def getCircleProjectionAxes(ax,
ad1,
ad2,
ad3,
length,
angle1radians,
angle2radians,
angle3radians=None):
'''
Project coordinates and orthogonal unit axes ax, ad1, ad2, ad3 by length in
direction of ad3, rotated towards ad1 by angle1radians and ad2 by
angle2radians such that it conforms to a circular arc of the given length,
tangential to ad3 at the start and the final bd3 at the end.
All vectors must be length 3.
Assumes angles 1 and 2 are not large e.g. less than 90 degrees.
Note: not robust for all inputs.
:param angle3radians: Optional final rotation of projection axes about bd3.
:return: Final coordinates and orthogonal unit axes: bx, bd1, bd2, bd3
'''
if (math.fabs(angle1radians) < 0.000001) and (math.fabs(angle2radians) <
0.000001):
bx = [(ax[c] + length * ad3[c]) for c in range(3)]
bd1 = copy.deepcopy(ad1)
bd2 = copy.deepcopy(ad2)
bd3 = copy.deepcopy(ad3)
else:
cosAngle1 = math.cos(angle1radians)
sinAngle1 = math.sin(angle1radians)
cosAngle2 = math.cos(angle2radians)
sinAngle2 = math.sin(angle2radians)
f1 = sinAngle1 * cosAngle2
f2 = cosAngle1 * sinAngle2
f3 = cosAngle1 * cosAngle2
angleAroundRadians = math.atan2(f2, f1)
fh = math.sqrt(f1 * f1 + f2 * f2)
arcAngleRadians = 0.5 * math.pi - math.atan2(f3, fh)
arcRadius = length / arcAngleRadians
br = arcRadius * (1.0 - math.cos(arcAngleRadians))
w1 = br * math.cos(angleAroundRadians) # f1/fh
w2 = br * math.sin(angleAroundRadians) # f2/fh
w3 = arcRadius * math.sin(arcAngleRadians)
bx = [(ax[c] + w1 * ad1[c] + w2 * ad2[c] + w3 * ad3[c])
for c in range(3)]
bd3 = vector.normalise([(f1 * ad1[c] + f2 * ad2[c] + f3 * ad3[c])
for c in range(3)])
bd1 = vector.normalise(vector.crossproduct3(ad2, bd3))
bd2 = vector.crossproduct3(bd3, bd1)
if angle3radians:
cosAngle3 = math.cos(angle3radians)
sinAngle3 = math.sin(angle3radians)
bd1, bd2 = [
(cosAngle3 * bd1[c] + sinAngle3 * bd2[c]) for c in range(3)
], [(cosAngle3 * bd2[c] - sinAngle3 * bd1[c]) for c in range(3)]
return bx, bd1, bd2, bd3
def calculate_surface_axes(d1, d2, direction):
'''
:return: Vectors ax1, ax2, ax3: ax1 in-plane in 3-D vector direction,
ax2 in-plane normal to a and ax3 normal to the surface plane.
Vectors all have unit magnitude.
'''
ax3 = vector.normalise(vector.crossproduct3(d1, d2))
delta_xi1, delta_xi2 = calculate_surface_delta_xi(d1, d2, direction)
ax1 = vector.normalise([ delta_xi1*d1[c] + delta_xi2*d2[c] for c in range(3) ])
ax2 = vector.normalise(vector.crossproduct3(ax3, ax1))
return ax1, ax2, ax3
def makeSideDerivativesNormal(cls, region, options, functionOptions, editGroupName):
makeD2Normal = options['D2 derivatives'] and functionOptions['Make D2 normal']
makeD3Normal = options['D3 derivatives'] and functionOptions['Make D3 normal']
if not (makeD2Normal or makeD3Normal):
return False, False
valueLabels = [ Node.VALUE_LABEL_D_DS1 ]
if options['D2 derivatives']:
valueLabels.append(Node.VALUE_LABEL_D_DS2)
if options['D3 derivatives']:
valueLabels.append(Node.VALUE_LABEL_D_DS3)
parameters = extractPathParametersFromRegion(region, valueLabels)
d1 = parameters[0]
modifyParameters = []
modifyValueLabels = []
if makeD2Normal:
d2 = parameters[1]
for c in range(len(d1)):
td2 = vector.vectorRejection(d2[c], d1[c])
d2[c] = vector.setMagnitude(td2, vector.magnitude(d2[c]))
modifyParameters.append(d2)
modifyValueLabels.append(Node.VALUE_LABEL_D_DS2)
if makeD3Normal:
d3 = parameters[-1]
if options['D2 derivatives']:
d2 = parameters[1]
for c in range(len(d1)):
d3[c] = vector.setMagnitude(vector.crossproduct3(d1[c], d2[c]), vector.magnitude(d3[c]))
else:
for c in range(len(d1)):
td3 = vector.vectorRejection(d3[c], d1[c])
d3[c] = vector.setMagnitude(td3, vector.magnitude(d3[c]))
modifyParameters.append(d3)
modifyValueLabels.append(Node.VALUE_LABEL_D_DS3)
setPathParameters(region, modifyValueLabels, modifyParameters, editGroupName)
return False, True # settings not changed, nodes changed
def __init__(self,
elementsCountAcrossMajor,
elementsCountAcrossMinor,
centre=None,
alongAxis=None,
majorAxis=None,
minorRadius=None):
"""
:param elementsCountAcrossMajor: Number of elements across major axis. Must be at least 2 + elementsCountRim for
half and 4 + elementsCountRim for full cylinder.
:param elementsCountAcrossMinor: Number of elements across minor axis.
:param centre: Centre of the ellipse.
:param alongAxis: The cylinder axis that the base is extruded along.
:param majorAxis: The major axis of the base. Should be perpendicular to alongAxis
:param minorRadius: The minor radius of the ellipse.
"""
self._centre = centre
self._alongAxis = alongAxis
self._majorAxis = majorAxis
self._minorRadius = minorRadius
if alongAxis:
self._minorAxis = vector.setMagnitude(
vector.crossproduct3(alongAxis, majorAxis), minorRadius)
self._elementsCountAcrossMinor = elementsCountAcrossMinor
self._elementsCountAcrossMajor = elementsCountAcrossMajor
self._majorRadius = vector.magnitude(majorAxis)
self.px = None
self.pd1 = None
self.pd2 = None
self.pd3 = None
def projectHermiteCurvesThroughWall(nx, nd1, nd2, n, wallThickness, loop = False):
'''
From Hermite curve nx, nd1 with cross direction nd2, project normal to wall
by wall thickness to get coordinates, d1 affected by curvature etc.
Assumes 3 components.
:param n: Index into nx, nd1, nd2 of where to project.
:param wallThickness: Use positive from in to out, negative from outside to in.
:return: x, d1, d2, d3
'''
maxPointIndex = len(nx) - 1
assert (0 <= n <= maxPointIndex), 'projectHermiteCurvesThroughWall. Invalid index'
unitNormal = vector.normalise(vector.crossproduct3(nd1[n], nd2[n]))
x = [ (nx[n][c] + wallThickness*unitNormal[c]) for c in range(3) ]
# calculate inner d1 from curvature around
curvature = 0.0
count = 0
if loop or (n > 0) and (nx[n - 1]):
curvature += getCubicHermiteCurvature(nx[n - 1], nd1[n - 1], nx[n], nd1[n], unitNormal, 1.0)
count += 1
if loop or (n < maxPointIndex) and (nx[n - maxPointIndex]):
curvature += getCubicHermiteCurvature(nx[n], nd1[n], nx[n - maxPointIndex], nd1[n - maxPointIndex], unitNormal, 0.0)
count += 1
curvature /= count
factor = 1.0 - curvature*wallThickness
d1 = [ factor*c for c in nd1[n] ]
d2 = copy.deepcopy(nd2[n]) # magnitude can't be determined here
d3 = vector.setMagnitude(unitNormal, math.fabs(wallThickness))
return x, d1, d2, d3
def createEllipsoidPoints(centre, poleAxis, sideAxis, elementsCountAround,
elementsCountUp, height):
'''
Generate a set of points and derivatives for circle of revolution of an ellipse
starting at pole poleAxis from centre.
:param centre: Centre of full ellipsoid.
:param poleAxis: Vector in direction of starting pole, magnitude is ellipse axis length.
:param sideAxis: Vector normal to poleAxis, magnitude is ellipse side axis length.
:param height: Height of arc of ellipsoid from starting pole along poleAxis.
:return: Lists nx, nd1, nd2. Ordered fastest around, starting at pole. Suitable for passing to TrackSurface.
'''
nx = []
nd1 = []
nd2 = []
magPoleAxis = vector.magnitude(poleAxis)
magSideAxis = vector.magnitude(sideAxis)
unitPoleAxis = vector.normalise(poleAxis)
unitSideAxis1 = vector.normalise(sideAxis)
unitSideAxis2 = vector.normalise(vector.crossproduct3(sideAxis, poleAxis))
useHeight = min(max(0.0, height), 2.0 * magPoleAxis)
totalRadiansUp = getEllipseRadiansToX(magPoleAxis,
0.0,
magPoleAxis - useHeight,
initialTheta=0.5 * math.pi *
useHeight / magPoleAxis)
radiansUp = 0.0
lengthUp = getEllipseArcLength(magPoleAxis, magSideAxis, radiansUp,
totalRadiansUp)
elementLengthUp = lengthUp / elementsCountUp
radiansPerElementAround = 2.0 * math.pi / elementsCountAround
for n2 in range(elementsCountUp + 1):
cosRadiansUp = math.cos(radiansUp)
sinRadiansUp = math.sin(radiansUp)
radius = sinRadiansUp * magSideAxis
d2r, d2z = vector.setMagnitude(
[cosRadiansUp * magSideAxis, sinRadiansUp * magPoleAxis],
elementLengthUp)
cx = [(centre[c] + cosRadiansUp * poleAxis[c]) for c in range(3)]
elementLengthAround = radius * radiansPerElementAround
radiansAround = 0.0
for n in range(elementsCountAround):
cosRadiansAround = math.cos(radiansAround)
sinRadiansAround = math.sin(radiansAround)
nx.append([(cx[c] + radius * (cosRadiansAround * unitSideAxis1[c] +
sinRadiansAround * unitSideAxis2[c]))
for c in range(3)])
nd1.append([
(elementLengthAround * (-sinRadiansAround * unitSideAxis1[c] +
cosRadiansAround * unitSideAxis2[c]))
for c in range(3)
])
nd2.append([(d2r * (cosRadiansAround * unitSideAxis1[c] +
sinRadiansAround * unitSideAxis2[c]) -
d2z * unitPoleAxis[c]) for c in range(3)])
radiansAround += radiansPerElementAround
radiansUp = updateEllipseAngleByArcLength(magPoleAxis, magSideAxis,
radiansUp, elementLengthUp)
return nx, nd1, nd2
def normalToEllipse(v1, v2):
"""
Find unit normal vector of an ellipse using two vectors in the ellipse. The direction is v1xv2
:param v1: vector 1.
:param v2: vector 2.
:return:
"""
nte = vector.normalise(vector.crossproduct3(v1, v2))
return nte
def getSurfaceProjectionAxes(ax, ad1, ad2, ad3, angle1radians, angle2radians, length):
'''
Project coordinates and orthogonal unit axes ax, ad1, ad2, ad3 in direction
of ad3, rotated towards ad1 by angle1radians and ad2 by angle2radians by
simple rotation.
All vectors are/must be length 3.
Assumes angles are not large e.g. less than 90 degrees.
Note: not robust for all inputs.
:return: Final coordinates and orthogonal unit axes: bx, bd1, bd2, bd3
'''
cosAngle1 = math.cos(angle1radians)
sinAngle1 = math.sin(angle1radians)
cosAngle2 = math.cos(angle2radians)
sinAngle2 = math.sin(angle2radians)
f1 = sinAngle1*cosAngle2
f2 = cosAngle1*sinAngle2
f3 = cosAngle1*cosAngle2
bd3 = [ (f1*ad1[c] + f2*ad2[c] + f3*ad3[c]) for c in range (3) ]
bx = [ (ax[c] + length*bd3[c]) for c in range(3) ]
bd1 = vector.crossproduct3(ad2, bd3)
bd2 = vector.crossproduct3(bd3, bd1)
return bx, bd1, bd2, bd3
def interpolateNodesCubicHermite(cache, coordinates, xi, normal_scale, \
node1, derivative1, scale1, cross_derivative1, cross_scale1, \
node2, derivative2, scale2, cross_derivative2, cross_scale2):
"""
Interpolates position and first derivative with cubic Hermite basis.
Interpolates cross derivative linearly.
:param cache: Field cache to evaluate in.
:param coordinates: Coordinates field.
:param xi: Element coordinate to interpolate at.
:param normal_scale: Magnitude of normal derivative to return.
:param node1, node2: Start and end nodes.
:param derivative1, derivative2: Node value label for derivatives.
:param scale1, scale2: Real value scaling derivatives, to reverse if needed.
:param cross_derivative1, cross_derivative2: Node value label for cross derivatives.
:param cross_scale1, cross_scale2: Real value scaling cross_derivatives, to reverse if needed.
:return: x, dx_ds, dx_ds_cross, dx_ds_normal
"""
cache.setNode(node1)
result, v1 = coordinates.getNodeParameters(cache, -1,
Node.VALUE_LABEL_VALUE, 1, 3)
result, d1 = coordinates.getNodeParameters(cache, -1, derivative1, 1, 3)
result, d1c = coordinates.getNodeParameters(cache, -1, cross_derivative1,
1, 3)
d1 = [scale1 * d for d in d1]
d1c = [cross_scale1 * d for d in d1c]
cache.setNode(node2)
result, v2 = coordinates.getNodeParameters(cache, -1,
Node.VALUE_LABEL_VALUE, 1, 3)
result, d2 = coordinates.getNodeParameters(cache, -1, derivative2, 1, 3)
result, d2c = coordinates.getNodeParameters(cache, -1, cross_derivative2,
1, 3)
d2 = [scale2 * d for d in d2]
d2c = [cross_scale2 * d for d in d2c]
arcLength = interp.computeCubicHermiteArcLength(v1, d1, v2, d2, True)
mag = arcLength / vector.magnitude(d1)
d1 = [mag * d for d in d1]
mag = arcLength / vector.magnitude(d2)
d2 = [mag * d for d in d2]
xr = 1.0 - xi
x = interp.interpolateCubicHermite(v1, d1, v2, d2, xi)
dx_ds = interp.interpolateCubicHermiteDerivative(v1, d1, v2, d2, xi)
scale = min(xi, xr)
dx_ds = [scale * d for d in dx_ds]
dx_ds_cross = [(xr * d1c[c] + xi * d2c[c]) for c in range(3)]
radialVector = vector.normalise(vector.crossproduct3(dx_ds_cross, dx_ds))
dx_ds_normal = [normal_scale * d for d in radialVector]
return x, dx_ds, dx_ds_cross, dx_ds_normal
def getCubicHermiteCurvatureSimple(v1, d1, v2, d2, xi):
"""
:param v1, v2: Values at xi = 0.0 and xi = 1.0, respectively.
:param d1, d2: Derivatives w.r.t. xi at xi = 0.0 and xi = 1.0, respectively.
:param xi: Position in curve, nominally in [0.0, 1.0].
:return: Scalar curvature (1/R) of the 1-D cubic Hermite curve.
"""
tangent = interpolateCubicHermiteDerivative(v1, d1, v2, d2, xi)
dTangent = interpolateCubicHermiteSecondDerivative(v1, d1, v2, d2, xi)
cp = vector.crossproduct3(tangent, dTangent)
curvature = vector.magnitude(cp) / (vector.magnitude(tangent)*vector.magnitude(tangent)*vector.magnitude(tangent))
return curvature
def generateBase1DMesh(self):
"""
Generate nodes around the perimeter of the ellipse.
"""
nx, nd1 = createEllipsePerimeter(self.centre, self.majorAxis,
self.minorAxis,
self.elementsCountAround,
self.majorRadius)
nte = normalToEllipse(self.majorAxis, self.minorAxis)
tbx, tbd1, tbd2, tbd3 = [], [], [], []
for n in range(self.elementsCountAround + 1):
tbx.append(nx[n])
tbd1.append(nd1[n])
tbd2.append(nte)
tbd3.append(vector.normalise(vector.crossproduct3(tbd1[n], nte)))
self.setRimNodes(tbx, tbd1, tbd2, tbd3)
def makeD3Normal(cls, region, options, editGroupName):
if not options['D3 derivatives']:
return
if options['D2 derivatives']:
d1, d2, d3 = extractPathParametersFromRegion(
region, [
Node.VALUE_LABEL_D_DS1, Node.VALUE_LABEL_D_DS2,
Node.VALUE_LABEL_D_DS3
])
for c in range(len(d1)):
d3[c] = vector.setMagnitude(vector.crossproduct3(d1[c], d2[c]),
vector.magnitude(d3[c]))
else:
d1, d3 = extractPathParametersFromRegion(
region, [Node.VALUE_LABEL_D_DS1, Node.VALUE_LABEL_D_DS3])
for c in range(len(d1)):
td3 = vector.vectorRejection(d3[c], d1[c])
d3[c] = vector.setMagnitude(td3, vector.magnitude(d3[c]))
setPathParameters(region, [Node.VALUE_LABEL_D_DS3], [d3],
editGroupName)
return False, True # settings not changed, nodes changed
def createMirrorCurve(self):
"""
generate coordinates and derivatives for the mirror curve
:return: Coordinates and derivatives for the mirror curve
"""
btx = self.px
btd1 = self.pd1
btd2 = self.pd2
btd3 = self.pd3
n2a = self.elementsCountAcrossShell
rcx = []
tmdx = btx[n2a][self.elementsCountAcrossMinor // 2]
tmdd3 = btd3[n2a][self.elementsCountAcrossMinor // 2]
tmux = [
0.5 * (btx[self.elementsCountUp][0][c] +
btx[self.elementsCountUp][self.elementsCountAcrossMinor][c])
for c in range(3)
]
rcx.append(tmdx)
rcx.append(tmux)
rcd3 = [vector.setMagnitude(tmdd3, -1), vector.setMagnitude(tmdd3, -1)]
rscx, rscd1 = sampleCubicHermiteCurves(rcx,
rcd3,
self.elementsCountUp - n2a,
arcLengthDerivatives=True)[0:2]
# get d2, d3
rscd2 = []
rscd3 = []
for n in range(len(rscx)):
d3 = vector.normalise([
btx[self.elementsCountUp][self.elementsCountAcrossMinor][c] -
btx[self.elementsCountUp][0][c] for c in range(3)
])
d2 = vector.normalise(vector.crossproduct3(d3, rscd1[n]))
rscd2.append(d2)
rscd3.append(d3)
return rscx, rscd1, rscd2, rscd3
def __init__(self,
elementsCountAcrossMajor,
elementsCountAcrossMinor,
elementsCountAcrossShell=0,
elementsCountAcrossTransition=1,
shellProportion=1.0,
centre=None,
alongAxis=None,
majorAxis=None,
minorRadius=None):
"""
:param elementsCountAcrossMajor: Number of elements across major axis. Must be at least 2 + elementsCountRim for
half and 4 + elementsCountRim for full cylinder.
:param elementsCountAcrossMinor: Number of elements across minor axis.
:param elementsCountAcrossShell: Number of elements across shell.
:param elementsCountAcrossTransition: Number of elements between core boundary and inner square.
:param shellProportion: Ratio of thickness of each layer in shell wrt thickness of each layer in core.
:param centre: Centre of the ellipse.
:param alongAxis: The cylinder axis that the base is extruded along.
:param majorAxis: The major axis of the base. Should be perpendicular to alongAxis
:param minorRadius: The minor radius of the ellipse.
"""
self._centre = centre
self._alongAxis = alongAxis
self._majorAxis = majorAxis
self._minorRadius = minorRadius
if alongAxis:
self._minorAxis = vector.setMagnitude(
vector.crossproduct3(alongAxis, majorAxis), minorRadius)
self._elementsCountAcrossMinor = elementsCountAcrossMinor
self._elementsCountAcrossMajor = elementsCountAcrossMajor
self._elementsCountAcrossShell = elementsCountAcrossShell
self._elementsCountAcrossTransition = elementsCountAcrossTransition
self._shellProportion = shellProportion
self._majorRadius = vector.magnitude(majorAxis)
self.px = None
self.pd1 = None
self.pd2 = None
self.pd3 = None
def generateBase1DMesh(self, rx):
"""
Generate nodes around the perimeter of the ellipse.
"""
btx = self.px
btd1 = self.pd1
btd2 = self.pd2
btd3 = self.pd3
ratio = rx / self.elementsCountAcrossShell if self.elementsCountAcrossShell > 0 else 0
majorAxis = [
d * (1 - ratio * (1 - self.coreMajorRadius / self.majorRadius))
for d in self.majorAxis
]
minorAxis = [
d * (1 - ratio * (1 - self.coreMinorRadius / self.minorRadius))
for d in self.minorAxis
]
majorRadius = vector.magnitude(majorAxis)
nx, nd1 = createEllipsePerimeter(self.centre, majorAxis, minorAxis,
self.elementsCountAround, majorRadius)
nte = normalToEllipse(self.majorAxis, self.minorAxis)
tbx, tbd1, tbd2, tbd3 = [], [], [], []
for n in range(self.elementsCountAround + 1):
tbx.append(nx[n])
tbd1.append(nd1[n])
tbd2.append(nte)
tbd3.append(vector.normalise(vector.crossproduct3(tbd1[n], nte)))
for n in range(self.elementsCountAround + 1):
n1, n2 = self.__shield.convertRimIndex(n, rx)
btx[n2][n1] = tbx[n]
btd1[n2][n1] = tbd1[n]
btd2[n2][n1] = tbd2[n]
btd3[n2][n1] = tbd3[n]
def getTriplePoints(self, n3):
'''
Compute coordinates and derivatives of points where 3 square elements merge.
:param n3: Index of through-wall coordinates to use.
'''
n1a = self.elementsCountRim
n1b = n1a + 1
n1c = n1a + 2
m1a = self.elementsCountAcross - self.elementsCountRim
m1b = m1a - 1
m1c = m1a - 2
n2a = self.elementsCountRim
n2b = n2a + 1
n2c = n2a + 2
# left
ltx = []
if self._type == ShieldRimDerivativeMode.SHIELD_RIM_DERIVATIVE_MODE_AROUND:
tx, td1 = sampleCubicHermiteCurves(
[self.px[n3][n2a][n1c], self.px[n3][n2c][n1b]],
[[(-self.pd1[n3][n2a][n1c][c] - self.pd3[n3][n2a][n1c][c])
for c in range(3)], self.pd1[n3][n2c][n1b]],
2,
arcLengthDerivatives=True)[0:2]
ltx.append(tx[1])
tx, td1 = sampleCubicHermiteCurves(
[self.px[n3][n2a][n1b], self.px[n3][n2c][n1c]],
[[-self.pd3[n3][n2a][n1b][c] for c in range(3)],
[(self.pd1[n3][n2c][n1c][c] + self.pd3[n3][n2c][n1c][c])
for c in range(3)]],
2,
arcLengthDerivatives=True)[0:2]
ltx.append(tx[1])
tx, td1 = sampleCubicHermiteCurves(
[self.px[n3][n2c][n1a], self.px[n3][n2b][n1c]],
[[(self.pd1[n3][n2c][n1a][c] - self.pd3[n3][n2c][n1a][c])
for c in range(3)], self.pd3[n3][n2b][n1c]],
2,
arcLengthDerivatives=True)[0:2]
ltx.append(tx[1])
elif self._type == ShieldRimDerivativeMode.SHIELD_RIM_DERIVATIVE_MODE_REGULAR:
tx, td1 = sampleCubicHermiteCurves(
[self.px[n3][n2a][n1c], self.px[n3][n2c][n1b]],
[[(-self.pd1[n3][n2a][n1c][c] + self.pd2[n3][n2a][n1c][c])
for c in range(3)], self.pd2[n3][n2c][n1b]],
2,
arcLengthDerivatives=True)[0:2]
ltx.append(tx[1])
tx, td1 = sampleCubicHermiteCurves(
[self.px[n3][n2a][n1b], self.px[n3][n2c][n1c]], [
self.pd2[n3][n2a][n1b],
[(self.pd1[n3][n2c][n1c][c] + self.pd2[n3][n2c][n1c][c])
for c in range(3)]
],
2,
arcLengthDerivatives=True)[0:2]
ltx.append(tx[1])
tx, td1 = sampleCubicHermiteCurves(
[self.px[n3][n2c][n1a], self.px[n3][n2b][n1c]],
[[(self.pd1[n3][n2c][n1a][c] - self.pd2[n3][n2c][n1a][c])
for c in range(3)], self.pd1[n3][n2b][n1c]],
2,
arcLengthDerivatives=True)[0:2]
ltx.append(tx[1])
#x = [ (ltx[0][c] + ltx[1][c] + ltx[2][c])/3.0 for c in range(3) ]
x = [(ltx[0][c] + ltx[2][c]) / 2.0 for c in range(3)]
if self.trackSurface:
p = self.trackSurface.findNearestPosition(
x,
startPosition=self.trackSurface.createPositionProportion(
*(self.pProportions[n2b][n1c])))
self.pProportions[n2b][n1b] = self.trackSurface.getProportion(p)
x, sd1, sd2 = self.trackSurface.evaluateCoordinates(
p, derivatives=True)
d1, d2, d3 = calculate_surface_axes(sd1, sd2,
vector.normalise(sd1))
self.pd3[n3][n2b][n1b] = d3
self.px[n3][n2b][n1b] = x
if self._type == ShieldRimDerivativeMode.SHIELD_RIM_DERIVATIVE_MODE_AROUND:
self.pd3[n3][n2b][n1b] = [
(self.px[n3][n2b][n1c][c] - self.px[n3][n2b][n1b][c])
for c in range(3)
]
self.pd1[n3][n2b][n1b] = [
(self.px[n3][n2c][n1b][c] - self.px[n3][n2b][n1b][c])
for c in range(3)
]
elif self._type == ShieldRimDerivativeMode.SHIELD_RIM_DERIVATIVE_MODE_REGULAR:
self.pd1[n3][n2b][n1b] = [
(self.px[n3][n2b][n1c][c] - self.px[n3][n2b][n1b][c])
for c in range(3)
]
self.pd2[n3][n2b][n1b] = [
(self.px[n3][n2c][n1b][c] - self.px[n3][n2b][n1b][c])
for c in range(3)
]
if not self.trackSurface:
if self._type == ShieldRimDerivativeMode.SHIELD_RIM_DERIVATIVE_MODE_AROUND:
self.pd2[n3][n2b][n1b] = vector.normalise(
vector.crossproduct3(self.pd3[n3][n2b][n1b],
self.pd1[n3][n2b][n1b]))
elif self._type == ShieldRimDerivativeMode.SHIELD_RIM_DERIVATIVE_MODE_REGULAR:
self.pd3[n3][n2b][n1b] = vector.normalise(
vector.crossproduct3(self.pd1[n3][n2b][n1b],
self.pd2[n3][n2b][n1b]))
# right
rtx = []
if self._type == ShieldRimDerivativeMode.SHIELD_RIM_DERIVATIVE_MODE_AROUND:
tx, td1 = sampleCubicHermiteCurves(
[self.px[n3][n2a][m1c], self.px[n3][n2c][m1b]],
[[(self.pd1[n3][n2a][m1c][c] - self.pd3[n3][n2a][m1c][c])
for c in range(3)], self.pd1[n3][n2c][m1b]],
2,
arcLengthDerivatives=True)[0:2]
rtx.append(tx[1])
tx, td1 = sampleCubicHermiteCurves(
[self.px[n3][n2a][m1b], self.px[n3][n2c][m1c]],
[[-self.pd3[n3][n2a][m1b][c] for c in range(3)],
[(-self.pd3[n3][n2c][m1c][c] + self.pd1[n3][n2c][m1c][c])
for c in range(3)]],
2,
arcLengthDerivatives=True)[0:2]
rtx.append(tx[1])
tx, td1 = sampleCubicHermiteCurves(
[self.px[n3][n2c][m1a], self.px[n3][n2b][m1c]],
[[(-self.pd1[n3][n2c][m1a][c] - self.pd3[n3][n2c][m1a][c])
for c in range(3)], [-d for d in self.pd3[n3][n2b][m1c]]],
2,
arcLengthDerivatives=True)[0:2]
rtx.append(tx[1])
elif self._type == ShieldRimDerivativeMode.SHIELD_RIM_DERIVATIVE_MODE_REGULAR:
tx, td1 = sampleCubicHermiteCurves(
[self.px[n3][n2a][m1c], self.px[n3][n2c][m1b]],
[[(self.pd1[n3][n2a][m1c][c] + self.pd2[n3][n2a][m1c][c])
for c in range(3)], self.pd2[n3][n2c][m1b]],
2,
arcLengthDerivatives=True)[0:2]
rtx.append(tx[1])
tx, td1 = sampleCubicHermiteCurves(
[self.px[n3][n2a][m1b], self.px[n3][n2c][m1c]], [
self.pd2[n3][n2a][m1b],
[(-self.pd1[n3][n2c][m1c][c] + self.pd2[n3][n2c][m1c][c])
for c in range(3)]
],
2,
arcLengthDerivatives=True)[0:2]
rtx.append(tx[1])
tx, td1 = sampleCubicHermiteCurves(
[self.px[n3][n2c][m1a], self.px[n3][n2b][m1c]],
[[(-self.pd1[n3][n2c][m1a][c] - self.pd2[n3][n2c][m1a][c])
for c in range(3)], [-d for d in self.pd1[n3][n2b][m1c]]],
2,
arcLengthDerivatives=True)[0:2]
rtx.append(tx[1])
#x = [ (rtx[0][c] + rtx[1][c] + rtx[2][c])/3.0 for c in range(3) ]
x = [(rtx[0][c] + rtx[2][c]) / 2.0 for c in range(3)]
if self.trackSurface:
p = self.trackSurface.findNearestPosition(
x,
startPosition=self.trackSurface.createPositionProportion(
*(self.pProportions[n2b][m1c])))
self.pProportions[n2b][m1b] = self.trackSurface.getProportion(p)
x, sd1, sd2 = self.trackSurface.evaluateCoordinates(
p, derivatives=True)
d1, d2, d3 = calculate_surface_axes(sd1, sd2,
vector.normalise(sd1))
self.pd3[n3][n2b][m1b] = d3
self.px[n3][n2b][m1b] = x
if self._type == ShieldRimDerivativeMode.SHIELD_RIM_DERIVATIVE_MODE_AROUND:
self.pd3[n3][n2b][m1b] = [
(self.px[n3][n2b][m1b][c] - self.px[n3][n2b][m1c][c])
for c in range(3)
]
self.pd1[n3][n2b][m1b] = [
(self.px[n3][n2c][m1b][c] - self.px[n3][n2b][m1b][c])
for c in range(3)
]
elif self._type == ShieldRimDerivativeMode.SHIELD_RIM_DERIVATIVE_MODE_REGULAR:
self.pd1[n3][n2b][m1b] = [
(self.px[n3][n2b][m1b][c] - self.px[n3][n2b][m1c][c])
for c in range(3)
]
self.pd2[n3][n2b][m1b] = [
(self.px[n3][n2c][m1b][c] - self.px[n3][n2b][m1b][c])
for c in range(3)
]
if not self.trackSurface:
if self._type == ShieldRimDerivativeMode.SHIELD_RIM_DERIVATIVE_MODE_AROUND:
self.pd2[n3][n2b][m1b] = vector.normalise(
vector.crossproduct3(self.pd3[n3][n2b][m1b],
self.pd1[n3][n2b][m1b]))
elif self._type == ShieldRimDerivativeMode.SHIELD_RIM_DERIVATIVE_MODE_REGULAR:
self.pd3[n3][n2b][m1b] = vector.normalise(
vector.crossproduct3(self.pd1[n3][n2b][m1b],
self.pd2[n3][n2b][m1b]))
def generateBaseMesh(cls,
region,
options,
baseCentre=[0.0, 0.0, 0.0],
axisSide1=[0.0, -1.0, 0.0],
axisUp=[0.0, 0.0, 1.0]):
"""
Generate the base bicubic-linear Hermite mesh. See also generateMesh().
