'''
Utility functions for easing use of Zinc API.
Created on Jan 4, 2018

@author: <NAME>
'''

from opencmiss.zinc.field import Field
from opencmiss.zinc.node import Node
from scaffoldmaker.utils.interpolation import *
import scaffoldmaker.utils.vector as vector

def getOrCreateCoordinateField(fieldmodule, name='coordinates', componentsCount=3):
    '''
    Finds or creates a rectangular cartesian coordinate field.
    New field has component names, 'x', 'y', 'z'.
    Raises exception if existing field of name is not finite element type or has incorrect attributes.
    :param fieldmodule:  Zinc fieldmodule to find or create field in.
    :param name:  Name of field to find or create.
    :param componentsCount: Number of components / dimension of field.
    '''
    assert (componentsCount > 0) and (componentsCount <= 3), 'getOrCreateCoordinateField.  Dimensions must be from 1 to 3'
    coordinates = fieldmodule.findFieldByName(name)
    if coordinates.isValid():
        coordinates = coordinates.castFiniteElement()
        assert coordinates.isValid(), 'getOrCreateCoordinateField.  Existing field \'' + name + '\' is not finite element type'
        assert coordinates.getNumberOfComponents() == componentsCount, 'getOrCreateCoordinateField.  Existing field \'' + name + '\' does not have ' + str(componentsCount) + ' components'
        assert coordinates.getCoordinateSystemType() == Field.COORDINATE_SYSTEM_TYPE_RECTANGULAR_CARTESIAN, 'getOrCreateCoordinateField.  Existing field \'' + name + '\' is not rectangular Cartesian'
        return coordinates
    fieldmodule.beginChange()
    coordinates = fieldmodule.createFieldFiniteElement(componentsCount)
    coordinates.setName(name)
    coordinates.setManaged(True)
    coordinates.setTypeCoordinate(True)
    coordinates.setCoordinateSystemType(Field.COORDINATE_SYSTEM_TYPE_RECTANGULAR_CARTESIAN)
    for c in range(componentsCount):
        coordinates.setComponentName(c + 1, ['x', 'y', 'z'][c])
    fieldmodule.endChange()
    return coordinates

def getOrCreateElementXiField(fieldmodule, name='element_xi', mesh=None):
    '''
    Finds or creates a stored mesh location field for storing locations in the
    supplied mesh e.g. for defining on annotation points with mesh locations.
    Raises exception if existing field of name is not stored mesh location type.
    Note can't currently verify existing field stores locations in the supplied mesh.
    :param fieldmodule:  Zinc fieldmodule to find or create field in.
    :param name:  Name of field to find or create.
    :param mesh:  Mesh to store locations in.
    '''
    if mesh is None:
        mesh = fieldmodule.findMeshByDimension(3)
    assert mesh.isValid(), 'getOrCreateElementXiField.  Invalid mesh'
    elementXiField = fieldmodule.findFieldByName(name)
    if elementXiField.isValid():
        elementXiField = elementXiField.castStoredMeshLocation()
        assert elementXiField.isValid(), 'getOrCreateElementXiField.  Existing field \'' + name + '\' is not stored mesh location type'
        return elementXiField
    fieldmodule.beginChange()
    elementXiField = fieldmodule.createFieldStoredMeshLocation(mesh)
    elementXiField.setName(name)
    elementXiField.setManaged(True)
    fieldmodule.endChange()
    return elementXiField

def getOrCreateLabelField(fieldmodule, name='label'):
    '''
    Finds or creates a stored string field for defining labels on nodes, e.g. annotation points.
    Raises exception if existing field of name is not string-valued.
    Note can't currently distinguish stored string from constant string fields.
    :param fieldmodule:  Zinc fieldmodule to find or create field in.
    :param name:  Name of field to find or create.
    '''
    labelField = fieldmodule.findFieldByName(name)
    if labelField.isValid():
        assert labelField.getValueType() == Field.VALUE_TYPE_STRING, 'getOrCreateLabelField.  Existing field \'' + name + '\' is not string valued'
        return labelField
    fieldmodule.beginChange()
    labelField = fieldmodule.createFieldStoredString()
    labelField.setName(name)
    labelField.setManaged(True)
    fieldmodule.endChange()
    return labelField

def getElementNodeIdentifiers(element, eft):
    '''
    Get identifiers of all nodes used by eft in element.
    '''
    nodeIdentifiers = []
    nodeCount = eft.getNumberOfLocalNodes()
    for n in range(nodeCount):
        node = element.getNode(eft, n + 1)
        nodeIdentifiers.append(node.getIdentifier())
    return nodeIdentifiers

