensions do not match")
## compute vertex correlates
# from fipy.tools.debug import PRINT
# PRINT("selfNumFaces", selfNumFaces)
# PRINT("otherNumFaces", otherNumVertices)
# PRINT("selfNumVertices", selfNumVertices)
# PRINT("otherNumVertices", otherNumVertices)
#
# from fipy.tools.debug import PRINT
# from fipy.tools.debug import PRINT
# PRINT("otherExt", otherc.exteriorFaces.value)
# raw_input()
# PRINT("selfExt", selfc.exteriorFaces.value)
#
# PRINT("self filled", selfc.faceVertexIDs.filled())
# PRINT("othe filled", otherc.faceVertexIDs.filled())
# raw_input()
#
# PRINT("selfc.faceVertexIDs.filled()\n",selfc.faceVertexIDs.filled())
# PRINT("flat\n",selfc.faceVertexIDs.filled()[...,
# selfc.exteriorFaces.value].flatten())
# PRINT("selfc.exteriorFaces.value\n",selfc.exteriorFaces.value)
# PRINT("extfaces type", type(selfc.exteriorFaces))
# PRINT("extfaces mesh", selfc.exteriorFaces.mesh)
## only try to match along the operation manifold
if hasattr(self, "opManifold"):
self_faces = self.opManifold(selfc)
else:
self_faces = selfc.exteriorFaces.value
if hasattr(other, "opManifold"):
other_faces = other.opManifold(otherc)
else:
other_faces = otherc.exteriorFaces.value
## only try to match exterior (X) vertices
self_Xvertices = numerix.unique(selfc.faceVertexIDs.filled()[...,
self_faces].flatten())
other_Xvertices = numerix.unique(otherc.faceVertexIDs.filled()[...,
other_faces].flatten())
self_XvertexCoords = selfc.vertexCoords[..., self_Xvertices]
other_XvertexCoords = otherc.vertexCoords[..., other_Xvertices]
closest = numerix.nearest(self_XvertexCoords, other_XvertexCoords)
# just because they're closest, doesn't mean they're close
tmp = self_XvertexCoords[..., closest] - other_XvertexCoords
distance = numerix.sqrtDot(tmp, tmp)
# only want vertex pairs that are 100x closer than the smallest
# cell-to-cell distance
close = distance < resolution * min(selfc._cellToCellDistances.min(),
otherc._cellToCellDistances.min())
vertexCorrelates = numerix.array((self_Xvertices[closest[close]],
other_Xvertices[close]))
# warn if meshes don't touch, but allow it
if (selfc._numberOfVertices > 0
and otherc._numberOfVertices > 0
and vertexCorrelates.shape[-1] == 0):
import warnings
warnings.warn("Vertices are not aligned", UserWarning, stacklevel=4)
## compute face correlates
# ensure that both sets of faceVertexIDs have the same maximum number of (masked) elements
self_faceVertexIDs = selfc.faceVertexIDs
other_faceVertexIDs = otherc.faceVertexIDs
diff = self_faceVertexIDs.shape[0] - other_faceVertexIDs.shape[0]
if diff > 0:
other_faceVertexIDs = numerix.append(other_faceVertexIDs,
-1 * numerix.ones((diff,)
+ other_faceVertexIDs.shape[1:], 'l'),
axis=0)
other_faceVertexIDs = MA.masked_values(other_faceVertexIDs, -1)
elif diff < 0:
self_faceVertexIDs = numerix.append(self_faceVertexIDs,
-1 * numerix.ones((-diff,)
+ self_faceVertexIDs.shape[1:], 'l'),
axis=0)
self_faceVertexIDs = MA.masked_values(self_faceVertexIDs, -1)
# want self's Faces for which all faceVertexIDs are in vertexCorrelates
self_matchingFaces = numerix.in1d(self_faceVertexIDs,
vertexCorrelates[0]).reshape(self_faceVertexIDs.shape).all(axis=0).nonzero()[0]
# want other's Faces for which all faceVertexIDs are in vertexCorrelates
other_matchingFaces = numerix.in1d(other_faceVertexIDs,
vertexCorrelates[1]).reshape(other_faceVertexIDs.shape).all(axis=0).nonzero()[0]
# map other's Vertex IDs to new Vertex IDs,
# accounting for overlaps with self's Vertex IDs
vertex_map = numerix.empty(otherNumVertices, dtype=numerix.INT_DTYPE)
verticesToAdd = numerix.delete(numerix.arange(otherNumVertices), vertexCorrelates[1])
vertex_map[verticesToAdd] = numerix.arange(otherNumVertices - len(vertexCorrelates[1])) + selfNumVertices