Optional extra parameters allow centre and axes to be set.
:param region: Zinc region to define model in. Must be empty.
:param options: Dict containing options. See getDefaultOptions().
:param baseCentre: Centre of valve on ventriculo-arterial junction.
:param axisSide: Unit vector in first side direction where angle around starts.
:param axisUp: Unit vector in outflow direction of valve.
:return: list of AnnotationGroup
"""
unitScale = options['Unit scale']
outerHeight = unitScale * options['Outer height']
innerDepth = unitScale * options['Inner depth']
cuspHeight = unitScale * options['Cusp height']
innerRadius = unitScale * 0.5 * options['Inner diameter']
sinusRadialDisplacement = unitScale * options[
'Sinus radial displacement']
wallThickness = unitScale * options['Wall thickness']
cuspThickness = unitScale * options['Cusp thickness']
aorticNotPulmonary = options['Aortic not pulmonary']
useCrossDerivatives = False
fm = region.getFieldmodule()
fm.beginChange()
coordinates = zinc_utils.getOrCreateCoordinateField(fm)
cache = fm.createFieldcache()
if aorticNotPulmonary:
arterialRootGroup = AnnotationGroup(region,
'root of aorta',
FMANumber=3740,
lyphID='Lyph ID unknown')
cuspGroups = [
AnnotationGroup(region,
'posterior cusp of aortic valve',
FMANumber=7253,
lyphID='Lyph ID unknown'),
AnnotationGroup(region,
'right cusp of aortic valve',
FMANumber=7252,
lyphID='Lyph ID unknown'),
AnnotationGroup(region,
'left cusp of aortic valve',
FMANumber=7251,
lyphID='Lyph ID unknown')
]
else:
arterialRootGroup = AnnotationGroup(region,
'root of pulmonary trunk',
FMANumber=8612,
lyphID='Lyph ID unknown')
cuspGroups = [
AnnotationGroup(region,
'right cusp of pulmonary valve',
FMANumber=7250,
lyphID='Lyph ID unknown'),
AnnotationGroup(region,
'anterior cusp of pulmonary valve',
FMANumber=7249,
lyphID='Lyph ID unknown'),
AnnotationGroup(region,
'left cusp of pulmonary valve',
FMANumber=7247,
lyphID='Lyph ID unknown')
]
allGroups = [arterialRootGroup
] # groups that all elements in scaffold will go in
annotationGroups = allGroups + cuspGroups
# annotation fiducial points
fiducialGroup = zinc_utils.getOrCreateGroupField(fm, 'fiducial')
fiducialCoordinates = zinc_utils.getOrCreateCoordinateField(
fm, 'fiducial_coordinates')
fiducialLabel = zinc_utils.getOrCreateLabelField(fm, 'fiducial_label')
#fiducialElementXi = zinc_utils.getOrCreateElementXiField(fm, 'fiducial_element_xi')
datapoints = fm.findNodesetByFieldDomainType(
Field.DOMAIN_TYPE_DATAPOINTS)
fiducialPoints = zinc_utils.getOrCreateNodesetGroup(
fiducialGroup, datapoints)
datapointTemplateExternal = datapoints.createNodetemplate()
datapointTemplateExternal.defineField(fiducialCoordinates)
datapointTemplateExternal.defineField(fiducialLabel)
#################
# Create nodes
#################
nodes = fm.findNodesetByFieldDomainType(Field.DOMAIN_TYPE_NODES)
nodetemplate = nodes.createNodetemplate()
nodetemplate.defineField(coordinates)
nodetemplate.setValueNumberOfVersions(coordinates, -1,
Node.VALUE_LABEL_VALUE, 1)
nodetemplate.setValueNumberOfVersions(coordinates, -1,
Node.VALUE_LABEL_D_DS1, 1)
nodetemplate.setValueNumberOfVersions(coordinates, -1,
Node.VALUE_LABEL_D_DS2, 1)
nodetemplate.setValueNumberOfVersions(coordinates, -1,
Node.VALUE_LABEL_D_DS3, 1)
# most nodes in this scaffold do not have a DS3 derivative
nodetemplateLinearS3 = nodes.createNodetemplate()
nodetemplateLinearS3.defineField(coordinates)
nodetemplateLinearS3.setValueNumberOfVersions(coordinates, -1,
Node.VALUE_LABEL_VALUE,
1)
nodetemplateLinearS3.setValueNumberOfVersions(coordinates, -1,
Node.VALUE_LABEL_D_DS1,
1)
nodetemplateLinearS3.setValueNumberOfVersions(coordinates, -1,
Node.VALUE_LABEL_D_DS2,
1)
# several only have a DS1 derivative
nodetemplateLinearS2S3 = nodes.createNodetemplate()
nodetemplateLinearS2S3.defineField(coordinates)
nodetemplateLinearS2S3.setValueNumberOfVersions(
coordinates, -1, Node.VALUE_LABEL_VALUE, 1)
nodetemplateLinearS2S3.setValueNumberOfVersions(
coordinates, -1, Node.VALUE_LABEL_D_DS1, 1)
nodeIdentifier = max(1, zinc_utils.getMaximumNodeIdentifier(nodes) + 1)
elementsCountAround = 6
radiansPerElementAround = 2.0 * math.pi / elementsCountAround
axisSide2 = vector.crossproduct3(axisUp, axisSide1)
outerRadius = innerRadius + wallThickness
cuspOuterLength2 = 0.5 * getApproximateEllipsePerimeter(
innerRadius, cuspHeight)
cuspOuterWallArcLength = cuspOuterLength2 * innerRadius / (
innerRadius + cuspHeight)
noduleOuterAxialArcLength = cuspOuterLength2 - cuspOuterWallArcLength
noduleOuterRadialArcLength = innerRadius
cuspOuterWalld1 = interp.interpolateLagrangeHermiteDerivative(
[innerRadius, outerHeight + innerDepth - cuspHeight], [0.0, 0.0],
[-innerRadius, 0.0], 0.0)
sin60 = math.sin(math.pi / 3.0)
cuspThicknessLowerFactor = 4.5 # GRC fudge factor
cuspInnerLength2 = 0.5 * getApproximateEllipsePerimeter(
innerRadius - cuspThickness / sin60,
cuspHeight - cuspThicknessLowerFactor * cuspThickness)
noduleInnerAxialArcLength = cuspInnerLength2 * (
cuspHeight - cuspThicknessLowerFactor * cuspThickness) / (
innerRadius - cuspThickness / sin60 + cuspHeight -
cuspThicknessLowerFactor * cuspThickness)
noduleInnerRadialArcLength = innerRadius - cuspThickness / math.tan(
math.pi / 3.0)
nMidCusp = 0 if aorticNotPulmonary else 1
# lower points
ix, id1 = createCirclePoints(
[(baseCentre[c] - axisUp[c] * innerDepth) for c in range(3)],
[axisSide1[c] * innerRadius for c in range(3)],
[axisSide2[c] * innerRadius
for c in range(3)], elementsCountAround)
ox, od1 = getSemilunarValveSinusPoints(baseCentre,
axisSide1,
axisSide2,
outerRadius,
sinusRadialDisplacement,
startMidCusp=aorticNotPulmonary)
lowerx, lowerd1 = [ix, ox], [id1, od1]
# upper points
topCentre = [(baseCentre[c] + axisUp[c] * outerHeight)
for c in range(3)]
# twice as many on inner:
ix, id1 = createCirclePoints(
topCentre, [axisSide1[c] * innerRadius for c in range(3)],
[axisSide2[c] * innerRadius
for c in range(3)], elementsCountAround * 2)
# tweak inner points so elements attached to cusps are narrower
cuspRadiansFactor = 0.25 # GRC fudge factor
midDerivativeFactor = 1.0 + 0.5 * (1.0 - cuspRadiansFactor
) # GRC test compromise
cuspAttachmentRadians = cuspRadiansFactor * radiansPerElementAround
cuspAttachmentRadialDisplacement = wallThickness * 0.333 # GRC fudge factor
cuspAttachmentRadius = innerRadius - cuspAttachmentRadialDisplacement
for cusp in range(3):
n1 = cusp * 2 - 1 + nMidCusp
n2 = n1 * 2
id1[n2 + 2] = [2.0 * d for d in id1[n2 + 2]]
# side 1
radiansAround = n1 * radiansPerElementAround + cuspAttachmentRadians
rcosRadiansAround = cuspAttachmentRadius * math.cos(radiansAround)
rsinRadiansAround = cuspAttachmentRadius * math.sin(radiansAround)
ix[n2 + 1] = [(topCentre[c] + rcosRadiansAround * axisSide1[c] +
rsinRadiansAround * axisSide2[c]) for c in range(3)]
id1[n2 + 1] = interp.interpolateLagrangeHermiteDerivative(
ix[n2 + 1], ix[n2 + 2], id1[n2 + 2], 0.0)
# side 2
n1 = ((cusp + 1) * 2 - 1 + nMidCusp) % elementsCountAround
n2 = n1 * 2
radiansAround = n1 * radiansPerElementAround - cuspAttachmentRadians
rcosRadiansAround = cuspAttachmentRadius * math.cos(radiansAround)
rsinRadiansAround = cuspAttachmentRadius * math.sin(radiansAround)
ix[n2 - 1] = [(topCentre[c] + rcosRadiansAround * axisSide1[c] +
rsinRadiansAround * axisSide2[c]) for c in range(3)]
id1[n2 - 1] = interp.interpolateHermiteLagrangeDerivative(
ix[n2 - 2], id1[n2 - 2], ix[n2 - 1], 1.0)
ox, od1 = createCirclePoints(
topCentre, [axisSide1[c] * outerRadius for c in range(3)],
[axisSide2[c] * outerRadius
for c in range(3)], elementsCountAround)
upperx, upperd1 = [ix, ox], [id1, od1]
# get lower and upper derivative 2
zero = [0.0, 0.0, 0.0]
upperd2factor = outerHeight
upd2 = [d * upperd2factor for d in axisUp]
lowerOuterd2 = interp.smoothCubicHermiteDerivativesLine(
[lowerx[1][nMidCusp], upperx[1][nMidCusp]], [upd2, upd2],
fixStartDirection=True,
fixEndDerivative=True)[0]
lowerd2factor = 2.0 * (outerHeight + innerDepth) - upperd2factor
lowerInnerd2 = [d * lowerd2factor for d in axisUp]
lowerd2 = [[lowerInnerd2] * elementsCountAround,
[lowerOuterd2] * elementsCountAround
] # some lowerd2[0] to be fitted below
upperd2 = [[upd2] * (elementsCountAround * 2),
[upd2] * elementsCountAround]
# get lower and upper derivative 1 or 2 pointing to/from cusps
for n1 in range(elementsCountAround):
radiansAround = n1 * radiansPerElementAround
cosRadiansAround = math.cos(radiansAround)
sinRadiansAround = math.sin(radiansAround)
if (n1 % 2) == nMidCusp:
lowerd2[0][n1] = [
-cuspOuterWallArcLength *
(cosRadiansAround * axisSide1[c] +
sinRadiansAround * axisSide2[c]) for c in range(3)
]
else:
upperd1[0][n1 * 2] = [
(cuspOuterWalld1[0] * (cosRadiansAround * axisSide1[c] +
sinRadiansAround * axisSide2[c]) +
cuspOuterWalld1[1] * axisUp[c]) for c in range(3)
]
# inner wall and mid sinus points; only every second one is used
sinusDepth = innerDepth - cuspThicknessLowerFactor * cuspThickness # GRC test
sinusCentre = [(baseCentre[c] - sinusDepth * axisUp[c])
for c in range(3)]
sinusx, sinusd1 = createCirclePoints(
sinusCentre, [axisSide1[c] * innerRadius for c in range(3)],
[axisSide2[c] * innerRadius
for c in range(3)], elementsCountAround)
# get sinusd2, parallel to lower inclined lines
sd2 = interp.smoothCubicHermiteDerivativesLine(
[[innerRadius, -sinusDepth], [innerRadius, outerHeight]],
[[wallThickness + sinusRadialDisplacement, innerDepth],
[0.0, upperd2factor]],
fixStartDirection=True,
fixEndDerivative=True)[0]
sinusd2 = [None] * elementsCountAround
for cusp in range(3):
n1 = cusp * 2 + nMidCusp
radiansAround = n1 * radiansPerElementAround
cosRadiansAround = math.cos(radiansAround)
sinRadiansAround = math.sin(radiansAround)
sinusd2[n1] = [(sd2[0] * (cosRadiansAround * axisSide1[c] +
sinRadiansAround * axisSide2[c]) +
sd2[1] * axisUp[c]) for c in range(3)]
# get points on arc between mid sinus and upper cusp points
arcx = []
arcd1 = []
scaled1 = 2.5 # GRC fudge factor
for cusp in range(3):
n1 = cusp * 2 + nMidCusp
n1m = n1 - 1
n1p = (n1 + 1) % elementsCountAround
n2m = n1m * 2 + 1
n2p = n1p * 2 - 1
ax, ad1 = interp.sampleCubicHermiteCurves(
[upperx[0][n2m], sinusx[n1]],
[[-scaled1 * d for d in upperd2[0][n2m]],
[scaled1 * d for d in sinusd1[n1]]],
elementsCountOut=2,
addLengthStart=0.5 * vector.magnitude(upperd2[0][n2m]),
lengthFractionStart=0.5,
addLengthEnd=0.5 * vector.magnitude(sinusd1[n1]),
lengthFractionEnd=0.5,
arcLengthDerivatives=False)[0:2]
arcx.append(ax[1])
arcd1.append(ad1[1])
ax, ad1 = interp.sampleCubicHermiteCurves(
[
sinusx[n1],
upperx[0][n2p],
], [[scaled1 * d for d in sinusd1[n1]],
[scaled1 * d for d in upperd2[0][n2p]]],
elementsCountOut=2,
addLengthStart=0.5 * vector.magnitude(sinusd1[n1]),
lengthFractionStart=0.5,
addLengthEnd=0.5 * vector.magnitude(upperd2[0][n2p]),
lengthFractionEnd=0.5,
arcLengthDerivatives=False)[0:2]
arcx.append(ax[1])
arcd1.append(ad1[1])
if nMidCusp == 0:
arcx.append(arcx.pop(0))
arcd1.append(arcd1.pop(0))
# cusp nodule points
noduleCentre = [(baseCentre[c] + axisUp[c] * (cuspHeight - innerDepth))
for c in range(3)]
nodulex = [[], []]
noduled1 = [[], []]
noduled2 = [[], []]
noduled3 = [[], []]
cuspRadialThickness = cuspThickness / sin60
for i in range(3):
nodulex[0].append(noduleCentre)
n1 = i * 2 + nMidCusp
radiansAround = n1 * radiansPerElementAround
cosRadiansAround = math.cos(radiansAround)
sinRadiansAround = math.sin(radiansAround)
nodulex[1].append([(noduleCentre[c] + cuspRadialThickness *
(cosRadiansAround * axisSide1[c] +
sinRadiansAround * axisSide2[c]))
for c in range(3)])
n1 = i * 2 - 1 + nMidCusp
radiansAround = n1 * radiansPerElementAround
cosRadiansAround = math.cos(radiansAround)
sinRadiansAround = math.sin(radiansAround)
noduled1[0].append([
noduleOuterRadialArcLength * (cosRadiansAround * axisSide1[c] +
sinRadiansAround * axisSide2[c])
for c in range(3)
])
noduled1[1].append(
vector.setMagnitude(noduled1[0][i],
noduleInnerRadialArcLength))
n1 = i * 2 + 1 + nMidCusp
radiansAround = n1 * radiansPerElementAround
cosRadiansAround = math.cos(radiansAround)
sinRadiansAround = math.sin(radiansAround)
noduled2[0].append([
noduleOuterRadialArcLength * (cosRadiansAround * axisSide1[c] +
sinRadiansAround * axisSide2[c])
for c in range(3)
])
noduled2[1].append(
vector.setMagnitude(noduled2[0][i],
noduleInnerRadialArcLength))
noduled3[0].append(
[noduleOuterAxialArcLength * axisUp[c] for c in range(3)])
noduled3[1].append(
[noduleInnerAxialArcLength * axisUp[c] for c in range(3)])
# Create nodes
lowerNodeId = [[], []]
for n3 in range(2):
for n1 in range(elementsCountAround):
node = nodes.createNode(nodeIdentifier, nodetemplateLinearS3)
cache.setNode(node)
coordinates.setNodeParameters(cache, -1,
Node.VALUE_LABEL_VALUE, 1,
lowerx[n3][n1])
coordinates.setNodeParameters(cache, -1,
Node.VALUE_LABEL_D_DS1, 1,
lowerd1[n3][n1])
coordinates.setNodeParameters(cache, -1,
Node.VALUE_LABEL_D_DS2, 1,
lowerd2[n3][n1])
lowerNodeId[n3].append(nodeIdentifier)
nodeIdentifier += 1
sinusNodeId = []
for n1 in range(elementsCountAround):
if (n1 % 2) != nMidCusp:
sinusNodeId.append(None)
continue
node = nodes.createNode(nodeIdentifier, nodetemplateLinearS3)
cache.setNode(node)
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_VALUE, 1,
sinusx[n1])
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS1, 1,
sinusd1[n1])
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS2, 1,
sinusd2[n1])
sinusNodeId.append(nodeIdentifier)
nodeIdentifier += 1
arcNodeId = []
for n1 in range(elementsCountAround):
node = nodes.createNode(nodeIdentifier, nodetemplateLinearS2S3)
cache.setNode(node)
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_VALUE, 1,
arcx[n1])
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS1, 1,
arcd1[n1])
arcNodeId.append(nodeIdentifier)
nodeIdentifier += 1
noduleNodeId = [[], []]
for n3 in range(2):
for n1 in range(3):
node = nodes.createNode(nodeIdentifier, nodetemplate)
cache.setNode(node)
coordinates.setNodeParameters(cache, -1,
Node.VALUE_LABEL_VALUE, 1,
nodulex[n3][n1])
coordinates.setNodeParameters(cache, -1,
Node.VALUE_LABEL_D_DS1, 1,
noduled1[n3][n1])
coordinates.setNodeParameters(cache, -1,
Node.VALUE_LABEL_D_DS2, 1,
noduled2[n3][n1])
coordinates.setNodeParameters(cache, -1,
Node.VALUE_LABEL_D_DS3, 1,
noduled3[n3][n1])
noduleNodeId[n3].append(nodeIdentifier)
nodeIdentifier += 1
upperNodeId = [[], []]
for n3 in range(2):
for n1 in range(len(upperx[n3])):
node = nodes.createNode(nodeIdentifier, nodetemplateLinearS3)
cache.setNode(node)
coordinates.setNodeParameters(cache, -1,
Node.VALUE_LABEL_VALUE, 1,
upperx[n3][n1])
coordinates.setNodeParameters(cache, -1,
Node.VALUE_LABEL_D_DS1, 1,
upperd1[n3][n1])
coordinates.setNodeParameters(cache, -1,
Node.VALUE_LABEL_D_DS2, 1,
upperd2[n3][n1])
upperNodeId[n3].append(nodeIdentifier)
nodeIdentifier += 1
#################
# Create elements
#################
mesh = fm.findMeshByDimension(3)
allMeshGroups = [allGroup.getMeshGroup(mesh) for allGroup in allGroups]
cuspMeshGroups = [
cuspGroup.getMeshGroup(mesh) for cuspGroup in cuspGroups
]
linearHermiteLinearBasis = fm.createElementbasis(
3, Elementbasis.FUNCTION_TYPE_LINEAR_LAGRANGE)
linearHermiteLinearBasis.setFunctionType(
2, Elementbasis.FUNCTION_TYPE_CUBIC_HERMITE)
hermiteLinearLinearBasis = fm.createElementbasis(
3, Elementbasis.FUNCTION_TYPE_LINEAR_LAGRANGE)
hermiteLinearLinearBasis.setFunctionType(
1, Elementbasis.FUNCTION_TYPE_CUBIC_HERMITE)
bicubichermitelinear = eftfactory_bicubichermitelinear(
mesh, useCrossDerivatives)
eftDefault = bicubichermitelinear.createEftNoCrossDerivatives()
elementIdentifier = max(
1,
zinc_utils.getMaximumElementIdentifier(mesh) + 1)
elementtemplate1 = mesh.createElementtemplate()
elementtemplate1.setElementShapeType(Element.SHAPE_TYPE_CUBE)
# wall elements
for cusp in range(3):
n1 = cusp * 2 - 1 + nMidCusp
n2 = n1 * 2
for e in range(6):
eft1 = None
scalefactors = None
if (e == 0) or (e == 5):
# 6 node linear-hermite-linear collapsed wedge element expanding from zero width on outer wall of root, attaching to vertical part of cusp
eft1 = mesh.createElementfieldtemplate(
linearHermiteLinearBasis)
# switch mappings to use DS2 instead of default DS1
remapEftNodeValueLabel(eft1, [1, 2, 3, 4, 5, 6, 7, 8],
Node.VALUE_LABEL_D_DS1,
[(Node.VALUE_LABEL_D_DS2, [])])
if e == 0:
nids = [
lowerNodeId[0][n1], arcNodeId[n1],
upperNodeId[0][n2], upperNodeId[0][n2 + 1],
lowerNodeId[1][n1], upperNodeId[1][n1]
]
setEftScaleFactorIds(eft1, [1], [])
scalefactors = [-1.0]
remapEftNodeValueLabel(eft1, [2],
Node.VALUE_LABEL_D_DS2,
[(Node.VALUE_LABEL_D_DS1, [1])])
else:
nids = [
arcNodeId[n1 + 1], lowerNodeId[0][n1 - 4],
upperNodeId[0][n2 + 3], upperNodeId[0][n2 - 8],
lowerNodeId[1][n1 - 4], upperNodeId[1][n1 - 4]
]
remapEftNodeValueLabel(eft1, [1],
Node.VALUE_LABEL_D_DS2,
[(Node.VALUE_LABEL_D_DS1, [])])
ln_map = [1, 2, 3, 4, 5, 5, 6, 6]
remapEftLocalNodes(eft1, 6, ln_map)
elif (e == 1) or (e == 4):
# 6 node hermite-linear-linear collapsed wedge element on lower wall
eft1 = mesh.createElementfieldtemplate(
hermiteLinearLinearBasis)
if e == 1:
nids = [
lowerNodeId[0][n1], lowerNodeId[0][n1 + 1],
arcNodeId[n1], sinusNodeId[n1 + 1],
lowerNodeId[1][n1], lowerNodeId[1][n1 + 1]
]
else:
nids = [
lowerNodeId[0][n1 + 1], lowerNodeId[0][n1 - 4],
sinusNodeId[n1 + 1], arcNodeId[n1 + 1],
lowerNodeId[1][n1 + 1], lowerNodeId[1][n1 - 4]
]
ln_map = [1, 2, 3, 4, 5, 6, 5, 6]
remapEftLocalNodes(eft1, 6, ln_map)
else:
# 8 node elements with wedges on two sides
if e == 2:
eft1 = bicubichermitelinear.createEftNoCrossDerivatives(
)
setEftScaleFactorIds(eft1, [1], [])
scalefactors = [-1.0]
nids = [
arcNodeId[n1], sinusNodeId[n1 + 1],
upperNodeId[0][n2 + 1], upperNodeId[0][n2 + 2],
lowerNodeId[1][n1], lowerNodeId[1][n1 + 1],
upperNodeId[1][n1], upperNodeId[1][n1 + 1]
]
remapEftNodeValueLabel(eft1, [1],
Node.VALUE_LABEL_D_DS2,
[(Node.VALUE_LABEL_D_DS1, [1])])
else:
eft1 = eftDefault
nids = [
sinusNodeId[n1 + 1], arcNodeId[n1 + 1],
upperNodeId[0][n2 + 2], upperNodeId[0][n2 + 3],
lowerNodeId[1][n1 + 1], lowerNodeId[1][n1 - 4],
upperNodeId[1][n1 + 1], upperNodeId[1][n1 - 4]
]
remapEftNodeValueLabel(eft1, [2],
Node.VALUE_LABEL_D_DS2,
[(Node.VALUE_LABEL_D_DS1, [])])
result = elementtemplate1.defineField(coordinates, -1, eft1)
element = mesh.createElement(elementIdentifier,
elementtemplate1)
result2 = element.setNodesByIdentifier(eft1, nids)
if scalefactors:
result3 = element.setScaleFactors(eft1, scalefactors)
else:
result3 = 7
#print('create arterial root wall', cusp, e, 'element',elementIdentifier, result, result2, result3, nids)
elementIdentifier += 1
for meshGroup in allMeshGroups:
meshGroup.addElement(element)
# cusps (leaflets)
for cusp in range(3):
n1 = cusp * 2 - 1 + nMidCusp
n2 = n1 * 2
meshGroups = allMeshGroups + [cuspMeshGroups[cusp]]
for e in range(2):
eft1 = bicubichermitelinear.createEftNoCrossDerivatives()
setEftScaleFactorIds(eft1, [1], [])
scalefactors = [-1.0]
if e == 0:
nids = [
lowerNodeId[0][n1], lowerNodeId[0][n1 + 1],
upperNodeId[0][n2], noduleNodeId[0][cusp],
arcNodeId[n1], sinusNodeId[n1 + 1],
upperNodeId[0][n2 + 1], noduleNodeId[1][cusp]
]
remapEftNodeValueLabel(eft1, [4, 8],
Node.VALUE_LABEL_D_DS1,
[(Node.VALUE_LABEL_D_DS1, [1])])
remapEftNodeValueLabel(eft1, [4, 8],
Node.VALUE_LABEL_D_DS2,
[(Node.VALUE_LABEL_D_DS3, [])])
remapEftNodeValueLabel(eft1, [5], Node.VALUE_LABEL_D_DS2,
[(Node.VALUE_LABEL_D_DS1, [1])])
remapEftNodeValueLabel(eft1, [6], Node.VALUE_LABEL_D_DS2,
[(Node.VALUE_LABEL_D_DS2, [1])])
remapEftNodeValueLabel(eft1, [7], Node.VALUE_LABEL_D_DS1,
[(Node.VALUE_LABEL_D_DS1, [1])])
else:
nids = [
lowerNodeId[0][n1 + 1], lowerNodeId[0][n1 - 4],
noduleNodeId[0][cusp], upperNodeId[0][n2 - 8],
sinusNodeId[n1 + 1], arcNodeId[n1 + 1],
noduleNodeId[1][cusp], upperNodeId[0][n2 + 3]
]
remapEftNodeValueLabel(eft1, [3, 7],
Node.VALUE_LABEL_D_DS2,
[(Node.VALUE_LABEL_D_DS3, [])])
remapEftNodeValueLabel(eft1, [3, 7],
Node.VALUE_LABEL_D_DS1,
[(Node.VALUE_LABEL_D_DS2, [])])
remapEftNodeValueLabel(eft1, [4, 8],
Node.VALUE_LABEL_D_DS1,
[(Node.VALUE_LABEL_D_DS1, [1])])
remapEftNodeValueLabel(eft1, [5], Node.VALUE_LABEL_D_DS2,
[(Node.VALUE_LABEL_D_DS2, [1])])
remapEftNodeValueLabel(eft1, [6], Node.VALUE_LABEL_D_DS2,
[(Node.VALUE_LABEL_D_DS1, [])])
result = elementtemplate1.defineField(coordinates, -1, eft1)
element = mesh.createElement(elementIdentifier,
elementtemplate1)
result2 = element.setNodesByIdentifier(eft1, nids)
if scalefactors:
result3 = element.setScaleFactors(eft1, scalefactors)
else:
result3 = 7
#print('create semilunar cusp', cusp, e, 'element',elementIdentifier, result, result2, result3, nids)
elementIdentifier += 1
for meshGroup in meshGroups:
meshGroup.addElement(element)
# create annotation points
datapoint = fiducialPoints.createNode(-1, datapointTemplateExternal)
cache.setNode(datapoint)
fiducialCoordinates.setNodeParameters(cache, -1,
Node.VALUE_LABEL_VALUE, 1,
noduleCentre)
fiducialLabel.assignString(
cache, 'aortic valve ctr'
if aorticNotPulmonary else 'pulmonary valve ctr')
fm.endChange()
return annotationGroups
def warpSegmentPoints(xList, d1List, d2List, segmentAxis, sx, sd1, sd2,
elementsCountAround, elementsCountAlongSegment,
refPointZ, innerRadiusAlong, closedProximalEnd):
"""
Warps points in segment to account for bending and twisting
along central path defined by nodes sx and derivatives sd1 and sd2.