def getElementNodeIdentifiers4Node(element, eft):
    '''
    Get 4 node identifiers for an element with 4 basis nodes, handling
    collapses e.g. where eft has fewer nodes. Asserts basis has 4 nodes.
    :param element: Element to query.
    :param eft: Element field template nodes are stored for in element.
    :return: List of 4 local node identifiers.
    '''
    elementbasis = eft.getElementbasis()
    basisNodesCount = elementbasis.getNumberOfNodes()
    assert basisNodesCount == 4, 'getElementNodeIdentifiers4Node:  Element ' + str(element.getIdentifier()) + ' is not using a 4 node basis'
    nodeIdentifiers = []
    fn = 1
    for n in range(basisNodesCount):
        ln = eft.getTermLocalNodeIndex(fn, 1)
        nodeIdentifiers.append(element.getNode(eft, ln).getIdentifier())
        fn += elementbasis.getNumberOfFunctionsPerNode(n + 1)
    return nodeIdentifiers

def getElementNodeIdentifiers8Node(element, eft):
    '''
    Get 8 node identifiers for an element with 8 basis nodes, handling
    collapses e.g. where eft has fewer nodes. Asserts basis has 8 nodes.
    :param element: Element to query.
    :param eft: Element field template nodes are stored for in element.
    :return: List of 8 local node identifiers.
    '''
    elementbasis = eft.getElementbasis()
    basisNodesCount = elementbasis.getNumberOfNodes()
    assert basisNodesCount == 8, 'getElementNodeIdentifiers8Node:  Element ' + str(element.getIdentifier()) + ' is not using an 8 node basis'
    nodeIdentifiers = []
    fn = 1
    for n in range(basisNodesCount):
        ln = eft.getTermLocalNodeIndex(fn, 1)
        nodeIdentifiers.append(element.getNode(eft, ln).getIdentifier())
        fn += elementbasis.getNumberOfFunctionsPerNode(n + 1)
    return nodeIdentifiers

def getMaximumNodeIdentifier(nodeset):
    """
    :return: Maximum node identifier in nodeset or -1 if none.
    """
    maximumNodeId = -1
    nodeiterator = nodeset.createNodeiterator()
    node = nodeiterator.next()
    while node.isValid():
        id = node.getIdentifier()
        if id > maximumNodeId:
            maximumNodeId = id
        node = nodeiterator.next()
    return maximumNodeId

def getMaximumElementIdentifier(mesh):
    """
    :return: Maximum element identifier in mesh or -1 if none.
    """
    maximumElementId = -1
    elementiterator = mesh.createElementiterator()
    element = elementiterator.next()
    while element.isValid():
        id = element.getIdentifier()
        if id > maximumElementId:
            maximumElementId = id
        element = elementiterator.next()
    return maximumElementId

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 = 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 = interpolateCubicHermite(v1, d1, v2, d2, xi)
    dx_ds = 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 computeNodeDerivativeHermiteLagrange(cache, coordinates, node1, derivative1, scale1, node2, scale2):
    """
    Computes the derivative at node2 from quadratic Hermite-Lagrange interpolation of
    node1 value and derivative1 to node2 value.
    :param cache: Field cache to evaluate in.
    :param coordinates: Coordinates field.
    :param node1, node2: Start and end nodes.
    :param derivative1: Node value label for derivative at node1.
    :param scale1, scale2: Scaling to apply to derivatives at nodes, e.g. -1.0 to reverse.
    :return: dx_dxi at node2
    """
    cache.setNode(node1)
    result, v1 = coordinates.getNodeParameters(cache, -1, Node.VALUE_LABEL_VALUE, 1, 3 )
    result, d1 = coordinates.getNodeParameters(cache, -1, derivative1, 1, 3 )
    d1 = [ d*scale1 for d in d1 ]
    cache.setNode(node2)
    result, v2 = coordinates.getNodeParameters(cache, -1, Node.VALUE_LABEL_VALUE, 1, 3 )
    d2 = interpolateHermiteLagrangeDerivative(v1, d1, v2, 1.0)
    d2 = [ d*scale2 for d in d2 ]
    return d2

'''
Utility functions for easing use of Zinc API.
Created on Jan 4, 2018

@author: <NAME>
'''

from opencmiss.zinc.field import Field
from opencmiss.zinc.node import Node
from scaffoldmaker.utils.interpolation import *
import scaffoldmaker.utils.vector as vector