vertex_map[vertexCorrelates[1]] = vertexCorrelates[0]
# calculate hashes of faceVertexIDs for comparing Faces
if self_matchingFaces.shape[-1] == 0:
self_faceHash = numerix.empty(self_matchingFaces.shape[:-1] + (0,), dtype="str")
else:
# sort each of self's Face's vertexIDs for canonical comparison
self_faceHash = numerix.sort(self_faceVertexIDs[..., self_matchingFaces], axis=0)
# then hash the Faces for comparison (NumPy set operations are only for 1D arrays)
self_faceHash = numerix.apply_along_axis(str, axis=0, arr=self_faceHash)
face_sort = numerix.argsort(self_faceHash)
self_faceHash = self_faceHash[face_sort]
self_matchingFaces = self_matchingFaces[face_sort]
if other_matchingFaces.shape[-1] == 0:
other_faceHash = numerix.empty(other_matchingFaces.shape[:-1] + (0,), dtype="str")
else:
# convert each of other's Face's vertexIDs to new IDs
other_faceHash = vertex_map[other_faceVertexIDs[..., other_matchingFaces]]
# sort each of other's Face's vertexIDs for canonical comparison
other_faceHash = numerix.sort(other_faceHash, axis=0)
# then hash the Faces for comparison (NumPy set operations are only for 1D arrays)
other_faceHash = numerix.apply_along_axis(str, axis=0, arr=other_faceHash)
face_sort = numerix.argsort(other_faceHash)
other_faceHash = other_faceHash[face_sort]
other_matchingFaces = other_matchingFaces[face_sort]
self_matchingFaces = self_matchingFaces[numerix.in1d(self_faceHash,
other_faceHash)]
other_matchingFaces = other_matchingFaces[numerix.in1d(other_faceHash,
self_faceHash)]
faceCorrelates = numerix.array((self_matchingFaces,
other_matchingFaces))
# warn if meshes don't touch, but allow it
if (selfc.numberOfFaces > 0
and otherc.numberOfFaces > 0
and faceCorrelates.shape[-1] == 0):
import warnings
warnings.warn("Faces are not aligned", UserWarning, stacklevel=4)
# map other's Face IDs to new Face IDs,
# accounting for overlaps with self's Face IDs
face_map = numerix.empty(otherNumFaces, dtype=numerix.INT_DTYPE)
facesToAdd = numerix.delete(numerix.arange(otherNumFaces), faceCorrelates[1])
face_map[facesToAdd] = numerix.arange(otherNumFaces - len(faceCorrelates[1])) + selfNumFaces
face_map[faceCorrelates[1]] = faceCorrelates[0]
other_faceVertexIDs = vertex_map[otherc.faceVertexIDs[..., facesToAdd]]
# ensure that both sets of cellFaceIDs have the same maximum number of (masked) elements
self_cellFaceIDs = selfc.cellFaceIDs
other_cellFaceIDs = face_map[otherc.cellFaceIDs]
diff = self_cellFaceIDs.shape[0] - other_cellFaceIDs.shape[0]
if diff > 0:
other_cellFaceIDs = numerix.append(other_cellFaceIDs,
-1 * numerix.ones((diff,)
+ other_cellFaceIDs.shape[1:], 'l'),
axis=0)
other_cellFaceIDs = MA.masked_values(other_cellFaceIDs, -1)
elif diff < 0:
self_cellFaceIDs = numerix.append(self_cellFaceIDs,
-1 * numerix.ones((-diff,)
+ self_cellFaceIDs.shape[1:], 'l'),
axis=0)
self_cellFaceIDs = MA.masked_values(self_cellFaceIDs, -1)
# concatenate everything and return
return {
'vertexCoords': numerix.concatenate((selfc.vertexCoords,
otherc.vertexCoords[..., verticesToAdd]), axis=1),
'faceVertexIDs': numerix.concatenate((self_faceVertexIDs,
other_faceVertexIDs), axis=1),
'cellFaceIDs': MA.concatenate((self_cellFaceIDs,
other_cellFaceIDs), axis=1)
}
def _getAddedMeshValues(self, other, resolution=1e-2):
"""Calculate the parameters to define a concatenation of `other` with `self`
:Parameters:
- `other`: The :class:`~fipy.meshes.numMesh.Mesh` to concatenate with `self`
- `resolution`: How close vertices have to be (relative to the smallest
cell-to-cell distance in either mesh) to be considered the same
:Returns:
A `dict` with 3 elements: the new mesh vertexCoords, faceVertexIDs, and cellFaceIDs.