:param xList: coordinates of segment points.
:param d1List: derivatives around axis of segment.
:param d2List: derivatives along axis of segment.
:param segmentAxis: axis perpendicular to segment plane.
:param sx: coordinates of points on central path.
:param sd1: derivatives of points along central path.
:param sd2: derivatives representing cross axes.
:param elementsCountAround: Number of elements around segment.
:param elementsCountAlongSegment: Number of elements along segment.
:param refPointZ: z-coordinate of reference point for each element
groups along the segment to be used for transformation.
:param innerRadiusAlong: radius of segment along length.
:param closedProximalEnd: True if proximal end of segment is a closed end.
:return coordinates and derivatives of warped points.
"""
xWarpedList = []
d1WarpedList = []
d2WarpedList = []
d2WarpedListFinal = []
d3WarpedUnitList = []
for nAlongSegment in range(elementsCountAlongSegment + 1):
xElementAlongSegment = xList[elementsCountAround *
nAlongSegment:elementsCountAround *
(nAlongSegment + 1)]
d1ElementAlongSegment = d1List[elementsCountAround *
nAlongSegment:elementsCountAround *
(nAlongSegment + 1)]
d2ElementAlongSegment = d2List[elementsCountAround *
nAlongSegment:elementsCountAround *
(nAlongSegment + 1)]
centroid = [0.0, 0.0, refPointZ[nAlongSegment]]
# Rotate to align segment axis with tangent of central line
unitTangent = vector.normalise(sd1[nAlongSegment])
cp = vector.crossproduct3(segmentAxis, unitTangent)
dp = vector.dotproduct(segmentAxis, unitTangent)
if vector.magnitude(
cp) > 0.0: # path tangent not parallel to segment axis
axisRot = vector.normalise(cp)
thetaRot = math.acos(vector.dotproduct(segmentAxis, unitTangent))
rotFrame = matrix.getRotationMatrixFromAxisAngle(axisRot, thetaRot)
centroidRot = [
rotFrame[j][0] * centroid[0] + rotFrame[j][1] * centroid[1] +
rotFrame[j][2] * centroid[2] for j in range(3)
]
else: # path tangent parallel to segment axis (z-axis)
if dp == -1.0: # path tangent opposite direction to segment axis
thetaRot = math.pi
axisRot = [1.0, 0, 0]
rotFrame = matrix.getRotationMatrixFromAxisAngle(
axisRot, thetaRot)
centroidRot = [
rotFrame[j][0] * centroid[0] +
rotFrame[j][1] * centroid[1] + rotFrame[j][2] * centroid[2]
for j in range(3)
]
else: # segment axis in same direction as unit tangent
rotFrame = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
centroidRot = centroid
translateMatrix = [
sx[nAlongSegment][j] - centroidRot[j] for j in range(3)
]
for n1 in range(elementsCountAround):
x = xElementAlongSegment[n1]
d1 = d1ElementAlongSegment[n1]
d2 = d2ElementAlongSegment[n1]
if vector.magnitude(
cp) > 0.0: # path tangent not parallel to segment axis
xRot1 = [
rotFrame[j][0] * x[0] + rotFrame[j][1] * x[1] +
rotFrame[j][2] * x[2] for j in range(3)
]
d1Rot1 = [
rotFrame[j][0] * d1[0] + rotFrame[j][1] * d1[1] +
rotFrame[j][2] * d1[2] for j in range(3)
]
d2Rot1 = [
rotFrame[j][0] * d2[0] + rotFrame[j][1] * d2[1] +
rotFrame[j][2] * d2[2] for j in range(3)
]
# xTranslate = [xRot1[j] + translateMatrix[j] for j in range(3)]
else: # path tangent parallel to segment axis
xRot1 = [
rotFrame[j][0] * x[0] + rotFrame[j][1] * x[1] +
rotFrame[j][2] * x[2] for j in range(3)
] if dp == -1.0 else x
d1Rot1 = [
rotFrame[j][0] * d1[0] + rotFrame[j][1] * d1[1] +
rotFrame[j][2] * d1[2] for j in range(3)
] if dp == -1.0 else d1
d2Rot1 = [
rotFrame[j][0] * d2[0] + rotFrame[j][1] * d2[1] +
rotFrame[j][2] * d2[2] for j in range(3)
] if dp == -1.0 else d2
# xTranslate = [xRot1[j] + translateMatrix[j] for j in range(3)]
if n1 == 0: # Find angle between xCentroidRot and first node in the face
vectorToFirstNode = [
xRot1[c] - centroidRot[c] for c in range(3)
]
if vector.magnitude(vectorToFirstNode) > 0.0:
cp = vector.crossproduct3(
vector.normalise(vectorToFirstNode),
vector.normalise(sd2[nAlongSegment]))
if vector.magnitude(cp) > 1e-7:
cp = vector.normalise(cp)
signThetaRot2 = vector.dotproduct(unitTangent, cp)
thetaRot2 = math.acos(
vector.dotproduct(
vector.normalise(vectorToFirstNode),
sd2[nAlongSegment]))
axisRot2 = unitTangent
rotFrame2 = matrix.getRotationMatrixFromAxisAngle(
axisRot2, signThetaRot2 * thetaRot2)
else:
rotFrame2 = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
else:
rotFrame2 = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
xRot2 = [
rotFrame2[j][0] * xRot1[0] + rotFrame2[j][1] * xRot1[1] +
rotFrame2[j][2] * xRot1[2] for j in range(3)
]
d1Rot2 = [
rotFrame2[j][0] * d1Rot1[0] + rotFrame2[j][1] * d1Rot1[1] +
rotFrame2[j][2] * d1Rot1[2] for j in range(3)
]
d2Rot2 = [
rotFrame2[j][0] * d2Rot1[0] + rotFrame2[j][1] * d2Rot1[1] +
rotFrame2[j][2] * d2Rot1[2] for j in range(3)
]
xTranslate = [xRot2[j] + translateMatrix[j] for j in range(3)]
xWarpedList.append(xTranslate)
d1WarpedList.append(d1Rot2)
d2WarpedList.append(d2Rot2)
# Scale d2 with curvature of central path
d2WarpedListScaled = []
vProjectedList = []
for nAlongSegment in range(elementsCountAlongSegment + 1):
for n1 in range(elementsCountAround):
n = nAlongSegment * elementsCountAround + n1
# Calculate norm
sd1Normalised = vector.normalise(sd1[nAlongSegment])
v = [xWarpedList[n][c] - sx[nAlongSegment][c] for c in range(3)]
dp = vector.dotproduct(v, sd1Normalised)
dpScaled = [dp * c for c in sd1Normalised]
vProjected = [v[c] - dpScaled[c] for c in range(3)]
vProjectedList.append(vProjected)
if vector.magnitude(vProjected) > 0.0:
vProjectedNormlised = vector.normalise(vProjected)
else:
vProjectedNormlised = [0.0, 0.0, 0.0]
# Calculate curvature along at each node
if nAlongSegment == 0:
curvature = interp.getCubicHermiteCurvature(
sx[0], sd1[0], sx[1], sd1[1], vProjectedNormlised, 0.0)
elif nAlongSegment == elementsCountAlongSegment:
curvature = interp.getCubicHermiteCurvature(
sx[-2], sd1[-2], sx[-1], sd1[-1], vProjectedNormlised, 1.0)
else:
curvature = 0.5 * (interp.getCubicHermiteCurvature(
sx[nAlongSegment - 1], sd1[nAlongSegment - 1],
sx[nAlongSegment], sd1[nAlongSegment], vProjectedNormlised,
1.0) + interp.getCubicHermiteCurvature(
sx[nAlongSegment], sd1[nAlongSegment],
sx[nAlongSegment + 1], sd1[nAlongSegment + 1],
vProjectedNormlised, 0.0))
# Scale
factor = 1.0 - curvature * innerRadiusAlong[nAlongSegment]
d2 = [factor * c for c in d2WarpedList[n]]
d2WarpedListScaled.append(d2)
# Smooth d2 for segment
smoothd2Raw = []
for n1 in range(elementsCountAround):
nx = []
nd2 = []
for n2 in range(elementsCountAlongSegment + 1):
n = n2 * elementsCountAround + n1
nx.append(xWarpedList[n])
nd2.append(d2WarpedListScaled[n])
smoothd2 = interp.smoothCubicHermiteDerivativesLine(
nx, nd2, fixStartDerivative=True, fixEndDerivative=True)
smoothd2Raw.append(smoothd2)
# Re-arrange smoothd2
for n2 in range(elementsCountAlongSegment + 1):
for n1 in range(elementsCountAround):
d2WarpedListFinal.append(smoothd2Raw[n1][n2])
# Calculate unit d3
for n in range(len(xWarpedList)):
d3Unit = vector.normalise(
vector.crossproduct3(vector.normalise(d1WarpedList[n]),
vector.normalise(d2WarpedListFinal[n])))
d3WarpedUnitList.append(d3Unit)
return xWarpedList, d1WarpedList, d2WarpedListFinal, d3WarpedUnitList
def generateOstiumMesh(region, options, trackSurface, centrePosition, axis1, startNodeIdentifier = 1, startElementIdentifier = 1,
vesselMeshGroups = None):
'''
:param vesselMeshGroups: List (over number of vessels) of list of mesh groups to add vessel elements to.
:return: nextNodeIdentifier, nextElementIdentifier, Ostium points tuple
(ox[n3][n1][c], od1[n3][n1][c], od2[n3][n1][c], od3[n3][n1][c], oNodeId[n3][n1], oPositions).
'''
vesselsCount = options['Number of vessels']
elementsCountAroundOstium = options['Number of elements around ostium']
elementsCountAcross = options['Number of elements across common']
elementsCountsAroundVessels, elementsCountAroundMid = getOstiumElementsCountsAroundVessels(elementsCountAroundOstium, elementsCountAcross, vesselsCount)
elementsCountAroundEnd = (elementsCountAroundOstium - 2*elementsCountAroundMid)//2
#print('\nvesselsCount', vesselsCount, 'elementsCountsAroundOstium', elementsCountAroundOstium, 'elementsCountAcross', elementsCountAcross)
#print('--> elementsCountsAroundVessels', elementsCountsAroundVessels, 'elementsCountAroundMid', elementsCountAroundMid)
elementsCountAlong = options['Number of elements along']
elementsCountThroughWall = options['Number of elements through wall']
unitScale = options['Unit scale']
isOutlet = options['Outlet']
ostiumRadius = 0.5*unitScale*options['Ostium diameter']
ostiumLength = unitScale*options['Ostium length']
ostiumWallThickness = unitScale*options['Ostium wall thickness']
interVesselHeight = unitScale*options['Ostium inter-vessel height']
interVesselDistance = unitScale*options['Ostium inter-vessel distance'] if (vesselsCount > 1) else 0.0
halfInterVesselDistance = 0.5*interVesselDistance
useCubicHermiteThroughOstiumWall = not(options['Use linear through ostium wall'])
vesselEndDerivative = ostiumLength*options['Vessel end length factor']/elementsCountAlong
vesselInnerRadius = 0.5*unitScale*options['Vessel inner diameter']
vesselWallThickness = unitScale*options['Vessel wall thickness']
vesselOuterRadius = vesselInnerRadius + vesselWallThickness
vesselAngle1Radians = math.radians(options['Vessel angle 1 degrees'])
vesselAngle1SpreadRadians = math.radians(options['Vessel angle 1 spread degrees'])
vesselAngle2Radians = math.radians(options['Vessel angle 2 degrees'])
useCubicHermiteThroughVesselWall = not(options['Use linear through vessel wall'])
useCrossDerivatives = False # options['Use cross derivatives'] # not implemented
fm = region.getFieldmodule()
fm.beginChange()
coordinates = findOrCreateFieldCoordinates(fm)
cache = fm.createFieldcache()
# track points in shape of ostium
# get directions in plane of surface at centre:
cx, cd1, cd2 = trackSurface.evaluateCoordinates(centrePosition, True)
trackDirection1, trackDirection2, centreNormal = calculate_surface_axes(cd1, cd2, axis1)
trackDirection2reverse = [ -d for d in trackDirection2 ]
halfCircumference = math.pi*ostiumRadius
circumference = 2.0*halfCircumference
distance = 0.0
elementLengthAroundOstiumMid = 0.0
vesselsSpanAll = interVesselDistance*(vesselsCount - 1)
vesselsSpanMid = interVesselDistance*(vesselsCount - 2)
if vesselsCount == 1:
elementLengthAroundOstiumEnd = circumference/elementsCountAroundOstium
vesselOstiumPositions = [ centrePosition ]
ocx = [ cx ]
ocd1 = [ trackDirection1 ]
ocd2 = [ trackDirection2 ]
ocd3 = [ centreNormal ]
else:
elementLengthAroundOstiumEnd = (circumference + 2.0*interVesselDistance)/(elementsCountAroundOstium - 2*elementsCountAroundMid)
if elementsCountAroundMid > 0:
elementLengthAroundOstiumMid = interVesselDistance*(vesselsCount - 2)/elementsCountAroundMid
vesselOstiumPositions = []
ocx = []
ocd1 = []
ocd2 = []
ocd3 = []
for v in range(vesselsCount):
vesselOstiumPositions.append(trackSurface.trackVector(centrePosition, trackDirection1, (v/(vesselsCount - 1) - 0.5)*vesselsSpanAll))
x, d1, d2 = trackSurface.evaluateCoordinates(vesselOstiumPositions[-1], -1)
d1, d2, d3 = calculate_surface_axes(d1, d2, trackDirection1)
ocx .append(x)
ocd1.append(d1)
ocd2.append(d2)
ocd3.append(d3)
# coordinates around ostium
ox = [ [], [] ]
od1 = [ [], [] ]
od2 = [ [], [] ]
od3 = [ [], [] ]
oPositions = []
for n1 in range(elementsCountAroundOstium):
elementLength = elementLengthAroundOstiumEnd
if distance <= (vesselsSpanMid + halfInterVesselDistance):
position = trackSurface.trackVector(centrePosition, trackDirection1, 0.5*vesselsSpanMid - distance)
sideDirection = trackDirection2reverse
if n1 < elementsCountAroundMid:
elementLength = elementLengthAroundOstiumMid
elif distance < (vesselsSpanMid + halfInterVesselDistance + halfCircumference):
position = vesselOstiumPositions[0]
angleRadians = (distance - (vesselsSpanMid + halfInterVesselDistance))/ostiumRadius
w1 = -math.sin(angleRadians)
w2 = -math.cos(angleRadians)
sideDirection = [ (w1*trackDirection1[c] + w2*trackDirection2[c]) for c in range(3) ]
elif distance < (2.0*vesselsSpanMid + halfInterVesselDistance + halfCircumference + interVesselDistance):
position = trackSurface.trackVector(centrePosition, trackDirection1, distance - (1.5*vesselsSpanMid + interVesselDistance + halfCircumference))
sideDirection = trackDirection2
if 0 <= (n1 - elementsCountAroundEnd - elementsCountAroundMid) < elementsCountAroundMid:
elementLength = elementLengthAroundOstiumMid
elif distance < (2.0*vesselsSpanMid + halfInterVesselDistance + circumference + interVesselDistance):
position = vesselOstiumPositions[-1]
angleRadians = (distance - (2.0*vesselsSpanMid + halfInterVesselDistance + halfCircumference + interVesselDistance))/ostiumRadius
w1 = math.sin(angleRadians)
w2 = math.cos(angleRadians)
sideDirection = [ (w1*trackDirection1[c] + w2*trackDirection2[c]) for c in range(3) ]
else:
position = trackSurface.trackVector(centrePosition, trackDirection1, 0.5*vesselsSpanMid + (circumference + 2.0*(vesselsSpanMid + interVesselDistance)) - distance)
sideDirection = trackDirection2reverse
position = trackSurface.trackVector(position, sideDirection, ostiumRadius)
oPositions.append(position)
px, d1, d2 = trackSurface.evaluateCoordinates(position, True)
pd2, pd1, pd3 = calculate_surface_axes(d1, d2, sideDirection)
# get outer coordinates
opx = px
opd1 = vector.setMagnitude([ -d for d in pd1 ], elementLengthAroundOstiumEnd)
opd2 = vector.setMagnitude(pd2, elementLengthAroundOstiumEnd) # smoothed later
opd3 = vector.setMagnitude(pd3, ostiumWallThickness)
# set inner and outer coordinates (use copy to avoid references to same list later)
ox [0].append([ (opx[c] - opd3[c]) for c in range(3) ])
od1[0].append(copy.copy(opd1))
od2[0].append(copy.copy(opd2))
ox [1].append(opx)
od1[1].append(opd1)
od2[1].append(opd2)
if useCubicHermiteThroughOstiumWall:
od3[0].append(copy.copy(opd3))
od3[1].append(opd3)
distance += elementLength
for n3 in range(2):
od1[n3] = interp.smoothCubicHermiteDerivativesLoop(ox[n3], od1[n3], fixAllDirections = True)
xx = []
xd1 = []
xd2 = []
xd3 = []
# coordinates across common ostium, between vessels
nodesCountFreeEnd = elementsCountsAroundVessels[0] + 1 - elementsCountAcross
oinc = 0 if (vesselsCount <= 2) else elementsCountAroundMid//(vesselsCount - 2)
for iv in range(vesselsCount - 1):
xx .append([ None, None ])
xd1.append([ None, None ])
xd2.append([ None, None ])
xd3.append([ None, None ])
oa = elementsCountAroundMid - iv*oinc
ob = elementsCountAroundMid + nodesCountFreeEnd - 1 + iv*oinc
nx = [ ox[1][oa], ox[1][ob] ]
nd1 = [ [ -d for d in od1[1][oa] ], od1[1][ob] ]
nd2 = [ [ -d for d in od2[1][oa] ], od2[1][ob] ]
if elementsCountAcross > 1:
# add centre point, displaced by interVesselHeight
if vesselsCount == 2:
position = centrePosition
else:
position = trackSurface.trackVector(centrePosition, trackDirection1, (iv/(vesselsCount - 2) - 0.5)*vesselsSpanMid)
mx, d1, d2 = trackSurface.evaluateCoordinates(position, derivatives = True)
md1, md2, md3 = calculate_surface_axes(d1, d2, trackDirection1)
nx .insert(1, [ (mx[c] + interVesselHeight*md3[c]) for c in range(3) ])
nd1.insert(1, vector.setMagnitude(md1, elementLengthAroundOstiumMid if (0 < iv < (vesselsCount - 2)) else elementLengthAroundOstiumEnd))
nd2.insert(1, vector.setMagnitude(md2, ostiumRadius))
nd2 = interp.smoothCubicHermiteDerivativesLine(nx, nd2, fixAllDirections = True)
px, pd2, pe, pxi = interp.sampleCubicHermiteCurves(nx, nd2, elementsCountAcross)[0:4]
pd1 = interp.interpolateSampleLinear(nd1, pe, pxi)
pd3 = [ vector.setMagnitude(vector.crossproduct3(pd1[n2], pd2[n2]), ostiumWallThickness) for n2 in range(elementsCountAcross + 1) ]
lx = [ ([ (px[n2][c] - pd3[n2][c]) for c in range(3) ]) for n2 in range(elementsCountAcross + 1) ]
ld2 = interp.smoothCubicHermiteDerivativesLine(lx, pd2, fixAllDirections = True)
xx [iv][0] = lx [1:elementsCountAcross]
xd1[iv][0] = copy.deepcopy(pd1[1:elementsCountAcross]) # to be smoothed later
xd2[iv][0] = ld2[1:elementsCountAcross]
xx [iv][1] = px [1:elementsCountAcross]
xd1[iv][1] = pd1[1:elementsCountAcross] # to be smoothed later
xd2[iv][1] = pd2[1:elementsCountAcross]
if useCubicHermiteThroughOstiumWall:
xd3[iv][0] = copy.deepcopy(pd3[1:elementsCountAcross])
xd3[iv][1] = pd3[1:elementsCountAcross]
# set smoothed d2 on ostium circumference
od2[0][oa] = [ -d for d in ld2[0] ]
od2[1][oa] = [ -d for d in pd2[0] ]
od2[0][ob] = ld2[-1]
od2[1][ob] = pd2[-1]
# get positions of vessel end centres and rings
vcx = []
vcd1 = []
vcd2 = []
vcd3 = []
vox = []
vod1 = []
vod2 = []
vod3 = []
for v in range(vesselsCount):
elementsCountAroundVessel = elementsCountsAroundVessels[v]
radiansPerElementVessel = 2.0*math.pi/elementsCountAroundVessel
useVesselAngleRadians = vesselAngle1Radians
if vesselsCount > 1:
useVesselAngleRadians += (v/(vesselsCount - 1) - 0.5)*vesselAngle1SpreadRadians
vx, vd1, vd2, vd3 = getCircleProjectionAxes(ocx[v], ocd1[v], ocd2[v], ocd3[v], ostiumLength, useVesselAngleRadians, vesselAngle2Radians)
vd1 = [ vesselOuterRadius*d for d in vd1 ]
vd2 = [ -vesselOuterRadius*d for d in vd2 ]
vd3 = [ -vesselEndDerivative*d for d in vd3 ]
vcx.append(vx)
vcd1.append(vd1)
vcd2.append(vd2)
vcd3.append(vd3)
vox.append([])
vod1.append([])
vod2.append([])
vod3.append([])
for n3 in range(2):
radius = vesselInnerRadius if (n3 == 0) else vesselOuterRadius
vAxis1 = vector.setMagnitude(vd1, radius)
vAxis2 = vector.setMagnitude(vd2, radius)
if vesselsCount == 1:
startRadians = 0.5*math.pi
else:
startRadians = 0.5*radiansPerElementVessel*elementsCountAcross
if v == (vesselsCount - 1):
startRadians -= math.pi
px, pd1 = createCirclePoints(vx, vAxis1, vAxis2, elementsCountAroundVessel, startRadians)
vox [-1].append(px)
vod1[-1].append(pd1)
vod2[-1].append([ vd3 ]*elementsCountAroundVessel)
if useCubicHermiteThroughVesselWall:
vod3[-1].append([ vector.setMagnitude(vector.crossproduct3(d1, vd3), vesselWallThickness) for d1 in pd1 ])
# calculate common ostium vessel node derivatives map
mvPointsx = [ None ]*vesselsCount
mvPointsd1 = [ None ]*vesselsCount
mvPointsd2 = [ None ]*vesselsCount
mvPointsd3 = [ None ]*vesselsCount
mvDerivativesMap = [ None ]*vesselsCount
mvMeanCount = [ None ]*vesselsCount # stores 1 if first reference to common point between vessels, 2 if second. Otherwise 0.
for v in range(vesselsCount):
if vesselsCount == 1:
mvPointsx[v], mvPointsd1[v], mvPointsd2[v], mvPointsd3[v], mvDerivativesMap[v] = \
ox, od1, od2, od3 if useCubicHermiteThroughOstiumWall else None, None
mvMeanCount[v] = [ 0 ]*elementsCountsAroundVessels[v]
else:
iv = max(0, v - 1)
oa = elementsCountAroundMid - iv*oinc
ob = elementsCountAroundMid + nodesCountFreeEnd - 1 + iv*oinc
mvPointsx [v] = []
mvPointsd1[v] = []
mvPointsd2[v] = []
mvPointsd3[v] = [] if useCubicHermiteThroughOstiumWall else None
mvDerivativesMap[v] = []
for n3 in range(2):
mvPointsd1[v].append([])
mvPointsd2[v].append([])
mvPointsx [v].append([])
if useCubicHermiteThroughOstiumWall:
mvPointsd3[v].append([])
mvDerivativesMap[v].append([])
if v == 0: # first end vessel
mvPointsd1[v][n3] += od1[n3][oa:ob + 1]
mvPointsd2[v][n3] += od2[n3][oa:ob + 1]
mvPointsx [v][n3] += ox [n3][oa:ob + 1]
if useCubicHermiteThroughOstiumWall:
mvPointsd3[v][n3] += od3[n3][oa:ob + 1]
mvDerivativesMap[v][n3].append( ( (0, 1, 0), (-1, 1, 0), None, (1, 0, 0) ) )
for i in range(nodesCountFreeEnd - 2):
mvDerivativesMap[v][n3].append( ( None, None, None ) )
mvDerivativesMap[v][n3].append( ( (1, 0, 0), (1, 1, 0), None, (0, -1, 0) ) )
mvPointsx [v][n3] += reversed(xx [iv][n3])
mvPointsd1[v][n3] += reversed(xd1[iv][n3])
mvPointsd2[v][n3] += reversed(xd2[iv][n3])
if useCubicHermiteThroughOstiumWall:
mvPointsd3[v][n3] += reversed(xd3[iv][n3])
for i in range(elementsCountAcross - 1):
mvDerivativesMap[v][n3].append( ( (0, -1, 0), (1, 0, 0), None ) )
if n3 == 0:
mvMeanCount[v] = [ 1 ] + [ 0 ]*(nodesCountFreeEnd - 2) + [ 1 ]*elementsCountAcross
elif v < (vesselsCount - 1): # middle vessels
# left:
mvPointsx [v][n3] += ox [n3][oa - oinc:oa + 1]
mvPointsd1[v][n3] += od1[n3][oa - oinc:oa + 1]
mvPointsd2[v][n3] += od2[n3][oa - oinc:oa + 1]
if useCubicHermiteThroughOstiumWall:
mvPointsd3[v][n3] += od3[n3][oa - oinc:oa + 1]
mvDerivativesMap[v][n3].append( ( (0, 1, 0), (-1, 1, 0), None, (1, 0, 0) ) )
for i in range(oinc - 1):
mvDerivativesMap[v][n3].append( ( None, None, None ) )
mvDerivativesMap[v][n3].append( ( (1, 0, 0), (1, 1, 0), None, (0, -1, 0) ) )
# across
mvPointsx [v][n3] += xx [iv][n3]
mvPointsd1[v][n3] += xd1[iv][n3]
mvPointsd2[v][n3] += xd2[iv][n3]
if useCubicHermiteThroughOstiumWall:
mvPointsd3[v][n3] += xd3[iv][n3]
for i in range(elementsCountAcross - 1):
mvDerivativesMap[v][n3].append( ( (0, 1, 0), (-1, 0, 0), None ) )
# right
mvPointsx [v][n3] += ox [n3][ob:ob + oinc + 1]
mvPointsd1[v][n3] += od1[n3][ob:ob + oinc + 1]
mvPointsd2[v][n3] += od2[n3][ob:ob + oinc + 1]
if useCubicHermiteThroughOstiumWall:
mvPointsd3[v][n3] += od3[n3][ob:ob + oinc + 1]
mvDerivativesMap[v][n3].append( ( (0, 1, 0), (-1, 1, 0), None, (1, 0, 0) ) )
for i in range(oinc - 1):
mvDerivativesMap[v][n3].append( ( None, None, None ) )
mvDerivativesMap[v][n3].append( ( (1, 0, 0), (1, 1, 0), None, (0, -1, 0) ) )
# across reverse
mvPointsx [v][n3] += reversed(xx [iv + 1][n3])
mvPointsd1[v][n3] += reversed(xd1[iv + 1][n3])
mvPointsd2[v][n3] += reversed(xd2[iv + 1][n3])
if useCubicHermiteThroughOstiumWall:
mvPointsd3[v][n3] += reversed(xd3[iv + 1][n3])
for i in range(elementsCountAcross - 1):
mvDerivativesMap[v][n3].append( ( (0, -1, 0), (1, 0, 0), None ) )
if n3 == 0:
mvMeanCount[v] = [ 1 ] + [ 0 ]*(oinc - 1) + [ 2 ]*(elementsCountAcross + 1) + [ 0 ]*(oinc - 1) + [ 1 ]*elementsCountAcross
else: # last end vessel
mvPointsx [v][n3] += ox [n3][ob:] + [ ox [n3][0] ]
mvPointsd1[v][n3] += od1[n3][ob:] + [ od1[n3][0] ]
mvPointsd2[v][n3] += od2[n3][ob:] + [ od2[n3][0] ]
if useCubicHermiteThroughOstiumWall:
mvPointsd3[v][n3] += od3[n3][ob:] + [ od3[n3][0] ]
mvDerivativesMap[v][n3].append( ( (0, 1, 0), (-1, 1, 0), None, (1, 0, 0) ) )
for i in range(nodesCountFreeEnd - 2):
mvDerivativesMap[v][n3].append( ( None, None, None ) )
mvDerivativesMap[v][n3].append( ( (1, 0, 0), (1, 1, 0), None, (0, -1, 0) ) )
mvPointsx [v][n3] += xx [iv][n3]
mvPointsd1[v][n3] += xd1[iv][n3]
mvPointsd2[v][n3] += xd2[iv][n3]
if useCubicHermiteThroughOstiumWall:
mvPointsd3[v][n3] += xd3[iv][n3]
for i in range(elementsCountAcross - 1):
mvDerivativesMap[v][n3].append( ( (0, 1, 0), (-1, 0, 0), None ) )
if n3 == 0:
mvMeanCount[v] = [ 2 ] + [ 0 ]*(nodesCountFreeEnd - 2) + [ 2 ]*elementsCountAcross
# calculate derivative 2 around free sides of inlets to fit vessel derivatives
for v in range(vesselsCount):
for n3 in range(2):
#print('v',v,'n3',n3,'elementsAround',elementsCountsAroundVessels[v])
#print('mvPointsx [v][n3]', mvPointsx [v][n3])
#print('mvPointsd1[v][n3]', mvPointsd1[v][n3])
#print('mvPointsd2[v][n3]', mvPointsd2[v][n3])
#print('mvDerivativesMap[v][n3]', mvDerivativesMap[v][n3])
for n1 in range(elementsCountsAroundVessels[v]):
d2Map = mvDerivativesMap[v][n3][n1][1] if (mvDerivativesMap[v] and mvDerivativesMap[v][n3][n1]) else None
sf1 = d2Map[0] if d2Map else 0.0
sf2 = d2Map[1] if d2Map else 1.0
nx = [ vox[v][n3][n1], mvPointsx[v][n3][n1] ]
nd2 = [ [ d*elementsCountAlong for d in vod2[v][n3][n1] ], [ (sf1*mvPointsd1[v][n3][n1][c] + sf2*mvPointsd2[v][n3][n1][c]) for c in range(3) ] ]
nd2f = interp.smoothCubicHermiteDerivativesLine(nx, nd2, fixStartDerivative = True, fixEndDirection = True)
ndf = [ d/elementsCountAlong for d in nd2f[1] ]
# assign components to set original values:
if sf1 == 0:
for c in range(3):
mvPointsd2[v][n3][n1][c] = sf2*ndf[c]
elif sf2 == 0:
if mvMeanCount[v][n1] < 2:
for c in range(3):
mvPointsd1[v][n3][n1][c] = sf1*ndf[c]
else:
# take mean of values from this and last vessel
for c in range(3):
mvPointsd1[v][n3][n1][c] = 0.5*(mvPointsd1[v][n3][n1][c] + sf1*ndf[c])
else:
#print('v', v, 'n3', n3, 'n1', n1, ':', vector.magnitude(ndf), 'vs.', vector.magnitude(nd2[1]), 'd2Map', d2Map)
pass
if isOutlet:
# reverse directions of d1 and d2 on vessels and ostium base
for c in range(3):
for n3 in range(2):
for n1 in range(elementsCountAroundOstium):
od1[n3][n1][c] = -od1[n3][n1][c]
od2[n3][n1][c] = -od2[n3][n1][c]
for iv in range(vesselsCount - 1):
for n1 in range(elementsCountAcross - 1):
xd1[iv][n3][n1][c] = -xd1[iv][n3][n1][c]
xd2[iv][n3][n1][c] = -xd2[iv][n3][n1][c]
for v in range(vesselsCount):
for n1 in range(elementsCountsAroundVessels[v]):
vod1[v][n3][n1][c] = -vod1[v][n3][n1][c]
# d2 is referenced all around, so only change once per vessel
for v in range(vesselsCount):
vod2[v][0][0][c] = -vod2[v][0][0][c]
##############
# Create nodes
##############
nodes = fm.findNodesetByFieldDomainType(Field.DOMAIN_TYPE_NODES)
nodetemplate = nodes.createNodetemplate()
nodetemplate.defineField(coordinates)
nodetemplate.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_VALUE, 1)
nodetemplate.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D_DS1, 1)
nodetemplate.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D_DS2, 1)
nodetemplate.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D_DS3, 1)
nodetemplateLinearS3 = nodes.createNodetemplate()
nodetemplateLinearS3.defineField(coordinates)
nodetemplateLinearS3.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_VALUE, 1)
nodetemplateLinearS3.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D_DS1, 1)
nodetemplateLinearS3.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D_DS2, 1)
nodeIdentifier = startNodeIdentifier
oNodeId = []
for n3 in range(2):
oNodeId.append([])
for n1 in range(elementsCountAroundOstium):
node = nodes.createNode(nodeIdentifier, nodetemplate if useCubicHermiteThroughOstiumWall else nodetemplateLinearS3)
cache.setNode(node)
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_VALUE, 1, ox [n3][n1])
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS1, 1, od1[n3][n1])
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS2, 1, od2[n3][n1])
if useCubicHermiteThroughOstiumWall:
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS3, 1, od3[n3][n1])
oNodeId[n3].append(nodeIdentifier)
nodeIdentifier += 1
xNodeId = []
for iv in range(vesselsCount - 1):
xNodeId.append([])
for n3 in range(2):
xNodeId[iv].append([])
for n2 in range(elementsCountAcross - 1):
node = nodes.createNode(nodeIdentifier, nodetemplate if useCubicHermiteThroughOstiumWall else nodetemplateLinearS3)
cache.setNode(node)
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_VALUE, 1, xx [iv][n3][n2])
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS1, 1, xd1[iv][n3][n2])
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS2, 1, xd2[iv][n3][n2])
if useCubicHermiteThroughOstiumWall:
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS3, 1, xd3[iv][n3][n2])
xNodeId[iv][n3].append(nodeIdentifier)
nodeIdentifier += 1
#for v in range(vesselsCount):
# node = nodes.createNode(nodeIdentifier, nodetemplate)
# cache.setNode(node)
# coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_VALUE, 1, vcx [v])
# coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS1, 1, vcd1[v])
# coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS2, 1, vcd2[v])
# coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS3, 1, vcd3[v])
# nodeIdentifier += 1
# for n3 in range(2):
# for n1 in range(elementsCountsAroundVessels[v]):
# node = nodes.createNode(nodeIdentifier, nodetemplate if useCubicHermiteThroughVesselWall else nodetemplateLinearS3)
# cache.setNode(node)
# coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_VALUE, 1, vox [v][n3][n1])
# coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS1, 1, vod1[v][n3][n1])
# coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS2, 1, vod2[v][n3][n1])
# if useCubicHermiteThroughVesselWall:
# coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS3, 1, vod3[v][n3][n1])
# #vNodeId.append(nodeIdentifier)
# nodeIdentifier += 1
# get identifiers of nodes around each vessel at ostium end
mvNodeId = [ None ]*vesselsCount
for v in range(vesselsCount):
if vesselsCount == 1:
mvNodeId[v] = oNodeId
else:
iv = max(0, v - 1)
mvNodeId[v] = [ None, None ]
oa = elementsCountAroundMid - iv*oinc
ob = elementsCountAroundMid + nodesCountFreeEnd - 1 + iv*oinc
for n3 in range(2):
if v == 0: # first end vessel
mvNodeId[v][n3] = oNodeId[n3][oa:ob + 1] + (list(reversed(xNodeId[iv][n3])) if (v == 0) else xNodeId[iv][n3])
elif v == (vesselsCount - 1): # last end vessels
mvNodeId[v][n3] = oNodeId[n3][ob:] + [ oNodeId[n3][0] ] + (list(reversed(xNodeId[iv][n3])) if (v == 0) else xNodeId[iv][n3])
else: # mid vessels
mvNodeId[v][n3] = oNodeId[n3][oa - oinc:oa + 1] + xNodeId[iv][n3] + oNodeId[n3][ob:ob + oinc + 1] + list(reversed(xNodeId[iv + 1][n3]))
#################
# Create elementss
#################
mesh = fm.findMeshByDimension(3)
elementIdentifier = startElementIdentifier
tricubichermite = eftfactory_tricubichermite(mesh, useCrossDerivatives)
#tricubicHermiteBasis = fm.createElementbasis(3, Elementbasis.FUNCTION_TYPE_CUBIC_HERMITE)
#eft = tricubichermite.createEftBasic()
#elementtemplate = mesh.createElementtemplate()
#elementtemplate.setElementShapeType(Element.SHAPE_TYPE_CUBE)
#elementtemplate.defineField(coordinates, -1, eft)
#elementtemplateX = mesh.createElementtemplate()
#elementtemplateX.setElementShapeType(Element.SHAPE_TYPE_CUBE)
for v in range(vesselsCount):
if isOutlet:
startPointsx, startPointsd1, startPointsd2, startPointsd3, startNodeId, startDerivativesMap = \
mvPointsx[v], mvPointsd1[v], mvPointsd2[v], mvPointsd3[v], mvNodeId[v], mvDerivativesMap[v]
endPointsx, endPointsd1, endPointsd2, endPointsd3, endNodeId, endDerivativesMap = \
vox[v], vod1[v], vod2[v], vod3[v] if useCubicHermiteThroughVesselWall else None, None, None
# reverse order of nodes around:
for px in [ startPointsx, startPointsd1, startPointsd2, startPointsd3, startNodeId, startDerivativesMap, \
endPointsx, endPointsd1, endPointsd2, endPointsd3, endNodeId, endDerivativesMap ]:
if px:
for n3 in range(2):
px[n3] = [ px[n3][0] ] + px[n3][len(px[n3]) - 1:0:-1]
if vesselsCount > 1:
# must switch in and out xi1 maps around corners in startDerivativesMap
for n3 in range(2):
for n1 in range(elementsCountsAroundVessels[v]):
derivativesMap = startDerivativesMap[n3][n1]
if len(derivativesMap) == 4:
startDerivativesMap[n3][n1] = derivativesMap[3], derivativesMap[1], derivativesMap[2], derivativesMap[0]
else:
startPointsx, startPointsd1, startPointsd2, startPointsd3, startNodeId, startDerivativesMap = \
vox[v], vod1[v], vod2[v], vod3[v] if useCubicHermiteThroughVesselWall else None, None, None
endPointsx, endPointsd1, endPointsd2, endPointsd3, endNodeId, endDerivativesMap = \
mvPointsx[v], mvPointsd1[v], mvPointsd2[v], mvPointsd3[v], mvNodeId[v], mvDerivativesMap[v]
#print('endPointsx ', endPointsx )
#print('endPointsd1', endPointsd1)
#print('endPointsd2', endPointsd2)
#print('endPointsd3', endPointsd3)
#print('endNodeId', endNodeId)
#print('endDerivativesMap', endDerivativesMap)
nodeIdentifier, elementIdentifier = createAnnulusMesh3d(
nodes, mesh, nodeIdentifier, elementIdentifier,
startPointsx, startPointsd1, startPointsd2, startPointsd3, startNodeId, startDerivativesMap,
endPointsx, endPointsd1, endPointsd2, endPointsd3, endNodeId, endDerivativesMap,
forceMidLinearXi3 = not useCubicHermiteThroughVesselWall,
elementsCountRadial = elementsCountAlong,
meshGroups = vesselMeshGroups[v] if vesselMeshGroups else [])
fm.endChange()
return nodeIdentifier, elementIdentifier, (ox, od1, od2, od3, oNodeId, oPositions)
def createAnnulusMesh3d(nodes, mesh, nextNodeIdentifier, nextElementIdentifier,
startPointsx, startPointsd1, startPointsd2, startPointsd3, startNodeId, startDerivativesMap,
endPointsx, endPointsd1, endPointsd2, endPointsd3, endNodeId, endDerivativesMap,
forceStartLinearXi3 = False, forceMidLinearXi3 = False, forceEndLinearXi3 = False,
maxStartThickness = None, maxEndThickness = None, useCrossDerivatives = False,
elementsCountRadial = 1, meshGroups = []):
'''
Create an annulus mesh from a loop of start points/nodes with specified derivative mappings to
a loop of end points/nodes with specified derivative mappings.
Derivative d3 is through the wall. Currently limited to single element layer through wall.
Points/nodes order cycles fastest around the annulus, then through the wall.
Note doesn't support cross derivatives.
Arrays are indexed by n3 (node through wall, size 2), n2 (node along/radial), n1 (node around, variable size)
and coordinate component c.
:param nodes: The nodeset to create nodes in.
:param mesh: The mesh to create elements in.
:param nextNodeIdentifier, nextElementIdentifier: Next identifiers to use and increment.
:param startPointsx, startPointsd1, startPointsd2, startPointsd3, endPointsx, endPointsd1, endPointsd2, endPointsd3:
List array[n3][n1][c] or start/point coordinates and derivatives. To linearise through the wall, pass None to d3.
If both ends are linear through the wall, interior points are linear through the wall.
:param startNodeId, endNodeId: List array [n3][n1] of existing node identifiers to use at start/end. Pass None for
argument if no nodes are specified at end. These arguments are 'all or nothing'.
:param startDerivativesMap, endDerivativesMap: List array[n3][n1] of mappings for d/dxi1, d/dxi2, d/dxi3 at start/end of form:
( (1, -1, 0), (1, 0, 0), None ) where the first tuple means d/dxi1 = d/ds1 - d/ds2. Only 0, 1 and -1 may be used.
None means use default e.g. d/dxi2 = d/ds2.
Pass None for the entire argument to use the defaults d/dxi1 = d/ds1, d/dxi2 = d/ds2, d/dxi3 = d/ds3.
Pass a 4th mapping to apply to d/dxi1 on other side of node; if not supplied first mapping applies both sides.
:param nodetemplate: Full tricubic Hermite node template, can omit cross derivatives.
:param forceStartLinearXi3, forceMidLinearXi3, forceEndLinearXi3: Force start, middle or
end elements to be linear through the wall, even if d3 is supplied at either end.
Can only use forceMidLinearXi3 only if at least one end is linear in d3.
:param maxStartThickness, maxEndThickness: Optional maximum override on start/end thicknesses.
:param useCrossDerivatives: May only be True if no derivatives maps are in use.
:param elementsCountRadial: Optional number of elements in radial direction between start and end.
:param meshGroups: Optional list of Zinc MeshGroup for adding new elements to.
:return: Final values of nextNodeIdentifier, nextElementIdentifier
'''
assert (elementsCountRadial >= 1), 'createAnnulusMesh3d: Invalid number of radial elements'
startLinearXi3 = (not startPointsd3) or forceStartLinearXi3
endLinearXi3 = (not endPointsd3) or forceEndLinearXi3
midLinearXi3 = (startLinearXi3 and endLinearXi3) or ((startLinearXi3 or endLinearXi3) and forceMidLinearXi3)
# get list whether each row of nodes in elements is linear in Xi3
# this is for element use; start/end nodes may have d3 even if element is linear
rowLinearXi3 = [ startLinearXi3 ] + [ midLinearXi3 ]*(elementsCountRadial - 1) + [ endLinearXi3 ]
assert (not useCrossDerivatives) or ((not startDerivativesMap) and (not endDerivativesMap)), \
'createAnnulusMesh3d: Cannot use cross derivatives with derivatives map'
elementsCountWall = 1
nodesCountWall = elementsCountWall + 1
assert (len(startPointsx) == nodesCountWall) and (len(startPointsd1) == nodesCountWall) and (len(startPointsd2) == nodesCountWall) and \
(startLinearXi3 or (len(startPointsd3) == nodesCountWall)) and \
(len(endPointsx) == nodesCountWall) and (len(endPointsd1) == nodesCountWall) and (len(endPointsd2) == nodesCountWall) and \
(endLinearXi3 or (len(endPointsd3) == nodesCountWall)) and \
((startNodeId is None) or (len(startNodeId) == nodesCountWall)) and \
((endNodeId is None) or (len(endNodeId) == nodesCountWall)) and \
((startDerivativesMap is None) or (len(startDerivativesMap) == nodesCountWall)) and \
((endDerivativesMap is None) or (len(endDerivativesMap) == nodesCountWall)), \
'createAnnulusMesh3d: Mismatch in number of layers through wall'
elementsCountAround = nodesCountAround = len(startPointsx[0])
assert (nodesCountAround > 1), 'createAnnulusMesh3d: Invalid number of points/nodes around annulus'
for n3 in range(nodesCountWall):
assert (len(startPointsx[n3]) == nodesCountAround) and (len(startPointsd1[n3]) == nodesCountAround) and (len(startPointsd2[n3]) == nodesCountAround) and \
(startLinearXi3 or (len(startPointsd3[n3]) == nodesCountAround)) and \
(len(endPointsx[n3]) == nodesCountAround) and (len(endPointsd1[n3]) == nodesCountAround) and (len(endPointsd2[n3]) == nodesCountAround) and \
(endLinearXi3 or (len(endPointsd3[n3]) == nodesCountAround)) and \
((startNodeId is None) or (len(startNodeId[n3]) == nodesCountAround)) and \
((endNodeId is None) or (len(endNodeId[n3]) == nodesCountAround)) and \
((startDerivativesMap is None) or (len(startDerivativesMap[n3]) == nodesCountAround)) and \
((endDerivativesMap is None) or (len(endDerivativesMap[n3]) == nodesCountAround)), \
'createAnnulusMesh3d: Mismatch in number of points/nodes in layers through wall'
fm = mesh.getFieldmodule()
fm.beginChange()
cache = fm.createFieldcache()
coordinates = zinc_utils.getOrCreateCoordinateField(fm)
# Build arrays of points from start to end
px = [ [], [] ]
pd1 = [ [], [] ]
pd2 = [ [], [] ]
pd3 = [ [], [] ]
for n3 in range(2):
px [n3] = [ startPointsx [n3], endPointsx [n3] ]
pd1[n3] = [ startPointsd1[n3], endPointsd1[n3] ]
pd2[n3] = [ startPointsd2[n3], endPointsd2[n3] ]
pd3[n3] = [ startPointsd3[n3] if (startPointsd3 is not None) else None, \
endPointsd3[n3] if (endPointsd3 is not None) else None ]