"""
selfc = self._getConcatenableMesh()
other = other._getConcatenableMesh()
selfNumFaces = selfc.faceVertexIDs.shape[-1]
selfNumVertices = selfc.vertexCoords.shape[-1]
otherNumFaces = other.faceVertexIDs.shape[-1]
otherNumVertices = other.vertexCoords.shape[-1]
## check dimensions
if(selfc.vertexCoords.shape[0] != other.vertexCoords.shape[0]):
raise MeshAdditionError, "Dimensions do not match"
## compute vertex correlates
## only try to match exterior (X) vertices
self_Xvertices = numerix.unique(selfc._getFaceVertexIDs().filled()[..., selfc.getExteriorFaces().getValue()].flatten())
other_Xvertices = numerix.unique(other._getFaceVertexIDs().filled()[..., other.getExteriorFaces().getValue()].flatten())
self_XvertexCoords = selfc.vertexCoords[..., self_Xvertices]
other_XvertexCoords = other.vertexCoords[..., other_Xvertices]
# lifted from Mesh._getNearestCellID()
other_vertexCoordMap = numerix.resize(other_XvertexCoords,
(self_XvertexCoords.shape[-1],
other_XvertexCoords.shape[0],
other_XvertexCoords.shape[-1])).swapaxes(0,1)
tmp = self_XvertexCoords[..., numerix.newaxis] - other_vertexCoordMap
closest = numerix.argmin(numerix.dot(tmp, tmp), axis=0)
# just because they're closest, doesn't mean they're close
tmp = self_XvertexCoords[..., closest] - other_XvertexCoords
distance = numerix.sqrtDot(tmp, tmp)
# only want vertex pairs that are 100x closer than the smallest
# cell-to-cell distance
close = distance < resolution * min(selfc._getCellToCellDistances().min(),
other._getCellToCellDistances().min())
vertexCorrelates = numerix.array((self_Xvertices[closest[close]],
other_Xvertices[close]))
# warn if meshes don't touch, but allow it
if (selfc._getNumberOfVertices() > 0
and other._getNumberOfVertices() > 0
and vertexCorrelates.shape[-1] == 0):
import warnings
warnings.warn("Vertices are not aligned", UserWarning, stacklevel=4)
## compute face correlates
# ensure that both sets of faceVertexIDs have the same maximum number of (masked) elements
self_faceVertexIDs = selfc.faceVertexIDs
other_faceVertexIDs = other.faceVertexIDs
diff = self_faceVertexIDs.shape[0] - other_faceVertexIDs.shape[0]
if diff > 0:
other_faceVertexIDs = numerix.append(other_faceVertexIDs,
-1 * numerix.ones((diff,)
+ other_faceVertexIDs.shape[1:]),
axis=0)
other_faceVertexIDs = MA.masked_values(other_faceVertexIDs, -1)
elif diff < 0:
self_faceVertexIDs = numerix.append(self_faceVertexIDs,
-1 * numerix.ones((-diff,)
+ self_faceVertexIDs.shape[1:]),
axis=0)
self_faceVertexIDs = MA.masked_values(self_faceVertexIDs, -1)
# want self's Faces for which all faceVertexIDs are in vertexCorrelates
self_matchingFaces = numerix.in1d(self_faceVertexIDs,
vertexCorrelates[0]).reshape(self_faceVertexIDs.shape).all(axis=0).nonzero()[0]
# want other's Faces for which all faceVertexIDs are in vertexCorrelates
other_matchingFaces = numerix.in1d(other_faceVertexIDs,
vertexCorrelates[1]).reshape(other_faceVertexIDs.shape).all(axis=0).nonzero()[0]
# map other's Vertex IDs to new Vertex IDs,
# accounting for overlaps with self's Vertex IDs
vertex_map = numerix.empty(otherNumVertices, dtype=int)
verticesToAdd = numerix.delete(numerix.arange(otherNumVertices), vertexCorrelates[1])
vertex_map[verticesToAdd] = numerix.arange(otherNumVertices - len(vertexCorrelates[1])) + selfNumVertices
vertex_map[vertexCorrelates[1]] = vertexCorrelates[0]
# calculate hashes of faceVertexIDs for comparing Faces
if self_matchingFaces.shape[-1] == 0:
self_faceHash = numerix.empty(self_matchingFaces.shape[:-1] + (0,), dtype="str")
else:
# sort each of self's Face's vertexIDs for canonical comparison
self_faceHash = numerix.sort(self_faceVertexIDs[..., self_matchingFaces], axis=0)
# then hash the Faces for comparison (NumPy set operations are only for 1D arrays)
self_faceHash = numerix.apply_along_axis(str, axis=0, arr=self_faceHash)
face_sort = numerix.argsort(self_faceHash)
self_faceHash = self_faceHash[face_sort]
self_matchingFaces = self_matchingFaces[face_sort]
if other_matchingFaces.shape[-1] == 0:
other_faceHash = numerix.empty(other_matchingFaces.shape[:-1] + (0,), dtype="str")
else:
# convert each of other's Face's vertexIDs to new IDs
other_faceHash = vertex_map[other_faceVertexIDs[..., other_matchingFaces]]
# sort each of other's Face's vertexIDs for canonical comparison
other_faceHash = numerix.sort(other_faceHash, axis=0)
# then hash the Faces for comparison (NumPy set operations are only for 1D arrays)
other_faceHash = numerix.apply_along_axis(str, axis=0, arr=other_faceHash)
face_sort = numerix.argsort(other_faceHash)
other_faceHash = other_faceHash[face_sort]
other_matchingFaces = other_matchingFaces[face_sort]
self_matchingFaces = self_matchingFaces[numerix.in1d(self_faceHash,
other_faceHash)]
other_matchingFaces = other_matchingFaces[numerix.in1d(other_faceHash,
self_faceHash)]
faceCorrelates = numerix.array((self_matchingFaces,
other_matchingFaces))
# warn if meshes don't touch, but allow it
if (selfc._getNumberOfFaces() > 0
and other._getNumberOfFaces() > 0
and faceCorrelates.shape[-1] == 0):
import warnings
warnings.warn("Faces are not aligned", UserWarning, stacklevel=4)
# map other's Face IDs to new Face IDs,
# accounting for overlaps with self's Face IDs
face_map = numerix.empty(otherNumFaces, dtype=int)
facesToAdd = numerix.delete(numerix.arange(otherNumFaces), faceCorrelates[1])
face_map[facesToAdd] = numerix.arange(otherNumFaces - len(faceCorrelates[1])) + selfNumFaces
face_map[faceCorrelates[1]] = faceCorrelates[0]
other_faceVertexIDs = vertex_map[other.faceVertexIDs[..., facesToAdd]]
# ensure that both sets of cellFaceIDs have the same maximum number of (masked) elements
self_cellFaceIDs = selfc.cellFaceIDs
other_cellFaceIDs = face_map[other.cellFaceIDs]
diff = self_cellFaceIDs.shape[0] - other_cellFaceIDs.shape[0]
if diff > 0:
other_cellFaceIDs = numerix.append(other_cellFaceIDs,
-1 * numerix.ones((diff,)
+ other_cellFaceIDs.shape[1:]),
axis=0)
other_cellFaceIDs = MA.masked_values(other_cellFaceIDs, -1)
elif diff < 0:
self_cellFaceIDs = numerix.append(self_cellFaceIDs,
-1 * numerix.ones((-diff,)
+ self_cellFaceIDs.shape[1:]),
axis=0)
self_cellFaceIDs = MA.masked_values(self_cellFaceIDs, -1)
# concatenate everything and return
return {
'vertexCoords': numerix.concatenate((selfc.vertexCoords,
other.vertexCoords[..., verticesToAdd]), axis=1),
'faceVertexIDs': numerix.concatenate((self_faceVertexIDs,
other_faceVertexIDs), axis=1),
'cellFaceIDs': MA.concatenate((self_cellFaceIDs,
other_cellFaceIDs), axis=1)
}
def _getPointToCellDistances(self, point):
tmp = self.cellCenters - PhysicalField(point)
return numerix.sqrtDot(tmp, tmp)
def _calcArea(self):
"""Area is length of vector between vertices.
"""
tangent=self.vertices[0].getCoordinates()-self.vertices[1].getCoordinates()
return numerix.sqrtDot(tangent,tangent)