if elementsCountRadial > 1:
# add in-between points
startPointsd = [ startPointsd1, startPointsd2, startPointsd3 ]
startPointsdslimit = 2 if (startPointsd3 is None) else 3
endPointsd = [ endPointsd1, endPointsd2, endPointsd3 ]
endPointsdslimit = 2 if (endPointsd3 is None) else 3
for n3 in range(2):
for n2 in range(1, elementsCountRadial):
px [n3].insert(n2, [ None ]*nodesCountAround)
pd1[n3].insert(n2, [ None ]*nodesCountAround)
pd2[n3].insert(n2, [ None ]*nodesCountAround)
pd3[n3].insert(n2, None if midLinearXi3 else [ None ]*nodesCountAround)
# compute on outside / n3 = 1, then map to inside using thickness
thicknesses = []
thicknesses.append([ vector.magnitude([ (startPointsx[1][n1][c] - startPointsx[0][n1][c]) for c in range(3) ]) for n1 in range(nodesCountAround) ])
if maxStartThickness:
for n1 in range(nodesCountAround):
thicknesses[0][n1] = min(thicknesses[0][n1], maxStartThickness)
for n2 in range(1, elementsCountRadial):
thicknesses.append([ None ]*nodesCountAround)
thicknesses.append([ vector.magnitude([ (endPointsx[1][n1][c] - endPointsx[0][n1][c]) for c in range(3) ]) for n1 in range(nodesCountAround) ])
if maxEndThickness:
for n1 in range(nodesCountAround):
thicknesses[-1][n1] = min(thicknesses[-1][n1], maxEndThickness)
n3 == 1
for n1 in range(nodesCountAround):
ax = startPointsx [n3][n1]
if (startDerivativesMap is None) or (startDerivativesMap[n3][n1][0] is None):
ad1 = startPointsd1[n3][n1]
else:
derivativesMap = startDerivativesMap[n3][n1][0]
ad1 = [ 0.0, 0.0, 0.0 ]
for ds in range(startPointsdslimit):
if derivativesMap[ds] != 0.0:
for c in range(3):
ad1[c] += derivativesMap[ds]*startPointsd[ds][n3][n1][c]
if len(startDerivativesMap[n3][n1]) > 3:
# average with d1 map for other side
derivativesMap = startDerivativesMap[n3][n1][3]
ad1 = [ 0.5*d for d in ad1 ]
if not derivativesMap:
for c in range(3):
ad1[c] += 0.5*startPointsd[0][n3][n1][c]
else:
for ds in range(startPointsdslimit):
if derivativesMap[ds] != 0.0:
for c in range(3):
ad1[c] += 0.5*derivativesMap[ds]*startPointsd[ds][n3][n1][c]
if (startDerivativesMap is None) or (startDerivativesMap[n3][n1][1] is None):
ad2 = startPointsd2[n3][n1]
else:
derivativesMap = startDerivativesMap[n3][n1][1]
ad2 = [ 0.0, 0.0, 0.0 ]
for ds in range(startPointsdslimit):
if derivativesMap[ds] != 0.0:
for c in range(3):
ad2[c] += derivativesMap[ds]*startPointsd[ds][n3][n1][c]
bx = endPointsx [n3][n1]
if (endDerivativesMap is None) or (endDerivativesMap[n3][n1][0] is None):
bd1 = endPointsd1[n3][n1]
else:
derivativesMap = endDerivativesMap[n3][n1][0]
bd1 = [ 0.0, 0.0, 0.0 ]
for ds in range(endPointsdslimit):
if derivativesMap[ds] != 0.0:
for c in range(3):
bd1[c] += derivativesMap[ds]*endPointsd[ds][n3][n1][c]
if len(endDerivativesMap[n3][n1]) > 3:
# average with d1 map for other side
derivativesMap = endDerivativesMap[n3][n1][3]
bd1 = [ 0.5*d for d in bd1 ]
if not derivativesMap:
for c in range(3):
bd1[c] += 0.5*endPointsd[0][n3][n1][c]
else:
for ds in range(endPointsdslimit):
if derivativesMap[ds] != 0.0:
for c in range(3):
bd1[c] += 0.5*derivativesMap[ds]*endPointsd[ds][n3][n1][c]
if (endDerivativesMap is None) or (endDerivativesMap[n3][n1][1] is None):
bd2 = endPointsd2[n3][n1]
else:
derivativesMap = endDerivativesMap[n3][n1][1]
bd2 = [ 0.0, 0.0, 0.0 ]
for ds in range(endPointsdslimit):
if derivativesMap[ds] != 0.0:
for c in range(3):
bd2[c] += derivativesMap[ds]*endPointsd[ds][n3][n1][c]
# scaling end derivatives to arc length gives even curvature along the curve
arcLength = interp.computeCubicHermiteArcLength(ax, ad2, bx, bd2, rescaleDerivatives = False)
scaledDerivatives = [ vector.setMagnitude(d2, arcLength) for d2 in [ ad2, bd2 ]]
mx, md2, me, mxi = interp.sampleCubicHermiteCurvesSmooth([ ax, bx ], scaledDerivatives, elementsCountRadial,
derivativeMagnitudeStart = vector.magnitude(ad2),
derivativeMagnitudeEnd = vector.magnitude(bd2))[0:4]
md1 = interp.interpolateSampleLinear([ ad1, bd1 ], me, mxi)
thi = interp.interpolateSampleLinear([ thicknesses[0][n1], thicknesses[-1][n1] ], me, mxi)
#md2 = interp.smoothCubicHermiteDerivativesLine(mx, md2, fixStartDerivative = True, fixEndDerivative = True)
for n2 in range(1, elementsCountRadial):
px [n3][n2][n1] = mx [n2]
pd1[n3][n2][n1] = md1[n2]
pd2[n3][n2][n1] = md2[n2]
thicknesses[n2][n1] = thi[n2]
# now get inner positions from normal and thickness, derivatives from curvature
for n2 in range(1, elementsCountRadial):
# first smooth derivative 1 around outer loop
pd1[1][n2] = interp.smoothCubicHermiteDerivativesLoop(px[1][n2], pd1[1][n2], magnitudeScalingMode = interp.DerivativeScalingMode.HARMONIC_MEAN)
for n1 in range(nodesCountAround):
normal = vector.normalise(vector.crossproduct3(pd1[1][n2][n1], pd2[1][n2][n1]))
thickness = thicknesses[n2][n1]
d3 = [ d*thickness for d in normal ]
px [0][n2][n1] = [ (px [1][n2][n1][c] - d3[c]) for c in range(3) ]
# calculate inner d1 from curvature around
n1m = n1 - 1
n1p = (n1 + 1)%nodesCountAround
curvature = 0.5*(
interp.getCubicHermiteCurvature(px[1][n2][n1m], pd1[1][n2][n1m], px[1][n2][n1 ], pd1[1][n2][n1 ], normal, 1.0) +
interp.getCubicHermiteCurvature(px[1][n2][n1 ], pd1[1][n2][n1 ], px[1][n2][n1p], pd1[1][n2][n1p], normal, 0.0))
factor = 1.0 + curvature*thickness
pd1[0][n2][n1] = [ factor*d for d in pd1[1][n2][n1] ]
# calculate inner d2 from curvature radially
n2m = n2 - 1
n2p = n2 + 1
curvature = 0.5*(
interp.getCubicHermiteCurvature(px[1][n2m][n1], pd2[1][n2m][n1], px[1][n2 ][n1], pd2[1][n2 ][n1], normal, 1.0) +
interp.getCubicHermiteCurvature(px[1][n2 ][n1], pd2[1][n2 ][n1], px[1][n2p][n1], pd2[1][n2p][n1], normal, 0.0))
factor = 1.0 + curvature*thickness
pd2[0][n2][n1] = [ factor*d for d in pd2[1][n2][n1] ]
if not midLinearXi3:
pd3[0][n2][n1] = pd3[1][n2][n1] = d3
# smooth derivative 1 around inner loop
pd1[0][n2] = interp.smoothCubicHermiteDerivativesLoop(px[0][n2], pd1[0][n2], magnitudeScalingMode = interp.DerivativeScalingMode.HARMONIC_MEAN)
for n3 in range(0, 1): # was (0, nodesCountWall)
# smooth derivative 2 radially/along annulus
for n1 in range(nodesCountAround):
sd2 = interp.smoothCubicHermiteDerivativesLine(
[ px [n3][n2][n1] for n2 in range(elementsCountRadial + 1) ],
[ pd2[n3][n2][n1] for n2 in range(elementsCountRadial + 1) ],
fixAllDirections = True, fixStartDerivative = True, fixEndDerivative = True,
magnitudeScalingMode = interp.DerivativeScalingMode.HARMONIC_MEAN)
for n2 in range(elementsCountRadial + 1):
pd2[n3][n2][n1] = sd2[n2]
##############
# Create nodes
##############
nodetemplate = nodes.createNodetemplate()
nodetemplate.defineField(coordinates)
nodetemplate.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_VALUE, 1)
nodetemplate.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D_DS1, 1)
nodetemplate.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D_DS2, 1)
if useCrossDerivatives:
nodetemplate.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D2_DS1DS2, 1)
nodetemplate.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D_DS3, 1)
if useCrossDerivatives:
nodetemplate.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D2_DS1DS3, 1)
nodetemplate.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D2_DS2DS3, 1)
nodetemplate.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D3_DS1DS2DS3, 1)
nodetemplateLinearS3 = nodes.createNodetemplate()
nodetemplateLinearS3.defineField(coordinates)
nodetemplateLinearS3.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_VALUE, 1)
nodetemplateLinearS3.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D_DS1, 1)
nodetemplateLinearS3.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D_DS2, 1)
if useCrossDerivatives:
nodetemplateLinearS3.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D2_DS1DS2, 1)
nodeIdentifier = nextNodeIdentifier
nodeId = [ [], [] ]
for n3 in range(2):
for n2 in range(elementsCountRadial + 1):
if (n2 == 0) and (startNodeId is not None):
rowNodeId = copy.deepcopy(startNodeId[n3])
elif (n2 == elementsCountRadial) and (endNodeId is not None):
rowNodeId = copy.deepcopy(endNodeId[n3])
else:
rowNodeId = []
nodetemplate1 = nodetemplate if pd3[n3][n2] else nodetemplateLinearS3
for n1 in range(nodesCountAround):
node = nodes.createNode(nodeIdentifier, nodetemplate1)
rowNodeId.append(nodeIdentifier)
cache.setNode(node)
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_VALUE, 1, px[n3][n2][n1])
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS1, 1, pd1[n3][n2][n1])
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS2, 1, pd2[n3][n2][n1])
if pd3[n3][n2]:
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS3, 1, pd3[n3][n2][n1])
nodeIdentifier = nodeIdentifier + 1
nodeId[n3].append(rowNodeId)
#################
# Create elements
#################
tricubichermite = eftfactory_tricubichermite(mesh, useCrossDerivatives)
bicubichermitelinear = eftfactory_bicubichermitelinear(mesh, useCrossDerivatives)
elementIdentifier = nextElementIdentifier
elementtemplateStandard = mesh.createElementtemplate()
elementtemplateStandard.setElementShapeType(Element.SHAPE_TYPE_CUBE)
elementtemplateX = mesh.createElementtemplate()
elementtemplateX.setElementShapeType(Element.SHAPE_TYPE_CUBE)
for e2 in range(elementsCountRadial):
nonlinearXi3 = (not rowLinearXi3[e2]) or (not rowLinearXi3[e2 + 1])
eftFactory = tricubichermite if nonlinearXi3 else bicubichermitelinear
eftStandard = eftFactory.createEftBasic()
elementtemplateStandard.defineField(coordinates, -1, eftStandard)
mapStartDerivatives = (e2 == 0) and (startDerivativesMap is not None)
mapStartLinearDerivativeXi3 = nonlinearXi3 and rowLinearXi3[e2]
mapEndDerivatives = (e2 == (elementsCountRadial - 1)) and (endDerivativesMap is not None)
mapEndLinearDerivativeXi3 = nonlinearXi3 and rowLinearXi3[e2 + 1]
mapDerivatives = mapStartDerivatives or mapStartLinearDerivativeXi3 or mapEndDerivatives or mapEndLinearDerivativeXi3
for e1 in range(elementsCountAround):
en = (e1 + 1)%elementsCountAround
nids = [ nodeId[0][e2][e1], nodeId[0][e2][en], nodeId[0][e2 + 1][e1], nodeId[0][e2 + 1][en],
nodeId[1][e2][e1], nodeId[1][e2][en], nodeId[1][e2 + 1][e1], nodeId[1][e2 + 1][en] ]
if mapDerivatives:
eft1 = eftFactory.createEftNoCrossDerivatives()
setEftScaleFactorIds(eft1, [1], [])
if mapStartLinearDerivativeXi3:
eftFactory.setEftLinearDerivative(eft1, [ 1, 5 ], Node.VALUE_LABEL_D_DS3, 1, 5, 1)
eftFactory.setEftLinearDerivative(eft1, [ 2, 6 ], Node.VALUE_LABEL_D_DS3, 2, 6, 1)
if mapStartDerivatives:
for i in range(2):
lns = [ 1, 5 ] if (i == 0) else [ 2, 6 ]
for n3 in range(2):
derivativesMap = startDerivativesMap[n3][e1] if (i == 0) else startDerivativesMap[n3][en]
# handle different d1 on each side of node
d1Map = derivativesMap[0] if ((i == 1) or (len(derivativesMap) < 4)) else derivativesMap[3]
d2Map = derivativesMap[1]
d3Map = derivativesMap[2]
# use temporary to safely swap DS1 and DS2:
ln = [ lns[n3] ]
if d1Map is not None:
remapEftNodeValueLabel(eft1, ln, Node.VALUE_LABEL_D_DS1, [ ( Node.VALUE_LABEL_D2_DS1DS2, [] ) ])
if d3Map is not None:
remapEftNodeValueLabel(eft1, ln, Node.VALUE_LABEL_D_DS3, [ ( Node.VALUE_LABEL_D2_DS2DS3, [] ) ])
if d2Map is not None:
remapEftNodeValueLabel(eft1, ln, Node.VALUE_LABEL_D_DS2, \
derivativeSignsToExpressionTerms( ( Node.VALUE_LABEL_D_DS1, Node.VALUE_LABEL_D_DS2, Node.VALUE_LABEL_D_DS3 ), d2Map))
if d1Map is not None:
remapEftNodeValueLabel(eft1, ln, Node.VALUE_LABEL_D2_DS1DS2, \
derivativeSignsToExpressionTerms( ( Node.VALUE_LABEL_D_DS1, Node.VALUE_LABEL_D_DS2, Node.VALUE_LABEL_D_DS3 ), d1Map))
if d3Map is not None:
remapEftNodeValueLabel(eft1, ln, Node.VALUE_LABEL_D2_DS2DS3, \
derivativeSignsToExpressionTerms( ( Node.VALUE_LABEL_D_DS1, Node.VALUE_LABEL_D_DS2, Node.VALUE_LABEL_D_DS3 ), d3Map))
if mapEndLinearDerivativeXi3:
eftFactory.setEftLinearDerivative(eft1, [ 3, 7 ], Node.VALUE_LABEL_D_DS3, 3, 7, 1)
eftFactory.setEftLinearDerivative(eft1, [ 4, 8 ], Node.VALUE_LABEL_D_DS3, 4, 8, 1)
if mapEndDerivatives:
for i in range(2):
lns = [ 3, 7 ] if (i == 0) else [ 4, 8 ]
for n3 in range(2):
derivativesMap = endDerivativesMap[n3][e1] if (i == 0) else endDerivativesMap[n3][en]
# handle different d1 on each side of node
d1Map = derivativesMap[0] if ((i == 1) or (len(derivativesMap) < 4)) else derivativesMap[3]
d2Map = derivativesMap[1]
d3Map = derivativesMap[2]
# use temporary to safely swap DS1 and DS2:
ln = [ lns[n3] ]
if d1Map is not None:
remapEftNodeValueLabel(eft1, ln, Node.VALUE_LABEL_D_DS1, [ ( Node.VALUE_LABEL_D2_DS1DS2, [] ) ])
if d3Map is not None:
remapEftNodeValueLabel(eft1, ln, Node.VALUE_LABEL_D_DS3, [ ( Node.VALUE_LABEL_D2_DS2DS3, [] ) ])
if d2Map is not None:
remapEftNodeValueLabel(eft1, ln, Node.VALUE_LABEL_D_DS2, \
derivativeSignsToExpressionTerms( ( Node.VALUE_LABEL_D_DS1, Node.VALUE_LABEL_D_DS2, Node.VALUE_LABEL_D_DS3 ), d2Map))
if d1Map is not None:
remapEftNodeValueLabel(eft1, ln, Node.VALUE_LABEL_D2_DS1DS2, \
derivativeSignsToExpressionTerms( ( Node.VALUE_LABEL_D_DS1, Node.VALUE_LABEL_D_DS2, Node.VALUE_LABEL_D_DS3 ), d1Map))
if d3Map is not None:
remapEftNodeValueLabel(eft1, ln, Node.VALUE_LABEL_D2_DS2DS3, \
derivativeSignsToExpressionTerms( ( Node.VALUE_LABEL_D_DS1, Node.VALUE_LABEL_D_DS2, Node.VALUE_LABEL_D_DS3 ), d3Map))
elementtemplateX.defineField(coordinates, -1, eft1)
elementtemplate1 = elementtemplateX
else:
eft1 = eftStandard
elementtemplate1 = elementtemplateStandard
element = mesh.createElement(elementIdentifier, elementtemplate1)
result2 = element.setNodesByIdentifier(eft1, nids)
if mapDerivatives:
result3 = element.setScaleFactors(eft1, [ -1.0 ])
#else:
# result3 = '-'
#print('create element annulus', element.isValid(), elementIdentifier, result2, result3, nids)
elementIdentifier += 1
for meshGroup in meshGroups:
meshGroup.addElement(element)
fm.endChange()
return nodeIdentifier, elementIdentifier
def replaceElementWithInlet4(self, element, startElementId, nodetemplate, startNodeId, tubeLength, innerDiameter, wallThickness):
'''
Replace element with 4 element X-layout tube inlet.
Inlet axis is at given length from centre of xi3=0 face, oriented with dx/dxi1.
8 new nodes are created.
'''
fm = self._mesh.getFieldmodule()
nodes = fm.findNodesetByFieldDomainType(Field.DOMAIN_TYPE_NODES)
fm.beginChange()
cache = fm.createFieldcache()
diff1 = self._mesh.getChartDifferentialoperator(1, 1)
diff2 = self._mesh.getChartDifferentialoperator(1, 2)
coordinates = getOrCreateCoordinateField(fm)
cache.setMeshLocation(element, [0.5, 0.5, 1.0])
result, fc = coordinates.evaluateReal(cache, 3)
resulta, a = coordinates.evaluateDerivative(diff1, cache, 3)
resultb, b = coordinates.evaluateDerivative(diff2, cache, 3)
n = vector.normalise(vector.crossproduct3(a, b))
#print(resulta, 'a =', a, ',', resultb, ' b=', b, ' fc=', fc, ' n=',n)
ic = [ (fc[i] + tubeLength*n[i]) for i in range(3) ]
na = vector.normalise(a)
nb = vector.normalise(b)
a = vector.normalise([ -(na[i] + nb[i]) for i in range(3) ])
b = vector.normalise(vector.crossproduct3(a, n))
zero = [ 0.0, 0.0, 0.0 ]
nodeIdentifier = startNodeId
elementsCountAround = 4
radiansPerElementAround = math.pi*2.0/elementsCountAround
for n3 in range(2):
radius = innerDiameter*0.5 + n3*wallThickness
for n1 in range(elementsCountAround):
radiansAround = n1*radiansPerElementAround
cosRadiansAround = math.cos(radiansAround)
sinRadiansAround = math.sin(radiansAround)
x = [ (ic[i] + radius*(cosRadiansAround*a[i] + sinRadiansAround*b[i])) for i in range(3) ]
dx_ds1 = [ radiansPerElementAround*radius*(-sinRadiansAround*a[i] + cosRadiansAround*b[i]) for i in range(3) ]
dx_ds2 = [ -tubeLength*c for c in n ]
dx_ds3 = [ wallThickness*(cosRadiansAround*a[i] + sinRadiansAround*b[i]) for i in range(3) ]
node = nodes.createNode(nodeIdentifier, nodetemplate)
cache.setNode(node)
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_VALUE, 1, x)
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS1, 1, dx_ds1)
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS2, 1, dx_ds2)
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS3, 1, dx_ds3)
if self._useCrossDerivatives:
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D2_DS1DS2, 1, zero)
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D2_DS1DS3, 1, zero)
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D2_DS2DS3, 1, zero)
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D3_DS1DS2DS3, 1, zero)
nodeIdentifier = nodeIdentifier + 1
eft0 = element.getElementfieldtemplate(coordinates, -1)
nids0 = getElementNodeIdentifiers(element, eft0)
orig_nids = [ nids0[0], nids0[2], nids0[3], nids0[1], nids0[4], nids0[6], nids0[7], nids0[5] ]
elementIdentifier = startElementId
elementtemplate1 = self._mesh.createElementtemplate()
elementtemplate1.setElementShapeType(Element.SHAPE_TYPE_CUBE)
for e in range(4):
eft1 = self.createEftNoCrossDerivatives()
setEftScaleFactorIds(eft1, [1], [])
if e == 0:
remapEftNodeValueLabel(eft1, [ 3, 7 ], Node.VALUE_LABEL_D_DS2, [ (Node.VALUE_LABEL_D_DS1, [1]), (Node.VALUE_LABEL_D_DS2, [1]) ])
remapEftNodeValueLabel(eft1, [ 3, 7 ], Node.VALUE_LABEL_D_DS1, [ (Node.VALUE_LABEL_D_DS2, []) ])
remapEftNodeValueLabel(eft1, [ 4, 8 ], Node.VALUE_LABEL_D_DS2, [ (Node.VALUE_LABEL_D_DS1, [1]), (Node.VALUE_LABEL_D_DS2, []) ])
remapEftNodeValueLabel(eft1, [ 4, 8 ], Node.VALUE_LABEL_D_DS1, [ (Node.VALUE_LABEL_D_DS2, []) ])
elif e == 1:
remapEftNodeValueLabel(eft1, [ 3, 7 ], Node.VALUE_LABEL_D_DS2, [ (Node.VALUE_LABEL_D_DS1, [1]), (Node.VALUE_LABEL_D_DS2, []) ])
remapEftNodeValueLabel(eft1, [ 4, 8 ], Node.VALUE_LABEL_D_DS2, [ (Node.VALUE_LABEL_D_DS1, []), (Node.VALUE_LABEL_D_DS2, []) ])
elif e == 2:
remapEftNodeValueLabel(eft1, [ 3, 7 ], Node.VALUE_LABEL_D_DS2, [ (Node.VALUE_LABEL_D_DS1, []), (Node.VALUE_LABEL_D_DS2, []) ])
remapEftNodeValueLabel(eft1, [ 3, 7 ], Node.VALUE_LABEL_D_DS1, [ (Node.VALUE_LABEL_D_DS2, [1]) ])
remapEftNodeValueLabel(eft1, [ 4, 8 ], Node.VALUE_LABEL_D_DS2, [ (Node.VALUE_LABEL_D_DS1, []), (Node.VALUE_LABEL_D_DS2, [1]) ])
remapEftNodeValueLabel(eft1, [ 4, 8 ], Node.VALUE_LABEL_D_DS1, [ (Node.VALUE_LABEL_D_DS2, [1]) ])
elif e == 3:
remapEftNodeValueLabel(eft1, [ 3, 7 ], Node.VALUE_LABEL_D_DS2, [ (Node.VALUE_LABEL_D_DS1, []), (Node.VALUE_LABEL_D_DS2, [1]) ])
remapEftNodeValueLabel(eft1, [ 3, 7 ], Node.VALUE_LABEL_D_DS1, [ (Node.VALUE_LABEL_D_DS1, [1]) ])
remapEftNodeValueLabel(eft1, [ 4, 8 ], Node.VALUE_LABEL_D_DS2, [ (Node.VALUE_LABEL_D_DS1, [1]), (Node.VALUE_LABEL_D_DS2, [1]) ])
remapEftNodeValueLabel(eft1, [ 4, 8 ], Node.VALUE_LABEL_D_DS1, [ (Node.VALUE_LABEL_D_DS1, [1]) ])
ea = e
eb = (e + 1) % 4
ec = ea + 4
ed = eb + 4
nids = [
startNodeId + ea, startNodeId + eb, orig_nids[ea], orig_nids[eb],
startNodeId + ec, startNodeId + ed, orig_nids[ec], orig_nids[ed]
]
elementtemplate1.defineField(coordinates, -1, eft1)
element = self._mesh.createElement(elementIdentifier, elementtemplate1)
result2 = element.setNodesByIdentifier(eft1, nids)
if eft1.getNumberOfLocalScaleFactors() == 1:
result3 = element.setScaleFactors(eft1, [ -1.0 ])
else:
result3 = 7
#print('create element in', element.isValid(), elementIdentifier, result2, result3, nids)
elementIdentifier += 1
fm.endChange()
def generateBaseMesh(cls, region, options):
'''
Generate the base bicubic Hermite mesh.
:param region: Zinc region to define model in. Must be empty.
:param options: Dict containing options. See getDefaultOptions().
:return: list of AnnotationGroup
'''
elementsCountUpNeck = options['Number of elements up neck']
elementsCountUpBody = options['Number of elements up body']
elementsCountAround = options['Number of elements around']
height = options['Height']
majorDiameter = options['Major diameter']
minorDiameter = options['Minor diameter']
radius = 0.5 * options['Urethra diameter']
bladderWallThickness = options['Bladder wall thickness']
useCrossDerivatives = options['Use cross derivatives']
elementsCountAroundOstium = options['Number of elements around ostium']
elementsCountAnnulusRadially = options['Number of elements radially on annulus']
ostiumPositionAround = options['Ostium position around']
ostiumPositionUp = options['Ostium position up']
ostiumOptions = options['Ureter']
ostiumDefaultOptions = ostiumOptions.getScaffoldSettings()
fm = region.getFieldmodule()
fm.beginChange()
coordinates = findOrCreateFieldCoordinates(fm)
cache = fm.createFieldcache()
mesh = fm.findMeshByDimension(3)
nodes = fm.findNodesetByFieldDomainType(Field.DOMAIN_TYPE_NODES)
nodetemplateApex = nodes.createNodetemplate()
nodetemplateApex.defineField(coordinates)
nodetemplateApex.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_VALUE, 1)
nodetemplateApex.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D_DS1, 1)
nodetemplateApex.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D_DS2, 1)
if useCrossDerivatives:
nodetemplate = nodes.createNodetemplate()
nodetemplate.defineField(coordinates)
nodetemplate.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_VALUE, 1)
nodetemplate.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D_DS1, 1)
nodetemplate.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D_DS2, 1)
nodetemplate.setValueNumberOfVersions(coordinates, -1, Node.VALUE_LABEL_D2_DS1DS2, 1)
else:
nodetemplate = nodetemplateApex
eftfactory = eftfactory_bicubichermitelinear(mesh, useCrossDerivatives)
eft = eftfactory.createEftBasic()
elementtemplate = mesh.createElementtemplate()
elementtemplate.setElementShapeType(Element.SHAPE_TYPE_CUBE)
elementtemplate.defineField(coordinates, -1, eft)
neckGroup = AnnotationGroup(region, get_bladder_term("neck of urinary bladder"))
bodyGroup = AnnotationGroup(region, get_bladder_term("dome of the bladder"))
urinaryBladderGroup = AnnotationGroup(region, get_bladder_term("urinary bladder"))
annotationGroups = [neckGroup, bodyGroup, urinaryBladderGroup]
neckMeshGroup = neckGroup.getMeshGroup(mesh)
bodyMeshGroup = bodyGroup.getMeshGroup(mesh)
urinaryBladderMeshGroup = urinaryBladderGroup.getMeshGroup(mesh)
# create nodes
# create neck of the bladder
nodeIdentifier = 1
radiansPerElementAround = 2.0*math.pi/elementsCountAround
radiansPerElementUpNeck = (math.pi/4)/elementsCountUpNeck
# create lower part of the ellipsoidal
neckHeight = height - height * math.cos(math.pi / 4)
ellipsoidal_x = []
ellipsoidal_d1 = []
ellipsoidal_d2 = []
for n2 in range(0, elementsCountUpNeck+1):
radiansUp = n2 * radiansPerElementUpNeck
cosRadiansUp = math.cos(radiansUp)
sinRadiansUp = math.sin(radiansUp)
majorRadius = 0.5 * majorDiameter * sinRadiansUp
minorRadius = 0.5 * minorDiameter * sinRadiansUp
if n2 == 0:
for n1 in range(elementsCountAround):
radiansAround = n1 * radiansPerElementAround
cosRadiansAround = math.cos(radiansAround)
sinRadiansAround = math.sin(radiansAround)
x = [
-majorRadius * sinRadiansAround,
minorRadius * cosRadiansAround,
-height - neckHeight
]
dx_ds1 = [
-majorRadius * cosRadiansAround * radiansPerElementAround,
minorRadius * -sinRadiansAround * radiansPerElementAround,
0.0
]
dx_ds2 = [
-0.5 * majorDiameter * sinRadiansAround * cosRadiansUp * radiansPerElementUpNeck,
0.5 * minorDiameter * cosRadiansAround * cosRadiansUp * radiansPerElementUpNeck,
height * sinRadiansUp * radiansPerElementUpNeck
]
ellipsoidal_x.append(x)
ellipsoidal_d1.append(dx_ds1)
ellipsoidal_d2.append(dx_ds2)
else:
for n1 in range(elementsCountAround):
neckHeight = height - height * math.cos(math.pi/4)
radiansAround = n1 * radiansPerElementAround
cosRadiansAround = math.cos(radiansAround)
sinRadiansAround = math.sin(radiansAround)
x = [
-majorRadius * sinRadiansAround,
minorRadius * cosRadiansAround,
-height - neckHeight + n2 * 2 * neckHeight / elementsCountUpNeck
]
dx_ds1 = [
-majorRadius * cosRadiansAround * radiansPerElementAround,
minorRadius * -sinRadiansAround * radiansPerElementAround,
0.0
]
dx_ds2 = [
-0.5 * majorDiameter * sinRadiansAround * cosRadiansUp * radiansPerElementUpNeck,
0.5 * minorDiameter * cosRadiansAround * cosRadiansUp * radiansPerElementUpNeck,
height * sinRadiansUp * radiansPerElementUpNeck
]
ellipsoidal_x.append(x)
ellipsoidal_d1.append(dx_ds1)
ellipsoidal_d2.append(dx_ds2)
# create tube nodes
radiansPerElementAround = 2.0 * math.pi / elementsCountAround
tube_x = []
tube_d1 = []
tube_d2 = []
for n2 in range(0, elementsCountUpNeck + 1):
radiansUp = n2 * radiansPerElementUpNeck
cosRadiansUp = math.cos(radiansUp)
sinRadiansUp = math.sin(radiansUp)
if n2 == 0:
for n1 in range(elementsCountAround):
radiansAround = n1 * radiansPerElementAround
cosRadiansAround = math.cos(radiansAround)
sinRadiansAround = math.sin(radiansAround)
x = [
-radius * sinRadiansAround,
radius * cosRadiansAround,
-height - neckHeight
]
dx_ds1 = [
-radiansPerElementAround * radius * cosRadiansAround,
radiansPerElementAround * radius * -sinRadiansAround,
0.0
]
dx_ds2 = [0, 0, height / (2 * elementsCountUpNeck)]
tube_x.append(x)
tube_d1.append(dx_ds1)
tube_d2.append(dx_ds2)
else:
for n1 in range(elementsCountAround):
neckHeight = height - height* math.cos(math.pi/4)
radiansAround = n1 * radiansPerElementAround
cosRadiansAround = math.cos(radiansAround)
sinRadiansAround = math.sin(radiansAround)
x = [
-radius * sinRadiansAround,
radius * cosRadiansAround,
-height - neckHeight + n2 * 2 * neckHeight / elementsCountUpNeck
]
dx_ds1 = [
-radiansPerElementAround * radius * cosRadiansAround,
radiansPerElementAround * radius * -sinRadiansAround,
0.0
]
dx_ds2 = [0, 0, height / elementsCountUpNeck]
tube_x.append(x)
tube_d1.append(dx_ds1)
tube_d2.append(dx_ds2)
# interpolation between the lower part of the ellipsoidal and the tube
m1 = 0
z_bottom = ellipsoidal_x[-1][2]
z_top = ellipsoidal_x[0][2]
delta_z = z_top - z_bottom
interpolatedNodes = []
interpolatedNodes_d1 = []
interpolatedNodes_d2 = []
for n2 in range(elementsCountUpNeck+1):
xi = 1.0 - (ellipsoidal_x[m1][2] - z_bottom) / delta_z
for n1 in range(elementsCountAround):
phi_inner, _, phi_outer, _ = getCubicHermiteBasis(xi)
x = [(phi_inner*tube_x[m1][c] + phi_outer*ellipsoidal_x[m1][c]) for c in range(3)]
d1 = [(phi_inner*tube_d1[m1][c] + phi_outer*ellipsoidal_d1[m1][c]) for c in range(3)]
d2 = [(phi_inner*tube_d2[m1][c] + phi_outer*ellipsoidal_d2[m1][c]) for c in range(3)]
interpolatedNodes.append(x)
interpolatedNodes_d1.append(d1)
interpolatedNodes_d2.append(d2)
m1 += 1
# smoothing the derivatives
sd2Raw = []
for n1 in range(elementsCountAround):
lineSmoothingNodes = []
lineSmoothingNodes_d2 = []
for n2 in range(elementsCountUpNeck+1):
lineSmoothingNodes.append(interpolatedNodes[n1 + n2 * elementsCountAround])
lineSmoothingNodes_d2.append(interpolatedNodes_d2[n1 + n2 * elementsCountAround])
sd2 = smoothCubicHermiteDerivativesLine(lineSmoothingNodes, lineSmoothingNodes_d2,
fixAllDirections=False,
fixStartDerivative=True, fixEndDerivative=True,
fixStartDirection=False, fixEndDirection=False)
sd2Raw.append(sd2)
# re-arrange the derivatives order
d2RearrangedList = []
for n2 in range(elementsCountUpNeck+1):
for n1 in range(elementsCountAround):
d2 = sd2Raw[n1][n2]
d2RearrangedList.append(d2)
# create tracksurface at the outer layer of the neck
nodesOnTrackSurface = []
nodesOnTrackSurface_d1 = []
nodesOnTrackSurface_d2 = []
for n2 in range(elementsCountUpNeck+1):
for n1 in range(elementsCountAround):
if (n1 <= elementsCountAround / 2):
nodesOnTrackSurface.append(interpolatedNodes[n2 * elementsCountAround + n1])
nodesOnTrackSurface_d1.append(interpolatedNodes_d1[n2 * elementsCountAround + n1])
nodesOnTrackSurface_d2.append(d2RearrangedList[n2 * elementsCountAround + n1])
# nodes and derivatives of the neck of the bladder
listOuterNeck_x = []
listOuterNeck_d1 = []
listOuterNeck_d2 = []
elementsCount1 = elementsCountAround // 2
elementsCount2 = elementsCountUpNeck
tracksurfaceOstium1 = TrackSurface(elementsCount1, elementsCount2, nodesOnTrackSurface, nodesOnTrackSurface_d1,
nodesOnTrackSurface_d2)
ostium1Position = tracksurfaceOstium1.createPositionProportion(ostiumPositionAround, ostiumPositionUp)
ostium1Position.xi1 = 1.0
ostium1Position.xi2 = 1.0
ostiumElementPositionAround = ostium1Position.e1
ostiumElementPositionUp = ostium1Position.e2
for n2 in range(len(interpolatedNodes)):
listOuterNeck_x.append(interpolatedNodes[n2])
listOuterNeck_d1.append(interpolatedNodes_d1[n2])
listOuterNeck_d2.append(d2RearrangedList[n2])
# create body of the bladder
radiansPerElementAround = 2.0 * math.pi / elementsCountAround
radiansPerElementUpBody = (3 * math.pi / 4) / elementsCountUpBody
# create regular rows
listOuterBody_x = []
listOuterBody_d1 = []
listOuterBody_d2 = []
for n2 in range(1, elementsCountUpBody):
radiansUp = (math.pi / 4) + n2 * radiansPerElementUpBody
cosRadiansUp = math.cos(radiansUp)
sinRadiansUp = math.sin(radiansUp)
majorRadius = 0.5 * majorDiameter * sinRadiansUp
minorRadius = 0.5 * minorDiameter * sinRadiansUp
for n1 in range(elementsCountAround):
radiansAround = n1 * radiansPerElementAround
cosRadiansAround = math.cos(radiansAround)
sinRadiansAround = math.sin(radiansAround)
x = [
-majorRadius * sinRadiansAround,
minorRadius * cosRadiansAround,
-height * cosRadiansUp
]
dx_ds1 = [
-majorRadius * cosRadiansAround * radiansPerElementAround,
minorRadius * -sinRadiansAround * radiansPerElementAround,
0.0
]
dx_ds2 = [
-0.5 * majorDiameter * sinRadiansAround * cosRadiansUp * radiansPerElementUpBody,
0.5 * minorDiameter * cosRadiansAround * cosRadiansUp * radiansPerElementUpBody,
height*sinRadiansUp * radiansPerElementUpBody
]
listOuterBody_x.append(x)
listOuterBody_d1.append(dx_ds1)
listOuterBody_d2.append(dx_ds2)
# create outer apex node
outerApexNode_x = []
outerApexNode_d1 = []
outerApexNode_d2 = []
x = [0.0, 0.0, height]
dx_ds1 = [height*radiansPerElementUpBody/2, 0.0, 0.0]
dx_ds2 = [0.0, height*radiansPerElementUpBody/2, 0.0]
outerApexNode_x.append(x)
outerApexNode_d1.append(dx_ds1)
outerApexNode_d2.append(dx_ds2)
# set nodes of outer layer of the bladder
listTotalOuter_x = listOuterNeck_x + listOuterBody_x + outerApexNode_x
listTotalOuter_d1 = listOuterNeck_d1 + listOuterBody_d1 + outerApexNode_d1
listTotalOuter_d2 = listOuterNeck_d2 + listOuterBody_d2 + outerApexNode_d2
outerLayer_x = []
outerLayer_d1 = []
outerLayer_d2 = []
for n2 in range(len(listTotalOuter_x)):
if (n2 != (ostiumElementPositionUp + 1) * elementsCountAround + ostiumElementPositionAround + 1) and\
(n2 != (ostiumElementPositionUp + 1) * elementsCountAround + elementsCountAround - ostiumElementPositionAround - 1):
node = nodes.createNode(nodeIdentifier, nodetemplate)
cache.setNode(node)
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_VALUE, 1, listTotalOuter_x[n2])
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS1, 1, listTotalOuter_d1[n2])
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS2, 1, listTotalOuter_d2[n2])
nodeIdentifier += 1
outerLayer_x.append(listTotalOuter_x[n2])
outerLayer_d1.append(listTotalOuter_d1[n2])
outerLayer_d2.append(listTotalOuter_d2[n2])
# create and set nodes of inner layer of the bladder
listTotalInner_x = []
listTotalInner_d1 = []
listTotalInner_d2 = []
for n2 in range(elementsCountUpNeck + elementsCountUpBody):
loop_x = [listTotalOuter_x[n2 * elementsCountAround + n1] for n1 in range(elementsCountAround)]
loop_d1 = [listTotalOuter_d1[n2 * elementsCountAround + n1] for n1 in range(elementsCountAround)]
loop_d2 = [listTotalOuter_d2[n2 * elementsCountAround + n1] for n1 in range(elementsCountAround)]
for n1 in range(elementsCountAround):
x, d1, _, _ = interp.projectHermiteCurvesThroughWall(loop_x, loop_d1, loop_d2, n1,
-bladderWallThickness, loop=True)
listTotalInner_x.append(x)
listTotalInner_d1.append(d1)
listInner_d2 = []
for n2 in range(elementsCountAround):
nx = [listTotalOuter_x[n1 * elementsCountAround + n2] for n1 in range(elementsCountUpNeck + elementsCountUpBody)]
nd1 = [listTotalOuter_d1[n1 * elementsCountAround + n2] for n1 in range(elementsCountUpNeck + elementsCountUpBody)]
nd2 = [listTotalOuter_d2[n1 * elementsCountAround + n2] for n1 in range(elementsCountUpNeck + elementsCountUpBody)]
for n1 in range(elementsCountUpNeck + elementsCountUpBody):
_, d2, _, _ = interp.projectHermiteCurvesThroughWall(nx, nd2, nd1, n1,
bladderWallThickness, loop=False)
listInner_d2.append(d2)
# re-arrange the derivatives order
for n2 in range(elementsCountUpNeck + elementsCountUpBody):
for n1 in range(elementsCountAround):
rearranged_d2 = listInner_d2[n1 * (elementsCountUpNeck + elementsCountUpBody) + n2]
listTotalInner_d2.append(rearranged_d2)
innerLayer_x = []
innerLayer_d1 = []
innerLayer_d2 = []
for n2 in range(len(listTotalInner_x)):
if (n2 != (ostiumElementPositionUp + 1) * elementsCountAround + ostiumElementPositionAround + 1) and \
(n2 != (ostiumElementPositionUp + 1) * elementsCountAround + elementsCountAround - ostiumElementPositionAround - 1):
node = nodes.createNode(nodeIdentifier, nodetemplate)
cache.setNode(node)
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_VALUE, 1, listTotalInner_x[n2])
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS1, 1, listTotalInner_d1[n2])
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS2, 1, listTotalInner_d2[n2])
nodeIdentifier += 1
innerLayer_x.append(listTotalInner_x[n2])
innerLayer_d1.append(listTotalInner_d1[n2])
innerLayer_d2.append(listTotalInner_d2[n2])
# create inner apex node
x = [0.0, 0.0, height - bladderWallThickness]
dx_ds1 = [height*radiansPerElementUpBody/2, 0.0, 0.0]
dx_ds2 = [0.0, height*radiansPerElementUpBody/2, 0.0]
node = nodes.createNode(nodeIdentifier, nodetemplate)
cache.setNode(node)
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_VALUE, 1, x)
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS1, 1, dx_ds1)
coordinates.setNodeParameters(cache, -1, Node.VALUE_LABEL_D_DS2, 1, dx_ds2)
listTotalInner_x.append(x)
listTotalInner_d1.append(dx_ds1)
listTotalInner_d2.append(dx_ds2)
innerLayer_x.append(x)
innerLayer_d1.append(dx_ds1)
innerLayer_d2.append(dx_ds2)
nodeIdentifier += 1
# create ureters on the surface
elementIdentifier = 1
# ureter 1
centerUreter1_x, centerUreter1_d1, centerUreter1_d2 = tracksurfaceOstium1.evaluateCoordinates(ostium1Position, derivatives=True)
td1, td2, td3 = calculate_surface_axes(centerUreter1_d1, centerUreter1_d2, [1.0, 0.0, 0.0])
m1 = ostiumElementPositionUp * elementsCountAround + ostiumElementPositionAround
ureter1StartCornerx = listOuterNeck_x[m1]
v1 = [(ureter1StartCornerx[c] - centerUreter1_x[c]) for c in range(3)]
ostium1Direction = vector.crossproduct3(td3, v1)
nodeIdentifier, elementIdentifier, (o1_x, o1_d1, o1_d2, _, o1_NodeId, o1_Positions) = \
generateOstiumMesh(region, ostiumDefaultOptions, tracksurfaceOstium1, ostium1Position, ostium1Direction,
startNodeIdentifier=nodeIdentifier, startElementIdentifier=elementIdentifier)
# ureter 2
tracksurfaceOstium2 = tracksurfaceOstium1.createMirrorX()
ostium2Position = TrackSurfacePosition(elementsCountAround - ostiumElementPositionAround, ostiumElementPositionUp - 1, 0.0, 1.0)
centerUreter2_x, centerUreter2_d1, centerUreter2_d2 = tracksurfaceOstium2.evaluateCoordinates(ostium2Position, derivatives =True)
ad1, ad2, ad3 = calculate_surface_axes(centerUreter2_d1, centerUreter2_d2, [1.0, 0.0, 0.0])
if elementsCountAroundOstium == 4:
m2 = ostiumElementPositionUp * elementsCountAround + elementsCountAround - ostiumElementPositionAround - 1
else:
m2 = ostiumElementPositionUp * elementsCountAround + elementsCountAround - ostiumElementPositionAround - 2
ureter2StartCornerx = listOuterNeck_x[m2]
v2 = [(ureter2StartCornerx[c] - centerUreter2_x[c]) for c in range(3)]
ostium2Direction = vector.crossproduct3(ad3, v2)
nodeIdentifier, elementIdentifier, (o2_x, o2_d1, o2_d2, _, o2_NodeId, o2_Positions) = \
generateOstiumMesh(region, ostiumDefaultOptions, tracksurfaceOstium2, ostium2Position, ostium2Direction,
startNodeIdentifier=nodeIdentifier, startElementIdentifier=elementIdentifier)
# create annulus mesh around ostium
endPoints1_x = [[None] * elementsCountAroundOstium, [None] * elementsCountAroundOstium]
endPoints1_d1 = [[None] * elementsCountAroundOstium, [None] * elementsCountAroundOstium]
endPoints1_d2 = [[None] * elementsCountAroundOstium, [None] * elementsCountAroundOstium]
endNode1_Id = [[None] * elementsCountAroundOstium, [None] * elementsCountAroundOstium]
endDerivativesMap = [[None] * elementsCountAroundOstium, [None] * elementsCountAroundOstium]
endPoints2_x = [[None] * elementsCountAroundOstium, [None] * elementsCountAroundOstium]
endPoints2_d1 = [[None] * elementsCountAroundOstium, [None] * elementsCountAroundOstium]
endPoints2_d2 = [[None] * elementsCountAroundOstium, [None] * elementsCountAroundOstium]
endNode2_Id = [[None] * elementsCountAroundOstium, [None] * elementsCountAroundOstium]
nodeCountsEachWallLayer = (elementsCountUpNeck + elementsCountUpBody) * elementsCountAround - 1
for n3 in range(2):
n1 = 0
endNode1_Id[n3][n1] = ((1 - n3) * nodeCountsEachWallLayer) + (ostiumElementPositionUp * elementsCountAround) + ostiumElementPositionAround + 1
endNode1_Id[n3][n1 + 1] = endNode1_Id[n3][n1] + elementsCountAround
endNode1_Id[n3][n1 + 2] = endNode1_Id[n3][n1 + 1] + elementsCountAround - 2
endNode1_Id[n3][n1 + 3] = endNode1_Id[n3][n1 + 2] + 1
endNode1_Id[n3][n1 + 4] = endNode1_Id[n3][n1 + 3] + 1
endNode1_Id[n3][n1 + 5] = endNode1_Id[n3][n1 + 1] + 1
endNode1_Id[n3][n1 + 6] = endNode1_Id[n3][n1] + 2
endNode1_Id[n3][n1 + 7] = endNode1_Id[n3][n1] + 1
if ostiumElementPositionAround == 0:
endNode2_Id[n3][n1] = ((1 - n3) * nodeCountsEachWallLayer) + (ostiumElementPositionUp * elementsCountAround)\
+ elementsCountAround - ostiumElementPositionAround - 1
endNode2_Id[n3][n1 + 1] = endNode2_Id[n3][n1] + elementsCountAround - 1
endNode2_Id[n3][n1 + 2] = endNode2_Id[n3][n1 + 1] + elementsCountAround - 1
endNode2_Id[n3][n1 + 3] = endNode2_Id[n3][n1 + 2] + 1
endNode2_Id[n3][n1 + 4] = endNode2_Id[n3][n1 + 3] - elementsCountAround + 1
endNode2_Id[n3][n1 + 5] = endNode2_Id[n3][n1 + 4] - elementsCountAround + 2
endNode2_Id[n3][n1 + 6] = endNode2_Id[n3][n1 + 5] - elementsCountAround
endNode2_Id[n3][n1 + 7] = endNode2_Id[n3][n1] + 1
else:
endNode2_Id[n3][n1] = ((1 - n3) * nodeCountsEachWallLayer) + (ostiumElementPositionUp * elementsCountAround)\
+ elementsCountAround - ostiumElementPositionAround - 1
endNode2_Id[n3][n1 + 1] = endNode2_Id[n3][n1] + elementsCountAround - 1
endNode2_Id[n3][n1 + 2] = endNode2_Id[n3][n1 + 1] + elementsCountAround - 1
endNode2_Id[n3][n1 + 3] = endNode2_Id[n3][n1 + 2] + 1
endNode2_Id[n3][n1 + 4] = endNode2_Id[n3][n1 + 3] + 1
endNode2_Id[n3][n1 + 5] = endNode2_Id[n3][n1 + 1] + 1
endNode2_Id[n3][n1 + 6] = endNode2_Id[n3][n1] + 2
endNode2_Id[n3][n1 + 7] = endNode2_Id[n3][n1] + 1
for n3 in range(2):
for n1 in range(elementsCountAroundOstium):
nc1 = endNode1_Id[n3][n1] - (1 - n3) * nodeCountsEachWallLayer - 1
endPoints1_x[n3][n1] = innerLayer_x[nc1]
endPoints1_d1[n3][n1] = innerLayer_d1[nc1]
endPoints1_d2[n3][n1] = [innerLayer_d2[nc1][c] for c in range(3)]
nc2 = endNode2_Id[n3][n1] - (1 - n3) * nodeCountsEachWallLayer - 1
endPoints2_x[n3][n1] = innerLayer_x[nc2]
endPoints2_d1[n3][n1] = innerLayer_d1[nc2]
endPoints2_d2[n3][n1] = innerLayer_d2[nc2]
for n1 in range(elementsCountAroundOstium):
if n1 == 0:
endDerivativesMap[0][n1] = ((-1, 0, 0), (-1, -1, 0), None, (0, 1, 0))
endDerivativesMap[1][n1] = ((-1, 0, 0), (-1, -1, 0), None, (0, 1, 0))
elif n1 == 1:
endDerivativesMap[0][n1] = ((0, 1, 0), (-1, 0, 0), None)
endDerivativesMap[1][n1] = ((0, 1, 0), (-1, 0, 0), None)
elif n1 == 2:
endDerivativesMap[0][n1] = ((0, 1, 0), (-1, 1, 0), None, (1, 0, 0))
endDerivativesMap[1][n1] = ((0, 1, 0), (-1, 1, 0), None, (1, 0, 0))
elif n1 == 3:
endDerivativesMap[0][n1] = ((1, 0, 0), (0, 1, 0), None)
endDerivativesMap[1][n1] = ((1, 0, 0), (0, 1, 0), None)
elif n1 == 4:
endDerivativesMap[0][n1] = ((1, 0, 0), (1, 1, 0), None, (0, -1, 0))
endDerivativesMap[1][n1] = ((1, 0, 0), (1, 1, 0), None, (0, -1, 0))
elif n1 == 5:
endDerivativesMap[0][n1] = ((0, -1, 0), (1, 0, 0), None)
endDerivativesMap[1][n1] = ((0, -1, 0), (1, 0, 0), None)
elif n1 == 6:
endDerivativesMap[0][n1] = ((0, -1, 0), (1, -1, 0), None, (-1, 0, 0))
endDerivativesMap[1][n1] = ((0, -1, 0), (1, -1, 0), None, (-1, 0, 0))
else:
endDerivativesMap[0][n1] = ((-1, 0, 0), (0, -1, 0), None)
endDerivativesMap[1][n1] = ((-1, 0, 0), (0, -1, 0), None)
nodeIdentifier, elementIdentifier = createAnnulusMesh3d(
nodes, mesh, nodeIdentifier, elementIdentifier,
o1_x, o1_d1, o1_d2, None, o1_NodeId, None,
endPoints1_x, endPoints1_d1, endPoints1_d2, None, endNode1_Id, endDerivativesMap,
elementsCountRadial=elementsCountAnnulusRadially, meshGroups=[neckMeshGroup, urinaryBladderMeshGroup])
nodeIdentifier, elementIdentifier = createAnnulusMesh3d(
nodes, mesh, nodeIdentifier, elementIdentifier,
o2_x, o2_d1, o2_d2, None, o2_NodeId, None,
endPoints2_x, endPoints2_d1, endPoints2_d2, None, endNode2_Id, endDerivativesMap,
elementsCountRadial=elementsCountAnnulusRadially, meshGroups=[neckMeshGroup, urinaryBladderMeshGroup])
# create elements
for e3 in range(1):
newl = (e3 + 1) * ((elementsCountUpNeck + elementsCountUpBody) * elementsCountAround - 1)
# create bladder neck elements
for e2 in range(elementsCountUpNeck):
for e1 in range(elementsCountAround):
if e2 == ostiumElementPositionUp:
if (e1 == ostiumElementPositionAround or e1 == ostiumElementPositionAround + 1):
pass
elif (e1 == elementsCountAround - ostiumElementPositionAround - 2 or e1 == elementsCountAround - 1 - ostiumElementPositionAround):
pass
else:
bni1 = e2 * elementsCountAround + e1 + 1
bni2 = e2 * elementsCountAround + (e1 + 1) % elementsCountAround + 1
if e1 < ostiumElementPositionAround:
bni3 = bni1 + elementsCountAround
bni4 = bni2 + elementsCountAround
elif (ostiumElementPositionAround + 1 < e1 < elementsCountAround - ostiumElementPositionAround - 2):
bni3 = bni1 + elementsCountAround - 1
bni4 = bni2 + elementsCountAround - 1
elif e1 > elementsCountAround - ostiumElementPositionAround - 1:
bni3 = bni1 + elementsCountAround - 2
if e1 == elementsCountAround - 1:
bni4 = bni2 + elementsCountAround
else:
bni4 = bni2 + elementsCountAround - 2
element = mesh.createElement(elementIdentifier, elementtemplate)
nodeIdentifiers = [bni1 + newl, bni2 + newl, bni3 + newl, bni4 + newl,
bni1, bni2, bni3, bni4]
result = element.setNodesByIdentifier(eft, nodeIdentifiers)
neckMeshGroup.addElement(element)
urinaryBladderMeshGroup.addElement(element)
elementIdentifier += 1
elif e2 == ostiumElementPositionUp + 1:
if (e1 == ostiumElementPositionAround or e1 == ostiumElementPositionAround + 1):
pass
elif (e1 == elementsCountAround - ostiumElementPositionAround - 2 or e1 == elementsCountAround - 1 - ostiumElementPositionAround):
pass
else:
if e1 < ostiumElementPositionAround:
bni1 = e2 * elementsCountAround + e1 + 1
bni2 = e2 * elementsCountAround + (e1 + 1) % elementsCountAround + 1
bni3 = bni1 + elementsCountAround - 2
bni4 = bni2 + elementsCountAround - 2
elif (ostiumElementPositionAround + 1 < e1 < elementsCountAround - ostiumElementPositionAround - 2):
bni1 = e2 * elementsCountAround + e1
bni2 = e2 * elementsCountAround + (e1 + 1) % elementsCountAround
bni3 = bni1 + elementsCountAround - 1
bni4 = bni2 + elementsCountAround - 1
elif e1 > elementsCountAround - ostiumElementPositionAround - 1:
bni1 = e2 * elementsCountAround + e1 - 1
bni3 = bni1 + elementsCountAround
if e1 == elementsCountAround - 1:
bni2 = e2 * elementsCountAround + (e1 + 1) % elementsCountAround + 1
bni4 = bni2 + elementsCountAround - 2
else:
bni2 = e2 * elementsCountAround + (e1 + 1) % elementsCountAround - 1
bni4 = bni2 + elementsCountAround
element = mesh.createElement(elementIdentifier, elementtemplate)
nodeIdentifiers = [bni1 + newl, bni2 + newl, bni3 + newl, bni4 + newl,
bni1, bni2, bni3, bni4]
result = element.setNodesByIdentifier(eft, nodeIdentifiers)
neckMeshGroup.addElement(element)
urinaryBladderMeshGroup.addElement(element)
elementIdentifier += 1
elif e2 > ostiumElementPositionUp + 1:
element = mesh.createElement(elementIdentifier, elementtemplate)
bni1 = e2 * elementsCountAround + e1 - 1
bni2 = e2 * elementsCountAround + (e1 + 1) % elementsCountAround - 1
bni3 = bni1 + elementsCountAround
bni4 = bni2 + elementsCountAround
nodeIdentifiers = [bni1 + newl, bni2 + newl, bni3 + newl, bni4 + newl,
bni1, bni2, bni3, bni4]
result = element.setNodesByIdentifier(eft, nodeIdentifiers)
neckMeshGroup.addElement(element)
urinaryBladderMeshGroup.addElement(element)
elementIdentifier += 1
else:
element = mesh.createElement(elementIdentifier, elementtemplate)
bni1 = e2 * elementsCountAround + e1 + 1
bni2 = e2 * elementsCountAround + (e1 + 1) % elementsCountAround + 1
bni3 = bni1 + elementsCountAround
bni4 = bni2 + elementsCountAround
nodeIdentifiers = [bni1 + newl, bni2 + newl, bni3 + newl, bni4 + newl,
bni1, bni2, bni3, bni4]
result = element.setNodesByIdentifier(eft, nodeIdentifiers)
neckMeshGroup.addElement(element)
urinaryBladderMeshGroup.addElement(element)
elementIdentifier += 1
# create bladder body elements
for e2 in range(elementsCountUpNeck, (elementsCountUpNeck + elementsCountUpBody - 1)):
for e1 in range(elementsCountAround):
element = mesh.createElement(elementIdentifier, elementtemplate)
bni1 = e2 * elementsCountAround + e1 - 1
bni2 = e2 * elementsCountAround + (e1 + 1) % elementsCountAround - 1
bni3 = bni1 + elementsCountAround
bni4 = bni2 + elementsCountAround
nodeIdentifiers = [bni1 + newl, bni2 + newl, bni3 + newl, bni4 + newl,
bni1, bni2, bni3, bni4]
result = element.setNodesByIdentifier(eft, nodeIdentifiers)
bodyMeshGroup.addElement(element)
urinaryBladderMeshGroup.addElement(element)
elementIdentifier += 1
# create apex elements
bni3 = (elementsCountUpNeck + elementsCountUpBody) * elementsCountAround - 1
elementtemplateApex = mesh.createElementtemplate()
elementtemplateApex.setElementShapeType(Element.SHAPE_TYPE_CUBE)
for e1 in range(elementsCountAround):
va = e1
vb = (e1 + 1) % elementsCountAround
eftApex = eftfactory.createEftShellPoleTop(va, vb)
elementtemplateApex.defineField(coordinates, -1, eftApex)
# redefine field in template for changes to eftApex:
element = mesh.createElement(elementIdentifier, elementtemplateApex)
bni1 = bni3 - elementsCountAround + e1
bni2 = bni3 - elementsCountAround + (e1 + 1) % elementsCountAround
nodeIdentifiers = [bni1 + newl, bni2 + newl, bni3 + newl, bni1, bni2, bni3]
result = element.setNodesByIdentifier(eftApex, nodeIdentifiers)
bodyMeshGroup.addElement(element)
urinaryBladderMeshGroup.addElement(element)
elementIdentifier += 1
fm.endChange()
return annotationGroups
def generateBaseMesh(cls, region, options):
"""
Generate the base tricubic Hermite mesh. See also generateMesh().
:param region: Zinc region to define model in. Must be empty.
:param options: Dict containing options. See getDefaultOptions().
:return: annotationGroups
"""
centralPath = options['Central path']
segmentCount = options['Number of segments']
elementsCountAround = options['Number of elements around']
elementsCountAlongSegment = options['Number of elements along segment']
elementsCountThroughWall = options['Number of elements through wall']
duodenumLength = options['Duodenum length']
jejunumLength = options['Jejunum length']
duodenumInnerRadius = options['Duodenum inner radius']
duodenumJejunumInnerRadius = options['Duodenum-jejunum inner radius']
jejunumIleumInnerRadius = options['Jejunum-ileum inner radius']
ileumInnerRadius = options['Ileum inner radius']
wallThickness = options['Wall thickness']
useCrossDerivatives = options['Use cross derivatives']
useCubicHermiteThroughWall = not(options['Use linear through wall'])
elementsCountAlong = int(elementsCountAlongSegment*segmentCount)
startPhase = 0.0
firstNodeIdentifier = 1
firstElementIdentifier = 1
# Central path
tmpRegion = region.createRegion()
centralPath.generate(tmpRegion)
cx, cd1, cd2, cd12 = extractPathParametersFromRegion(tmpRegion)
# for i in range(len(cx)):
# print(i, '[', cx[i], ',', cd1[i], ',', cd2[i],',', cd12[i], '],')
del tmpRegion
# find arclength of colon
length = 0.0
elementsCountIn = len(cx) - 1
sd1 = interp.smoothCubicHermiteDerivativesLine(cx, cd1, fixAllDirections = True,
magnitudeScalingMode = interp.DerivativeScalingMode.HARMONIC_MEAN)
for e in range(elementsCountIn):
arcLength = interp.getCubicHermiteArcLength(cx[e], sd1[e], cx[e + 1], sd1[e + 1])
# print(e+1, arcLength)
length += arcLength
segmentLength = length / segmentCount
elementAlongLength = length / elementsCountAlong
# print('Length = ', length)
# Sample central path
sx, sd1, se, sxi, ssf = interp.sampleCubicHermiteCurves(cx, cd1, elementsCountAlongSegment*segmentCount)
sd2, sd12 = interp.interpolateSampleCubicHermite(cd2, cd12, se, sxi, ssf)
# Generate variation of radius & tc width along length
lengthList = [0.0, duodenumLength, duodenumLength + jejunumLength, length]
innerRadiusList = [duodenumInnerRadius, duodenumJejunumInnerRadius, jejunumIleumInnerRadius, ileumInnerRadius]
innerRadiusSegmentList, dInnerRadiusSegmentList = interp.sampleParameterAlongLine(lengthList, innerRadiusList,
segmentCount)
# Create annotation groups for small intestine sections
elementsAlongDuodenum = round(duodenumLength / elementAlongLength)
elementsAlongJejunum = round(jejunumLength / elementAlongLength)
elementsAlongIleum = elementsCountAlong - elementsAlongDuodenum - elementsAlongJejunum
elementsCountAlongGroups = [elementsAlongDuodenum, elementsAlongJejunum, elementsAlongIleum]
smallintestineGroup = AnnotationGroup(region, get_smallintestine_term("small intestine"))
duodenumGroup = AnnotationGroup(region, get_smallintestine_term("duodenum"))
jejunumGroup = AnnotationGroup(region, get_smallintestine_term("jejunum"))
ileumGroup = AnnotationGroup(region, get_smallintestine_term("ileum"))
annotationGroupAlong = [[smallintestineGroup, duodenumGroup],
[smallintestineGroup, jejunumGroup],
[smallintestineGroup, ileumGroup]]
annotationGroupsAlong = []
for i in range(len(elementsCountAlongGroups)):
elementsCount = elementsCountAlongGroups[i]
for n in range(elementsCount):
annotationGroupsAlong.append(annotationGroupAlong[i])
annotationGroupsAround = []
for i in range(elementsCountAround):
annotationGroupsAround.append([ ])
annotationGroupsThroughWall = []
for i in range(elementsCountThroughWall):
annotationGroupsThroughWall.append([ ])
xExtrude = []
d1Extrude = []
d2Extrude = []
d3UnitExtrude = []
# Create object
smallIntestineSegmentTubeMeshInnerPoints = CylindricalSegmentTubeMeshInnerPoints(
elementsCountAround, elementsCountAlongSegment, segmentLength,
wallThickness, innerRadiusSegmentList, dInnerRadiusSegmentList, startPhase)
for nSegment in range(segmentCount):
# Create inner points
xInner, d1Inner, d2Inner, transitElementList, segmentAxis, radiusAlongSegmentList = \
smallIntestineSegmentTubeMeshInnerPoints.getCylindricalSegmentTubeMeshInnerPoints(nSegment)
# Project reference point for warping onto central path
start = nSegment*elementsCountAlongSegment
end = (nSegment + 1)*elementsCountAlongSegment + 1
sxRefList, sd1RefList, sd2ProjectedListRef, zRefList = \
tubemesh.getPlaneProjectionOnCentralPath(xInner, elementsCountAround, elementsCountAlongSegment,
segmentLength, sx[start:end], sd1[start:end], sd2[start:end],
sd12[start:end])
# Warp segment points
xWarpedList, d1WarpedList, d2WarpedList, d3WarpedUnitList = tubemesh.warpSegmentPoints(
xInner, d1Inner, d2Inner, segmentAxis, sxRefList, sd1RefList, sd2ProjectedListRef,
elementsCountAround, elementsCountAlongSegment, zRefList, radiusAlongSegmentList,
closedProximalEnd=False)
# Store points along length
xExtrude = xExtrude + (xWarpedList if nSegment == 0 else xWarpedList[elementsCountAround:])
d1Extrude = d1Extrude + (d1WarpedList if nSegment == 0 else d1WarpedList[elementsCountAround:])
# Smooth d2 for nodes between segments and recalculate d3
if nSegment == 0:
d2Extrude = d2Extrude + (d2WarpedList[:-elementsCountAround])
d3UnitExtrude = d3UnitExtrude + (d3WarpedUnitList[:-elementsCountAround])
else:
xSecondFace = xWarpedList[elementsCountAround:elementsCountAround*2]
d2SecondFace = d2WarpedList[elementsCountAround:elementsCountAround*2]
for n1 in range(elementsCountAround):
nx = [xLastTwoFaces[n1], xLastTwoFaces[n1 + elementsCountAround], xSecondFace[n1]]
nd2 = [d2LastTwoFaces[n1], d2LastTwoFaces[n1 + elementsCountAround], d2SecondFace[n1]]
d2 = interp.smoothCubicHermiteDerivativesLine(nx, nd2, fixStartDerivative = True,
fixEndDerivative = True)[1]
d2Extrude.append(d2)
d3Unit = vector.normalise(vector.crossproduct3(vector.normalise(d1LastTwoFaces[n1 + elementsCountAround]),
vector.normalise(d2)))
d3UnitExtrude.append(d3Unit)
d2Extrude = d2Extrude + \
(d2WarpedList[elementsCountAround:-elementsCountAround] if nSegment < segmentCount - 1 else
d2WarpedList[elementsCountAround:])
d3UnitExtrude = d3UnitExtrude + \
(d3WarpedUnitList[elementsCountAround:-elementsCountAround] if nSegment < segmentCount - 1 else
d3WarpedUnitList[elementsCountAround:])
xLastTwoFaces = xWarpedList[-elementsCountAround*2:]
d1LastTwoFaces = d1WarpedList[-elementsCountAround*2:]
d2LastTwoFaces = d2WarpedList[-elementsCountAround*2:]
# Create coordinates and derivatives
xList, d1List, d2List, d3List, curvatureList = tubemesh.getCoordinatesFromInner(xExtrude, d1Extrude,
d2Extrude, d3UnitExtrude, [wallThickness]*(elementsCountAlong+1),
elementsCountAround, elementsCountAlong, elementsCountThroughWall, transitElementList)
flatWidthList, xiList = smallIntestineSegmentTubeMeshInnerPoints.getFlatWidthAndXiList()
# Create flat and texture coordinates
xFlat, d1Flat, d2Flat, xTexture, d1Texture, d2Texture = tubemesh.createFlatAndTextureCoordinates(
xiList, flatWidthList, length, wallThickness, elementsCountAround,
elementsCountAlong, elementsCountThroughWall, transitElementList)
# Create nodes and elements
nextNodeIdentifier, nextElementIdentifier, annotationGroups = tubemesh.createNodesAndElements(
region, xList, d1List, d2List, d3List, xFlat, d1Flat, d2Flat, xTexture, d1Texture, d2Texture,
elementsCountAround, elementsCountAlong, elementsCountThroughWall,
annotationGroupsAround, annotationGroupsAlong, annotationGroupsThroughWall,
firstNodeIdentifier, firstElementIdentifier, useCubicHermiteThroughWall, useCrossDerivatives,
closedProximalEnd=False)
return annotationGroups
def createHermiteCurvePoints(self,
aProportion1,
aProportion2,
bProportion1,
bProportion2,
elementsCount,
derivativeStart=None,
derivativeEnd=None,
curveMode=HermiteCurveMode.SMOOTH):
'''
Create hermite curve points between two points a and b on the surface, each defined
by their proportions over the surface in directions 1 and 2.
Also returns cross direction 2 in plane of surface with similar magnitude to curve derivative 1,
and unit surface normals.
:param derivativeStart, derivativeEnd: Optional derivative vectors in 3-D world coordinates
to match at the start and end of the curves. If omitted, fits in with other derivative or is
in a straight line from a to b.
:param elementsCount: Number of elements out.
:return: nx[], nd1[], nd2[], nd3[], nProportions[]
'''
#print('createHermiteCurvePoints', aProportion1, aProportion2, bProportion1, bProportion2, elementsCount, derivativeStart, derivativeEnd)
if derivativeStart:
position = self.createPositionProportion(aProportion1,
aProportion2)
_, sd1, sd2 = self.evaluateCoordinates(position, derivatives=True)
delta_xi1, delta_xi2 = calculate_surface_delta_xi(
sd1, sd2, derivativeStart)
dp1Start = delta_xi1 / self.elementsCount1
if self.loop1:
dp1Start *= 2.0
dp2Start = delta_xi2 / self.elementsCount2
derivativeMagnitudeStart = math.sqrt(dp1Start * dp1Start +
dp2Start * dp2Start)
dp1Start *= elementsCount
dp2Start *= elementsCount
#print('start delta_xi1', delta_xi1, 'delta_xi2', delta_xi2)
#print('dp1Start', dp1Start, 'dp2Start', dp2Start)
if derivativeEnd:
position = self.createPositionProportion(bProportion1,
bProportion2)
_, sd1, sd2 = self.evaluateCoordinates(position, derivatives=True)
delta_xi1, delta_xi2 = calculate_surface_delta_xi(
sd1, sd2, derivativeEnd)
dp1End = delta_xi1 / self.elementsCount1
dp2End = delta_xi2 / self.elementsCount2
derivativeMagnitudeEnd = math.sqrt(dp1End * dp1End +
dp2End * dp2End)
dp1End *= elementsCount
if self.loop1:
dp1End *= 2.0
dp2End *= elementsCount
#print('end delta_xi1', delta_xi1, 'delta_xi2', delta_xi2)
#print('dp1End', dp1End, 'dp2End', dp2End)
if not derivativeStart:
if derivativeEnd:
dp1Start, dp2Start = interp.interpolateLagrangeHermiteDerivative(
[aProportion1, aProportion2], [bProportion1, bProportion2],
[dp1End, dp2End], 0.0)
else:
dp1Start = bProportion1 - aProportion1
dp2Start = bProportion2 - aProportion2
derivativeMagnitudeStart = math.sqrt(
dp1Start * dp1Start + dp2Start * dp2Start) / elementsCount
if not derivativeEnd:
if derivativeStart:
dp1End, dp2End = interp.interpolateHermiteLagrangeDerivative(
[aProportion1, aProportion2], [dp1Start, dp2Start],
[bProportion1, bProportion2], 1.0)
else:
dp1End = bProportion1 - aProportion1
dp2End = bProportion2 - aProportion2
derivativeMagnitudeEnd = math.sqrt(dp1End * dp1End +
dp2End * dp2End) / elementsCount
maxProportion1 = 2.0 if self.loop1 else 1.0
#print('derivativeMagnitudeStart', derivativeMagnitudeStart, 'derivativeMagnitudeEnd', derivativeMagnitudeEnd)
proportions, dproportions = interp.sampleCubicHermiteCurvesSmooth([ [ aProportion1, aProportion2 ], [ bProportion1, bProportion2 ] ], \
[ [ dp1Start, dp2Start ], [ dp1End, dp2End ] ], elementsCount, derivativeMagnitudeStart, derivativeMagnitudeEnd)[0:2]
if curveMode != self.HermiteCurveMode.SMOOTH:
if derivativeStart and (curveMode in [
self.HermiteCurveMode.TRANSITION_START,
self.HermiteCurveMode.TRANSITION_START_AND_END
]):
addLengthStart = 0.5 * derivativeMagnitudeStart
lengthFractionStart = 0.5
else:
addLengthStart = 0.0
lengthFractionStart = 1.0
if derivativeEnd and (curveMode in [
self.HermiteCurveMode.TRANSITION_END,
self.HermiteCurveMode.TRANSITION_START_AND_END
]):
addLengthEnd = 0.5 * derivativeMagnitudeEnd
lengthFractionEnd = 0.5
else:
addLengthEnd = 0.0
lengthFractionEnd = 1.0
proportions, dproportions = interp.sampleCubicHermiteCurves(
proportions, dproportions, elementsCount, addLengthStart,
addLengthEnd, lengthFractionStart, lengthFractionEnd)[0:2]
#print(' proportions', proportions)
#print('dproportions', dproportions)
nx = []
nd1 = []
nd2 = []
nd3 = []
for n in range(0, elementsCount + 1):
position = self.createPositionProportion(proportions[n][0],
proportions[n][1])
x, sd1, sd2 = self.evaluateCoordinates(position, derivatives=True)
f1 = dproportions[n][0] * self.elementsCount1 / maxProportion1
f2 = dproportions[n][1] * self.elementsCount2
d1 = [(f1 * sd1[c] + f2 * sd2[c]) for c in range(3)]
d3 = vector.crossproduct3(sd1, sd2)
# handle zero magnitude of d3
mag = math.sqrt(sum(d3[c] * d3[c] for c in range(3)))
if mag > 0.0:
d3 = [(d3[c] / mag) for c in range(3)]
d2 = vector.crossproduct3(d3, d1)
nx.append(x)
nd2.append(d2)
nd1.append(d1)
nd3.append(d3)
#print('createHermiteCurvePoints end \n nx', nx,'\nnd1',nd1,'\nnd2',nd2,'\nnd3',nd3)
return nx, nd1, nd2, nd3, proportions
def createAnnulusMesh3d(nodes,
mesh,
nextNodeIdentifier,
nextElementIdentifier,
startPointsx,
startPointsd1,
startPointsd2,
startPointsd3,
startNodeId,
startDerivativesMap,
endPointsx,
endPointsd1,
endPointsd2,
endPointsd3,
endNodeId,
endDerivativesMap,
forceStartLinearXi3=False,
forceMidLinearXi3=False,
forceEndLinearXi3=False,
maxStartThickness=None,
maxEndThickness=None,
useCrossDerivatives=False,
elementsCountRadial=1,
meshGroups=None,
wallAnnotationGroups=None,
tracksurface=None,
startProportions=None,
endProportions=None,
rescaleStartDerivatives=False,
rescaleEndDerivatives=False,
sampleBlend=0.0):
"""
Create an annulus mesh from a loop of start points/nodes with specified derivative mappings to
a loop of end points/nodes with specified derivative mappings.
Derivative d3 is through the wall. Currently limited to single element layer through wall.
Points/nodes order cycles fastest around the annulus, then through the wall.
Note doesn't support cross derivatives.
Arrays are indexed by n3 (node through wall, size 2), n2 (node along/radial), n1 (node around, variable size)
and coordinate component c.
:param nodes: The nodeset to create nodes in.
:param mesh: The mesh to create elements in.
:param nextNodeIdentifier, nextElementIdentifier: Next identifiers to use and increment.
:param startPointsx, startPointsd1, startPointsd2, startPointsd3, endPointsx, endPointsd1, endPointsd2, endPointsd3:
List array[n3][n1][c] or start/point coordinates and derivatives. To linearise through the wall, pass None to
d3. If both ends are linear through the wall, interior points are linear through the wall.
:param startNodeId, endNodeId: List array [n3][n1] of existing node identifiers to use at start/end. Pass None for
argument if no nodes are specified at end. These arguments are 'all or nothing'.
:param startDerivativesMap, endDerivativesMap: List array[n3][n1] of mappings for d/dxi1, d/dxi2, d/dxi3 at
start/end of form:
( (1, -1, 0), (1, 0, 0), None ) where the first tuple means d/dxi1 = d/ds1 - d/ds2. Only 0, 1 and -1 may be
used.
None means use default e.g. d/dxi2 = d/ds2.
Pass None for the entire argument to use the defaults d/dxi1 = d/ds1, d/dxi2 = d/ds2, d/dxi3 = d/ds3.
Pass a 4th mapping to apply to d/dxi1 on other side of node; if not supplied first mapping applies both sides.
:param forceStartLinearXi3, forceMidLinearXi3, forceEndLinearXi3: Force start, middle or
end elements to be linear through the wall, even if d3 is supplied at either end.
Can only use forceMidLinearXi3 only if at least one end is linear in d3.
:param maxStartThickness, maxEndThickness: Optional maximum override on start/end thicknesses.
:param useCrossDerivatives: May only be True if no derivatives maps are in use.
:param elementsCountRadial: Optional number of elements in radial direction between start and end.
:param meshGroups: Optional sequence of Zinc MeshGroup for adding all new elements to, or a sequence of
length elementsCountRadial containing sequences of mesh groups to add rows of radial elements to
from start to end.
:param wallAnnotationGroups: Annotation groups for adding all new elements to a sequence
of groups to add to elements through wall.
:param tracksurface: Description for outer surface representation used for creating annulus mesh. Provides
information for creating radial nodes on annulus that sit on tracksurface. Need startProportions and endProportions
to work.
:param startProportions: Proportion around and along of startPoints on tracksurface. These vary with nodes
around as for startPoints. Values only given for tracksurface for outer layer (xi3 == 1).
:param endProportions: Proportion around and along of endPoints on track surface. These vary with nodes
around as for endPoints. Values only given for tracksurface for outer layer (xi3 == 1).
:param rescaleStartDerivatives, rescaleEndDerivatives: Optional flags to compute and multiply additional scale
factors on start, end or both radial derivatives to fit arc length, needed if derivatives are of the wrong scale
for the radial distances and the chosen elementsCountRadial. If either is True, derivatives and sampled radial
nodes are spaced for a gradual change of derivative from that at the other end. If both are True, scaling is set to
give even sampling and arclength derivatives.
:param sampleBlend: Real value varying from 0.0 to 1.0 controlling weighting of start and end
derivatives when interpolating extra points in-between, where 0.0 = sample with equal end derivatives,
and 1.0 = proportional to current magnitudes, interpolated in between.
:return: Final values of nextNodeIdentifier, nextElementIdentifier
"""
assert (elementsCountRadial >=
1), 'createAnnulusMesh3d: Invalid number of radial elements'
startLinearXi3 = (not startPointsd3) or forceStartLinearXi3
endLinearXi3 = (not endPointsd3) or forceEndLinearXi3
midLinearXi3 = (startLinearXi3 and endLinearXi3) or (
(startLinearXi3 or endLinearXi3) and forceMidLinearXi3)
# get list whether each row of nodes in elements is linear in Xi3
# this is for element use; start/end nodes may have d3 even if element is linear
rowLinearXi3 = [
startLinearXi3
] + [midLinearXi3] * (elementsCountRadial - 1) + [endLinearXi3]
assert (not useCrossDerivatives) or ((not startDerivativesMap) and (not endDerivativesMap)), \
'createAnnulusMesh3d: Cannot use cross derivatives with derivatives map'
nodesCountWall = len(startPointsx)
assert (len(startPointsd1) == nodesCountWall) and (len(startPointsd2) == nodesCountWall) and \
(startLinearXi3 or (len(startPointsd3) == nodesCountWall)) and \
(len(endPointsx) == nodesCountWall) and (len(endPointsd1) == nodesCountWall) and \
(len(endPointsd2) == nodesCountWall) and (endLinearXi3 or (len(endPointsd3) == nodesCountWall)) and \
((startNodeId is None) or (len(startNodeId) == nodesCountWall)) and \
((endNodeId is None) or (len(endNodeId) == nodesCountWall)) and \
((startDerivativesMap is None) or (len(startDerivativesMap) == nodesCountWall)) and \
((endDerivativesMap is None) or (len(endDerivativesMap) == nodesCountWall)),\
'createAnnulusMesh3d: Mismatch in number of layers through wall'
elementsCountAround = nodesCountAround = len(startPointsx[0])
assert (
nodesCountAround > 1
), 'createAnnulusMesh3d: Invalid number of points/nodes around annulus'
for n3 in range(nodesCountWall):
assert (len(startPointsx[n3]) == nodesCountAround) and (len(startPointsd1[n3]) == nodesCountAround) and \
(len(startPointsd2[n3]) == nodesCountAround) and \
(startLinearXi3 or (len(startPointsd3[n3]) == nodesCountAround)) and\
(len(endPointsx[n3]) == nodesCountAround) and (len(endPointsd1[n3]) == nodesCountAround) and \
(len(endPointsd2[n3]) == nodesCountAround) and \
(endLinearXi3 or (len(endPointsd3[n3]) == nodesCountAround)) and \
((startNodeId is None) or (len(startNodeId[n3]) == nodesCountAround)) and\
((endNodeId is None) or (len(endNodeId[n3]) == nodesCountAround)) and \
((startDerivativesMap is None) or (len(startDerivativesMap[n3]) == nodesCountAround)) and \
((endDerivativesMap is None) or (len(endDerivativesMap[n3]) == nodesCountAround)), \
'createAnnulusMesh3d: Mismatch in number of points/nodes in layers through wall'
rowMeshGroups = meshGroups
if meshGroups:
assert isinstance(
meshGroups,
Sequence), 'createAnnulusMesh3d: Mesh groups is not a sequence'
if (len(meshGroups) == 0) or (not isinstance(meshGroups[0], Sequence)):
rowMeshGroups = [meshGroups] * elementsCountRadial
else:
assert len(meshGroups) == elementsCountRadial, \
'createAnnulusMesh3d: Length of meshGroups sequence does not equal elementsCountRadial'
if wallAnnotationGroups:
assert len(wallAnnotationGroups) == nodesCountWall - 1, \
'createAnnulusMesh3d: Length of wallAnnotationGroups sequence does not equal elementsCountThroughWall'
if tracksurface:
assert startProportions and endProportions, \
'createAnnulusMesh3d: Missing start and/or end proportions for use with tracksurface'
assert len(startProportions) == nodesCountAround, \
'createAnnulusMesh3d: Length of startProportions does not equal nodesCountAround'
assert len(endProportions) == nodesCountAround, \
'createAnnulusMesh3d: Length of endProportions does not equal nodesCountAround'
fm = mesh.getFieldmodule()
fm.beginChange()
cache = fm.createFieldcache()
coordinates = findOrCreateFieldCoordinates(fm)
# Build arrays of points from start to end
px = [[] for n3 in range(nodesCountWall)]
pd1 = [[] for n3 in range(nodesCountWall)]
pd2 = [[] for n3 in range(nodesCountWall)]
pd3 = [[] for n3 in range(nodesCountWall)]
# Find total wall thickness
thicknessProportions = []
thicknesses = []
thicknesses.append([
vector.magnitude([
(startPointsx[nodesCountWall - 1][n1][c] - startPointsx[0][n1][c])
for c in range(3)
]) for n1 in range(nodesCountAround)
])
for n2 in range(1, elementsCountRadial):
thicknesses.append([None] * nodesCountAround)
thicknesses.append([
vector.magnitude([
(endPointsx[nodesCountWall - 1][n1][c] - endPointsx[0][n1][c])
for c in range(3)
]) for n1 in range(nodesCountAround)
])
for n3 in range(nodesCountWall):
px[n3] = [startPointsx[n3], endPointsx[n3]]
pd1[n3] = [startPointsd1[n3], endPointsd1[n3]]
pd2[n3] = [startPointsd2[n3], endPointsd2[n3]]
pd3[n3] = [
startPointsd3[n3] if (startPointsd3 is not None) else None,
endPointsd3[n3] if (endPointsd3 is not None) else None
]
startThicknessList = \
[vector.magnitude([(startPointsx[n3][n1][c] - startPointsx[n3 - (1 if n3 > 0 else 0)][n1][c])
for c in range(3)]) for n1 in range(len(startPointsx[n3]))]
endThicknessList = \
[vector.magnitude([(endPointsx[n3][n1][c] - endPointsx[n3 - (1 if n3 > 0 else 0)][n1][c])
for c in range(3)]) for n1 in range(len(endPointsx[n3]))]
thicknessList = [startThicknessList,
endThicknessList] # thickness of each layer
startThicknessProportions = [
thicknessList[0][c] / thicknesses[0][c]
for c in range(nodesCountAround)
]
endThicknessProportions = [
thicknessList[1][c] / thicknesses[-1][c]
for c in range(nodesCountAround)
]
thicknessProportions.append(
[startThicknessProportions, endThicknessProportions])
if rescaleStartDerivatives:
scaleFactorMapStart = [[] for n3 in range(nodesCountWall)]
if rescaleEndDerivatives:
scaleFactorMapEnd = [[] for n3 in range(nodesCountWall)]
# following code adds in-between points, but also handles rescaling for 1 radial element
for n3 in range(nodesCountWall):
for n2 in range(1, elementsCountRadial):
px[n3].insert(n2, [None] * nodesCountAround)
pd1[n3].insert(n2, [None] * nodesCountAround)
pd2[n3].insert(n2, [None] * nodesCountAround)
pd3[n3].insert(n2,
None if midLinearXi3 else [None] * nodesCountAround)
thicknessProportions[n3].insert(n2, [None] * nodesCountAround)
if maxStartThickness:
for n1 in range(nodesCountAround):
thicknesses[0][n1] = min(thicknesses[0][n1], maxStartThickness)
if maxEndThickness:
for n1 in range(nodesCountAround):
thicknesses[-1][n1] = min(thicknesses[-1][n1], maxEndThickness)
n3 = nodesCountWall - 1
for n1 in range(nodesCountAround):
ax = startPointsx[n3][n1]
ad1, ad2 = getMappedD1D2(
[startPointsd1[n3][n1], startPointsd2[n3][n1]] +
([startPointsd3[n3][n1]] if startPointsd3 else []),
startDerivativesMap[n3][n1] if startDerivativesMap else None)
bx = endPointsx[n3][n1]
bd1, bd2 = getMappedD1D2(
[endPointsd1[n3][n1], endPointsd2[n3][n1]] +
([endPointsd3[n3][n1]] if endPointsd3 else []),
endDerivativesMap[n3][n1] if endDerivativesMap else None)
# sample between start and end points and derivatives
# scaling end derivatives to arc length gives even curvature along the curve
aMag = vector.magnitude(ad2)
bMag = vector.magnitude(bd2)
ad2Scaled = vector.setMagnitude(
ad2,
0.5 * ((1.0 + sampleBlend) * aMag + (1.0 - sampleBlend) * bMag))
bd2Scaled = vector.setMagnitude(
bd2,
0.5 * ((1.0 + sampleBlend) * bMag + (1.0 - sampleBlend) * aMag))
scaling = interp.computeCubicHermiteDerivativeScaling(
ax, ad2Scaled, bx, bd2Scaled)
ad2Scaled = [d * scaling for d in ad2Scaled]
bd2Scaled = [d * scaling for d in bd2Scaled]
derivativeMagnitudeStart = None if rescaleStartDerivatives else vector.magnitude(
ad2)
derivativeMagnitudeEnd = None if rescaleEndDerivatives else vector.magnitude(
bd2)
if tracksurface:
mx, md2, md1, md3, mProportions = \
tracksurface.createHermiteCurvePoints(startProportions[n1][0], startProportions[n1][1],
endProportions[n1][0], endProportions[n1][1], elementsCountRadial,
derivativeStart=[d / elementsCountRadial for d in ad2Scaled],
derivativeEnd=[d / elementsCountRadial for d in bd2Scaled])
mx, md2, md1 = \
tracksurface.resampleHermiteCurvePointsSmooth(mx, md2, md1, md3, mProportions,
derivativeMagnitudeStart, derivativeMagnitudeEnd)[0:3]
# interpolate thicknesses using xi calculated from radial arclength distances to points
arcLengthInsideToRadialPoint = \
[0.0] + [interp.getCubicHermiteArcLength(mx[n2], md2[n2], mx[n2 + 1], md2[n2 + 1])
for n2 in range(elementsCountRadial)]
arclengthInsideToOutside = sum(arcLengthInsideToRadialPoint)
thi = []
for n2 in range(elementsCountRadial + 1):
xi2 = arcLengthInsideToRadialPoint[
n2 - 1] / arclengthInsideToOutside
thi.append(thicknesses[-1][n1] * xi2 + thicknesses[0][n1] *
(1.0 - xi2))
thiProportion = []
for m3 in range(nodesCountWall):
thiProportionRadial = []
for n2 in range(elementsCountRadial + 1):
xi2 = arcLengthInsideToRadialPoint[
n2 - 1] / arclengthInsideToOutside
thiProportionRadial.append(
thicknessProportions[m3][-1][n1] * xi2 +
thicknessProportions[m3][0][n1] * (1.0 - xi2))
thiProportion.append(thiProportionRadial)
else:
mx, md2, me, mxi = interp.sampleCubicHermiteCurvesSmooth(
[ax, bx], [ad2Scaled, bd2Scaled], elementsCountRadial,
derivativeMagnitudeStart, derivativeMagnitudeEnd)[0:4]
md1 = interp.interpolateSampleLinear([ad1, bd1], me, mxi)
thi = interp.interpolateSampleLinear(
[thicknesses[0][n1], thicknesses[-1][n1]], me, mxi)
thiProportion = []
for m3 in range(nodesCountWall):
thiProportion.append(
interp.interpolateSampleLinear([
thicknessProportions[m3][0][n1],
thicknessProportions[m3][-1][n1]
], me, mxi))
# set scalefactors if rescaling, make same on inside for now
if rescaleStartDerivatives:
scaleFactor = vector.magnitude(md2[0]) / vector.magnitude(ad2)
scaleFactorMapStart[n3].append(scaleFactor)
if rescaleEndDerivatives:
scaleFactor = vector.magnitude(md2[-1]) / vector.magnitude(bd2)
scaleFactorMapEnd[n3].append(scaleFactor)
for n2 in range(1, elementsCountRadial):
px[n3][n2][n1] = mx[n2]
pd1[n3][n2][n1] = md1[n2]
pd2[n3][n2][n1] = md2[n2]
thicknesses[n2][n1] = thi[n2]
for m3 in range(nodesCountWall):
thicknessProportions[m3][n2][n1] = thiProportion[m3][n2]
xi3List = [[[[] for n1 in range(nodesCountAround)]
for n2 in range(elementsCountRadial + 1)]
for n3 in range(nodesCountWall)]
for n1 in range(nodesCountAround):
for n2 in range(elementsCountRadial + 1):
xi3 = 0.0
for n3 in range(nodesCountWall):
xi3 += thicknessProportions[n3][n2][n1]
xi3List[n3][n2][n1] = xi3
# now get inner positions from normal and thickness, derivatives from curvature
for n2 in range(1, elementsCountRadial):
# first smooth derivative 1 around outer loop
pd1[-1][n2] = \
interp.smoothCubicHermiteDerivativesLoop(px[-1][n2], pd1[-1][n2],
magnitudeScalingMode=interp.DerivativeScalingMode.HARMONIC_MEAN)
for n3 in range(0, nodesCountWall - 1):
for n1 in range(nodesCountAround):
xi3 = 1 - xi3List[n3][n2][n1]
normal = vector.normalise(
vector.crossproduct3(pd1[-1][n2][n1], pd2[-1][n2][n1]))
thickness = thicknesses[n2][n1] * xi3
d3 = [d * thickness for d in normal]
px[n3][n2][n1] = [(px[-1][n2][n1][c] - d3[c])
for c in range(3)]
# calculate inner d1 from curvature around
n1m = n1 - 1
n1p = (n1 + 1) % nodesCountAround
curvature = 0.5 * (interp.getCubicHermiteCurvature(
px[-1][n2][n1m], pd1[-1][n2][n1m], px[-1][n2][n1], pd1[-1]
[n2][n1], normal, 1.0) + interp.getCubicHermiteCurvature(
px[-1][n2][n1], pd1[-1][n2][n1], px[-1][n2][n1p],
pd1[-1][n2][n1p], normal, 0.0))
factor = 1.0 + curvature * thickness
pd1[n3][n2][n1] = [factor * d for d in pd1[-1][n2][n1]]
# calculate inner d2 from curvature radially
n2m = n2 - 1
n2p = n2 + 1
curvature = 0.5 * (interp.getCubicHermiteCurvature(
px[-1][n2m][n1], pd2[-1][n2m][n1], px[-1][n2][n1], pd2[-1]
[n2][n1], normal, 1.0) + interp.getCubicHermiteCurvature(
px[-1][n2][n1], pd2[-1][n2][n1], px[-1][n2p][n1],
pd2[-1][n2p][n1], normal, 0.0))
factor = 1.0 + curvature * thickness
pd2[n3][n2][n1] = [factor * d for d in pd2[-1][n2][n1]]
d2Scaled = [factor * d for d in pd2[-1][n2][n1]]
if vector.dotproduct(vector.normalise(pd2[-1][n2][n1]),
vector.normalise(d2Scaled)) == -1:
pd2[n3][n2][n1] = [-factor * d for d in pd2[-1][n2][n1]]
if not midLinearXi3:
pd3[n3][n2][n1] = pd3[-1][n2][n1] = \
[d * thicknesses[n2][n1] * thicknessProportions[n3 + 1][n2][n1] for d in normal]
# smooth derivative 1 around inner loop
pd1[n3][n2] = interp.smoothCubicHermiteDerivativesLoop(
px[n3][n2],
pd1[n3][n2],
magnitudeScalingMode=interp.DerivativeScalingMode.HARMONIC_MEAN
)
for n3 in range(0, nodesCountWall):
# smooth derivative 2 radially/along annulus
for n1 in range(nodesCountAround):
mx = [px[n3][n2][n1] for n2 in range(elementsCountRadial + 1)]
md2 = [pd2[n3][n2][n1] for n2 in range(elementsCountRadial + 1)]
# replace mapped start/end d2
md2[0] = getMappedD1D2(
[startPointsd1[n3][n1], startPointsd2[n3][n1]] +
([startPointsd3[n3][n1]] if startPointsd3 else []),
startDerivativesMap[n3][n1]
if startDerivativesMap else None)[1]
md2[-1] = getMappedD1D2(
[endPointsd1[n3][n1], endPointsd2[n3][n1]] +
([endPointsd3[n3][n1]] if endPointsd3 else []),
endDerivativesMap[n3][n1] if endDerivativesMap else None)[1]
sd2 = interp.smoothCubicHermiteDerivativesLine(
mx,
md2,
fixAllDirections=True,
fixStartDerivative=not rescaleStartDerivatives,
fixStartDirection=rescaleStartDerivatives,
fixEndDerivative=not rescaleEndDerivatives,
fixEndDirection=rescaleEndDerivatives,
magnitudeScalingMode=interp.DerivativeScalingMode.HARMONIC_MEAN
)
if rescaleStartDerivatives:
scaleFactor = vector.magnitude(sd2[0]) / vector.magnitude(
md2[0])
scaleFactorMapStart[n3].append(scaleFactor)
if rescaleEndDerivatives:
scaleFactor = vector.magnitude(sd2[-1]) / vector.magnitude(
md2[-1])
scaleFactorMapEnd[n3].append(scaleFactor)
for n2 in range(1, elementsCountRadial):
pd2[n3][n2][n1] = sd2[n2]
##############
# Create nodes
##############
nodetemplate = nodes.createNodetemplate()
nodetemplate.defineField(coordinates)
nodetemplate.setValueNumberOfVersions(coordinates, -1,
Node.VALUE_LABEL_VALUE, 1)
nodetemplate.setValueNumberOfVersions(coordinates, -1,
Node.VALUE_LABEL_D_DS1, 1)
nodetemplate.setValueNumberOfVersions(coordinates, -1,
Node.VALUE_LABEL_D_DS2, 1)
if useCrossDerivatives:
nodetemplate.setValueNumberOfVersions(coordinates, -1,
Node.VALUE_LABEL_D2_DS1DS2, 1)
nodetemplate.setValueNumberOfVersions(coordinates, -1,
Node.VALUE_LABEL_D_DS3, 1)
if useCrossDerivatives:
nodetemplate.setValueNumberOfVersions(coordinates, -1,
Node.VALUE_LABEL_D2_DS1DS3, 1)
nodetemplate.setValueNumberOfVersions(coordinates, -1,
Node.VALUE_LABEL_D2_DS2DS3, 1)
nodetemplate.setValueNumberOfVersions(coordinates, -1,
Node.VALUE_LABEL_D3_DS1DS2DS3, 1)
nodetemplateLinearS3 = nodes.createNodetemplate()
nodetemplateLinearS3.defineField(coordinates)
nodetemplateLinearS3.setValueNumberOfVersions(coordinates, -1,
Node.VALUE_LABEL_VALUE, 1)
nodetemplateLinearS3.setValueNumberOfVersions(coordinates, -1,
Node.VALUE_LABEL_D_DS1, 1)
nodetemplateLinearS3.setValueNumberOfVersions(coordinates, -1,
Node.VALUE_LABEL_D_DS2, 1)
if useCrossDerivatives:
nodetemplateLinearS3.setValueNumberOfVersions(
coordinates, -1, Node.VALUE_LABEL_D2_DS1DS2, 1)
nodeIdentifier = nextNodeIdentifier
nodeId = [[] for n3 in range(nodesCountWall)]
for n2 in range(elementsCountRadial + 1):
for n3 in range(nodesCountWall):
if (n2 == 0) and (startNodeId is not None):
rowNodeId = copy.deepcopy(startNodeId[n3])
elif (n2 == elementsCountRadial) and (endNodeId is not None):
rowNodeId = copy.deepcopy(endNodeId[n3])
else:
rowNodeId = []
nodetemplate1 = nodetemplate if pd3[n3][
n2] else nodetemplateLinearS3
for n1 in range(nodesCountAround):
node = nodes.createNode(nodeIdentifier, nodetemplate1)
rowNodeId.append(nodeIdentifier)
cache.setNode(node)
coordinates.setNodeParameters(cache, -1,
Node.VALUE_LABEL_VALUE, 1,
px[n3][n2][n1])
coordinates.setNodeParameters(cache, -1,
Node.VALUE_LABEL_D_DS1, 1,
pd1[n3][n2][n1])
coordinates.setNodeParameters(cache, -1,
Node.VALUE_LABEL_D_DS2, 1,
pd2[n3][n2][n1])
if pd3[n3][n2]:
coordinates.setNodeParameters(cache, -1,
Node.VALUE_LABEL_D_DS3,
1, pd3[n3][n2][n1])
nodeIdentifier = nodeIdentifier + 1
nodeId[n3].append(rowNodeId)
#################
# Create elements
#################
tricubichermite = eftfactory_tricubichermite(mesh, useCrossDerivatives)
bicubichermitelinear = eftfactory_bicubichermitelinear(
mesh, useCrossDerivatives)
elementIdentifier = nextElementIdentifier
elementtemplateStandard = mesh.createElementtemplate()
elementtemplateStandard.setElementShapeType(Element.SHAPE_TYPE_CUBE)
elementtemplateX = mesh.createElementtemplate()
elementtemplateX.setElementShapeType(Element.SHAPE_TYPE_CUBE)
elementsCountWall = nodesCountWall - 1
for e2 in range(elementsCountRadial):
nonlinearXi3 = (not rowLinearXi3[e2]) or (not rowLinearXi3[e2 + 1])
eftFactory = tricubichermite if nonlinearXi3 else bicubichermitelinear
eftStandard = eftFactory.createEftBasic()
elementtemplateStandard.defineField(coordinates, -1, eftStandard)
mapStartDerivatives = (e2 == 0) and (startDerivativesMap
or rescaleStartDerivatives)
mapStartLinearDerivativeXi3 = nonlinearXi3 and rowLinearXi3[e2]
mapEndDerivatives = (e2 == (elementsCountRadial - 1)) and (
endDerivativesMap or rescaleEndDerivatives)
mapEndLinearDerivativeXi3 = nonlinearXi3 and rowLinearXi3[e2 + 1]
mapDerivatives = mapStartDerivatives or mapStartLinearDerivativeXi3 or \
mapEndDerivatives or mapEndLinearDerivativeXi3
for e3 in range(elementsCountWall):
for e1 in range(elementsCountAround):
en = (e1 + 1) % elementsCountAround
nids = [
nodeId[e3][e2][e1], nodeId[e3][e2][en],
nodeId[e3][e2 + 1][e1], nodeId[e3][e2 + 1][en],
nodeId[e3 + 1][e2][e1], nodeId[e3 + 1][e2][en],
nodeId[e3 + 1][e2 + 1][e1], nodeId[e3 + 1][e2 + 1][en]
]
scaleFactors = []
if mapDerivatives:
eft1 = eftFactory.createEftNoCrossDerivatives()
# work out if scaling by global -1
scaleMinus1 = mapStartLinearDerivativeXi3 or mapEndLinearDerivativeXi3
if (not scaleMinus1
) and mapStartDerivatives and startDerivativesMap:
for n3 in range(2):
n3Idx = n3 + e3
# need to handle 3 or 4 maps (e1 uses last 3, en uses first 3)
for map in startDerivativesMap[n3Idx][e1][-3:]:
if map and (-1 in map):
scaleMinus1 = True
break
for map in startDerivativesMap[n3Idx][en][:3]:
if map and (-1 in map):
scaleMinus1 = True
break
if (not scaleMinus1
) and mapEndDerivatives and endDerivativesMap:
for n3 in range(2):
n3Idx = n3 + e3
# need to handle 3 or 4 maps (e1 uses last 3, en uses first 3)
for map in endDerivativesMap[n3Idx][e1][-3:]:
if map and (-1 in map):
scaleMinus1 = True
break
for map in endDerivativesMap[n3Idx][en][:3]:
if map and (-1 in map):
scaleMinus1 = True
break
# make node scale factors vary fastest by local node varying across lower xi
nodeScaleFactorIds = []
for n3 in range(2):
n3Idx = n3 + e3
if mapStartDerivatives and rescaleStartDerivatives:
for i in range(2):
derivativesMap = (
startDerivativesMap[n3Idx][e1][1] if
(i == 0) else startDerivativesMap[n3Idx]
[en][1]) if startDerivativesMap else None
nodeScaleFactorIds.append(
getQuadrantID(derivativesMap
if derivativesMap else (0, 1,
0)))
if mapEndDerivatives and rescaleEndDerivatives:
for i in range(2):
derivativesMap = (
endDerivativesMap[n3Idx][e1][1] if
(i == 0) else endDerivativesMap[n3Idx][en]
[1]) if endDerivativesMap else None
nodeScaleFactorIds.append(
getQuadrantID(derivativesMap
if derivativesMap else (0, 1,
0)))
setEftScaleFactorIds(eft1, [1] if scaleMinus1 else [],
nodeScaleFactorIds)
firstNodeScaleFactorIndex = 2 if scaleMinus1 else 1
firstStartNodeScaleFactorIndex = \
firstNodeScaleFactorIndex if (mapStartDerivatives and rescaleStartDerivatives) else None
firstEndNodeScaleFactorIndex = \
(firstNodeScaleFactorIndex + (2 if firstStartNodeScaleFactorIndex else 0)) \
if (mapEndDerivatives and rescaleEndDerivatives) else None
layerNodeScaleFactorIndexOffset = \
4 if (firstStartNodeScaleFactorIndex and firstEndNodeScaleFactorIndex) else 2
if scaleMinus1:
scaleFactors.append(-1.0)
for n3 in range(2):
n3Idx = n3 + e3
if firstStartNodeScaleFactorIndex:
scaleFactors.append(scaleFactorMapStart[n3Idx][e1])
scaleFactors.append(scaleFactorMapStart[n3Idx][en])
if firstEndNodeScaleFactorIndex:
scaleFactors.append(scaleFactorMapEnd[n3Idx][e1])
scaleFactors.append(scaleFactorMapEnd[n3Idx][en])
if mapStartLinearDerivativeXi3:
eftFactory.setEftLinearDerivative2(
eft1, [1, 5, 2, 6], Node.VALUE_LABEL_D_DS3,
[Node.VALUE_LABEL_D2_DS1DS3])
if mapStartDerivatives:
for i in range(2):
lns = [1, 5] if (i == 0) else [2, 6]
for n3 in range(2):
n3Idx = n3 + e3
derivativesMap = \
(startDerivativesMap[n3Idx][e1] if (i == 0) else startDerivativesMap[n3Idx][en]) \
if startDerivativesMap else (None, None, None)
# handle different d1 on each side of node
d1Map = \
derivativesMap[0] if ((i == 1) or (len(derivativesMap) < 4)) else derivativesMap[3]
d2Map = derivativesMap[1] if derivativesMap[
1] else (0, 1, 0)
d3Map = derivativesMap[2]
# use temporary to safely swap DS1 and DS2:
ln = [lns[n3]]
if d1Map:
remapEftNodeValueLabel(
eft1, ln, Node.VALUE_LABEL_D_DS1,
[(Node.VALUE_LABEL_D2_DS1DS2, [])])
if d3Map:
remapEftNodeValueLabel(
eft1, ln, Node.VALUE_LABEL_D_DS3,
[(Node.VALUE_LABEL_D2_DS2DS3, [])])
if d2Map:
remapEftNodeValueLabel(
eft1, ln, Node.VALUE_LABEL_D_DS2,
derivativeSignsToExpressionTerms(
(Node.VALUE_LABEL_D_DS1,
Node.VALUE_LABEL_D_DS2,
Node.VALUE_LABEL_D_DS3), d2Map,
(firstStartNodeScaleFactorIndex +
i + n3 *
layerNodeScaleFactorIndexOffset)
if rescaleStartDerivatives else
None))
if d1Map:
remapEftNodeValueLabel(
eft1, ln, Node.VALUE_LABEL_D2_DS1DS2,
derivativeSignsToExpressionTerms(
(Node.VALUE_LABEL_D_DS1,
Node.VALUE_LABEL_D_DS2,
Node.VALUE_LABEL_D_DS3), d1Map))
if d3Map:
remapEftNodeValueLabel(
eft1, ln, Node.VALUE_LABEL_D2_DS2DS3,
derivativeSignsToExpressionTerms(
(Node.VALUE_LABEL_D_DS1,
Node.VALUE_LABEL_D_DS2,
Node.VALUE_LABEL_D_DS3), d3Map))
if mapEndLinearDerivativeXi3:
eftFactory.setEftLinearDerivative2(
eft1, [3, 7, 4, 8], Node.VALUE_LABEL_D_DS3,
[Node.VALUE_LABEL_D2_DS1DS3])
if mapEndDerivatives:
for i in range(2):
lns = [3, 7] if (i == 0) else [4, 8]
for n3 in range(2):
n3Idx = n3 + e3
derivativesMap = \
(endDerivativesMap[n3Idx][e1] if (i == 0) else endDerivativesMap[n3Idx][en]) \
if endDerivativesMap else (None, None, None)
# handle different d1 on each side of node
d1Map = derivativesMap[0] if ((i == 1) or (len(derivativesMap) < 4)) else \
derivativesMap[3]
d2Map = derivativesMap[1] if derivativesMap[
1] else (0, 1, 0)
d3Map = derivativesMap[2]
# use temporary to safely swap DS1 and DS2:
ln = [lns[n3]]
if d1Map:
remapEftNodeValueLabel(
eft1, ln, Node.VALUE_LABEL_D_DS1,
[(Node.VALUE_LABEL_D2_DS1DS2, [])])
if d3Map:
remapEftNodeValueLabel(
eft1, ln, Node.VALUE_LABEL_D_DS3,
[(Node.VALUE_LABEL_D2_DS2DS3, [])])
if d2Map:
remapEftNodeValueLabel(
eft1, ln, Node.VALUE_LABEL_D_DS2,
derivativeSignsToExpressionTerms(
(Node.VALUE_LABEL_D_DS1,
Node.VALUE_LABEL_D_DS2,
Node.VALUE_LABEL_D_DS3), d2Map,
(firstEndNodeScaleFactorIndex + i +
n3 *
layerNodeScaleFactorIndexOffset)
if rescaleEndDerivatives else
None))
if d1Map:
remapEftNodeValueLabel(
eft1, ln, Node.VALUE_LABEL_D2_DS1DS2,
derivativeSignsToExpressionTerms(
(Node.VALUE_LABEL_D_DS1,
Node.VALUE_LABEL_D_DS2,
Node.VALUE_LABEL_D_DS3), d1Map))
if d3Map:
remapEftNodeValueLabel(
eft1, ln, Node.VALUE_LABEL_D2_DS2DS3,
derivativeSignsToExpressionTerms(
(Node.VALUE_LABEL_D_DS1,
Node.VALUE_LABEL_D_DS2,
Node.VALUE_LABEL_D_DS3), d3Map))
elementtemplateX.defineField(coordinates, -1, eft1)
elementtemplate1 = elementtemplateX
else:
eft1 = eftStandard
elementtemplate1 = elementtemplateStandard
element = mesh.createElement(elementIdentifier,
elementtemplate1)
result2 = element.setNodesByIdentifier(eft1, nids)
if scaleFactors:
result3 = element.setScaleFactors(eft1, scaleFactors)
# print('create element annulus', element.isValid(), elementIdentifier, eft1.validate(),
# result2, result3 if scaleFactors else None, nids)
elementIdentifier += 1
if rowMeshGroups:
for meshGroup in rowMeshGroups[e2]:
meshGroup.addElement(element)
if wallAnnotationGroups:
for annotationGroup in wallAnnotationGroups[e3]:
meshGroup = annotationGroup.getMeshGroup(mesh)
meshGroup.addElement(element)
fm.endChange()
return nodeIdentifier, elementIdentifier
def warpSegmentPoints(xList, d1List, d2List, segmentAxis, segmentLength, sx,
sd1, sd2, elementsCountAround, elementsCountAlongSegment,
nSegment, faceMidPointZ):
"""
Warps points in segment to account for bending and twisting
along central path defined by nodes sx and derivatives sd1 and sd2.
:param xList: coordinates of segment points.
:param d1List: derivatives around axis of segment.
:param d2List: derivatives along axis of segment.
:param segmentAxis: axis perpendicular to segment plane.
:param sx: coordinates of points on central path.
:param sd1: derivatives of points along central path.
:param sd2: derivatives representing cross axes.
:param elementsCountAround: Number of elements around segment.
:param elementsCountAlongSegment: Number of elements along segment.
:param nSegment: Segment index along central path.
:param faceMidPointZ: z-coordinate of midpoint for each element
groups along the segment.
:return coordinates and derivatives of warped points.
"""
xWarpedList = []
d1WarpedList = []
d2WarpedList = []
smoothd2WarpedList = []
d3WarpedUnitList = []
for nAlongSegment in range(elementsCountAlongSegment + 1):
n2 = elementsCountAlongSegment * nSegment + nAlongSegment
xElementAlongSegment = xList[elementsCountAround *
nAlongSegment:elementsCountAround *
(nAlongSegment + 1)]
d1ElementAlongSegment = d1List[elementsCountAround *
nAlongSegment:elementsCountAround *
(nAlongSegment + 1)]
d2ElementAlongSegment = d2List[elementsCountAround *
nAlongSegment:elementsCountAround *
(nAlongSegment + 1)]
xMid = [0.0, 0.0, faceMidPointZ[nAlongSegment]]
# Rotate to align segment axis with tangent of central line
unitTangent = vector.normalise(sd1[n2])
cp = vector.crossproduct3(segmentAxis, unitTangent)
dp = vector.dotproduct(segmentAxis, unitTangent)
if vector.magnitude(
cp) > 0.0: # path tangent not parallel to segment axis
axisRot = vector.normalise(cp)
thetaRot = math.acos(vector.dotproduct(segmentAxis, unitTangent))
rotFrame = matrix.getRotationMatrixFromAxisAngle(axisRot, thetaRot)
midRot = [
rotFrame[j][0] * xMid[0] + rotFrame[j][1] * xMid[1] +
rotFrame[j][2] * xMid[2] for j in range(3)
]
else: # path tangent parallel to segment axis (z-axis)
if dp == -1.0: # path tangent opposite direction to segment axis
thetaRot = math.pi
axisRot = [1.0, 0, 0]
rotFrame = matrix.getRotationMatrixFromAxisAngle(
axisRot, thetaRot)
midRot = [
rotFrame[j][0] * xMid[0] + rotFrame[j][1] * xMid[1] +
rotFrame[j][2] * xMid[2] for j in range(3)
]
else: # segment axis in same direction as unit tangent
midRot = xMid
translateMatrix = [sx[n2][j] - midRot[j] for j in range(3)]
for n1 in range(elementsCountAround):
x = xElementAlongSegment[n1]
d1 = d1ElementAlongSegment[n1]
d2 = d2ElementAlongSegment[n1]
if vector.magnitude(
cp) > 0.0: # path tangent not parallel to segment axis
xRot1 = [
rotFrame[j][0] * x[0] + rotFrame[j][1] * x[1] +
rotFrame[j][2] * x[2] for j in range(3)
]
d1Rot1 = [
rotFrame[j][0] * d1[0] + rotFrame[j][1] * d1[1] +
rotFrame[j][2] * d1[2] for j in range(3)
]
d2Rot1 = [
rotFrame[j][0] * d2[0] + rotFrame[j][1] * d2[1] +
rotFrame[j][2] * d2[2] for j in range(3)
]
if n1 == 0:
# Project sd2 onto plane normal to sd1
v = sd2[n2]
pt = [midRot[j] + sd2[n2][j] for j in range(3)]
dist = vector.dotproduct(v, unitTangent)
ptOnPlane = [
pt[j] - dist * unitTangent[j] for j in range(3)
]
newVector = [ptOnPlane[j] - midRot[j] for j in range(3)]
# Rotate first point to align with planar projection of sd2
firstVector = vector.normalise(
[xRot1[j] - midRot[j] for j in range(3)])
thetaRot2 = math.acos(
vector.dotproduct(vector.normalise(newVector),
firstVector))
cp2 = vector.crossproduct3(vector.normalise(newVector),
firstVector)
if vector.magnitude(cp2) > 0.0:
cp2 = vector.normalise(cp2)
signThetaRot2 = vector.dotproduct(unitTangent, cp2)
axisRot2 = unitTangent
rotFrame2 = matrix.getRotationMatrixFromAxisAngle(
axisRot2, -signThetaRot2 * thetaRot2)
else:
rotFrame2 = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
else: # path tangent parallel to segment axis
xRot1 = [
rotFrame[j][0] * x[0] + rotFrame[j][1] * x[1] +
rotFrame[j][2] * x[2] for j in range(3)
] if dp == -1.0 else x
d1Rot1 = [
rotFrame[j][0] * d1[0] + rotFrame[j][1] * d1[1] +
rotFrame[j][2] * d1[2] for j in range(3)
] if dp == -1.0 else d1
d2Rot1 = [
rotFrame[j][0] * d2[0] + rotFrame[j][1] * d2[1] +
rotFrame[j][2] * d2[2] for j in range(3)
] if dp == -1.0 else d2
# Rotate to align start of elementsAround with sd2
if n1 == 0:
v = vector.normalise(sd2[n2])
startVector = vector.normalise(
[xRot1[j] - midRot[j] for j in range(3)])
axisRot2 = unitTangent
thetaRot2 = dp * -math.acos(
vector.dotproduct(v, startVector))
rotFrame2 = matrix.getRotationMatrixFromAxisAngle(
axisRot2, thetaRot2)
xRot2 = [
rotFrame2[j][0] * xRot1[0] + rotFrame2[j][1] * xRot1[1] +
rotFrame2[j][2] * xRot1[2] for j in range(3)
]
d1Rot2 = [
rotFrame2[j][0] * d1Rot1[0] + rotFrame2[j][1] * d1Rot1[1] +
rotFrame2[j][2] * d1Rot1[2] for j in range(3)
]
d2Rot2 = [
rotFrame2[j][0] * d2Rot1[0] + rotFrame2[j][1] * d2Rot1[1] +
rotFrame2[j][2] * d2Rot1[2] for j in range(3)
]
xTranslate = [xRot2[j] + translateMatrix[j] for j in range(3)]
xWarpedList.append(xTranslate)
d1WarpedList.append(d1Rot2)
d2WarpedList.append(d2Rot2)
# Smooth d2 for segment
smoothd2Raw = []
for n1 in range(elementsCountAround):
nx = []
nd2 = []
for n2 in range(elementsCountAlongSegment + 1):
n = n2 * elementsCountAround + n1
nx.append(xWarpedList[n])
nd2.append(d2WarpedList[n])
smoothd2 = interp.smoothCubicHermiteDerivativesLine(
nx, nd2, fixStartDerivative=True, fixEndDerivative=True)
smoothd2Raw.append(smoothd2)
# Re-arrange smoothd2
for n2 in range(elementsCountAlongSegment + 1):
for n1 in range(elementsCountAround):
smoothd2WarpedList.append(smoothd2Raw[n1][n2])
# Calculate unit d3
for n in range(len(xWarpedList)):
d3Unit = vector.normalise(
vector.crossproduct3(vector.normalise(d1WarpedList[n]),
vector.normalise(smoothd2WarpedList[n])))
d3WarpedUnitList.append(d3Unit)
return xWarpedList, d1WarpedList, smoothd2WarpedList, d3WarpedUnitList