def getOrCreateCoordinateField(fieldmodule, name='coordinates', componentsCount=3):
    '''
    Finds or creates a rectangular cartesian coordinate field.
    New field has component names, 'x', 'y', 'z'.
    Raises exception if existing field of name is not finite element type or has incorrect attributes.
    :param fieldmodule:  Zinc fieldmodule to find or create field in.
    :param name:  Name of field to find or create.
    :param componentsCount: Number of components / dimension of field.
    '''
    assert (componentsCount > 0) and (componentsCount <= 3), 'getOrCreateCoordinateField.  Dimensions must be from 1 to 3'
    coordinates = fieldmodule.findFieldByName(name)
    if coordinates.isValid():
        coordinates = coordinates.castFiniteElement()
        assert coordinates.isValid(), 'getOrCreateCoordinateField.  Existing field \'' + name + '\' is not finite element type'
        assert coordinates.getNumberOfComponents() == componentsCount, 'getOrCreateCoordinateField.  Existing field \'' + name + '\' does not have ' + str(componentsCount) + ' components'
        assert coordinates.getCoordinateSystemType() == Field.COORDINATE_SYSTEM_TYPE_RECTANGULAR_CARTESIAN, 'getOrCreateCoordinateField.  Existing field \'' + name + '\' is not rectangular Cartesian'
        return coordinates
    fieldmodule.beginChange()
    coordinates = fieldmodule.createFieldFiniteElement(componentsCount)
    coordinates.setName(name)
    coordinates.setManaged(True)
    coordinates.setTypeCoordinate(True)
    coordinates.setCoordinateSystemType(Field.COORDINATE_SYSTEM_TYPE_RECTANGULAR_CARTESIAN)
    for c in range(componentsCount):
        coordinates.setComponentName(c + 1, ['x', 'y', 'z'][c])
    fieldmodule.endChange()
    return coordinates

def getOrCreateElementXiField(fieldmodule, name='element_xi', mesh=None):
    '''
    Finds or creates a stored mesh location field for storing locations in the
    supplied mesh e.g. for defining on annotation points with mesh locations.
    Raises exception if existing field of name is not stored mesh location type.
    Note can't currently verify existing field stores locations in the supplied mesh.
    :param fieldmodule:  Zinc fieldmodule to find or create field in.
    :param name:  Name of field to find or create.
    :param mesh:  Mesh to store locations in.
    '''
    if mesh is None:
        mesh = fieldmodule.findMeshByDimension(3)
    assert mesh.isValid(), 'getOrCreateElementXiField.  Invalid mesh'
    elementXiField = fieldmodule.findFieldByName(name)
    if elementXiField.isValid():
        elementXiField = elementXiField.castStoredMeshLocation()
        assert elementXiField.isValid(), 'getOrCreateElementXiField.  Existing field \'' + name + '\' is not stored mesh location type'
        return elementXiField
    fieldmodule.beginChange()
    elementXiField = fieldmodule.createFieldStoredMeshLocation(mesh)
    elementXiField.setName(name)
    elementXiField.setManaged(True)
    fieldmodule.endChange()
    return elementXiField

def getOrCreateLabelField(fieldmodule, name='label'):
    '''
    Finds or creates a stored string field for defining labels on nodes, e.g. annotation points.
    Raises exception if existing field of name is not string-valued.
    Note can't currently distinguish stored string from constant string fields.
    :param fieldmodule:  Zinc fieldmodule to find or create field in.
    :param name:  Name of field to find or create.
    '''
    labelField = fieldmodule.findFieldByName(name)
    if labelField.isValid():
        assert labelField.getValueType() == Field.VALUE_TYPE_STRING, 'getOrCreateLabelField.  Existing field \'' + name + '\' is not string valued'
        return labelField
    fieldmodule.beginChange()
    labelField = fieldmodule.createFieldStoredString()
    labelField.setName(name)
    labelField.setManaged(True)
    fieldmodule.endChange()
    return labelField

def getElementNodeIdentifiers(element, eft):
    '''
    Get identifiers of all nodes used by eft in element.
    '''
    nodeIdentifiers = []
    nodeCount = eft.getNumberOfLocalNodes()
    for n in range(nodeCount):
        node = element.getNode(eft, n + 1)
        nodeIdentifiers.append(node.getIdentifier())
    return nodeIdentifiers

def getElementNodeIdentifiers4Node(element, eft):
    '''
    Get 4 node identifiers for an element with 4 basis nodes, handling
    collapses e.g. where eft has fewer nodes. Asserts basis has 4 nodes.
    :param element: Element to query.
    :param eft: Element field template nodes are stored for in element.
    :return: List of 4 local node identifiers.
    '''
    elementbasis = eft.getElementbasis()
    basisNodesCount = elementbasis.getNumberOfNodes()
    assert basisNodesCount == 4, 'getElementNodeIdentifiers4Node:  Element ' + str(element.getIdentifier()) + ' is not using a 4 node basis'
    nodeIdentifiers = []
    fn = 1
    for n in range(basisNodesCount):
        ln = eft.getTermLocalNodeIndex(fn, 1)
        nodeIdentifiers.append(element.getNode(eft, ln).getIdentifier())
        fn += elementbasis.getNumberOfFunctionsPerNode(n + 1)
    return nodeIdentifiers

def getElementNodeIdentifiers8Node(element, eft):
    '''
    Get 8 node identifiers for an element with 8 basis nodes, handling
    collapses e.g. where eft has fewer nodes. Asserts basis has 8 nodes.
    :param element: Element to query.
    :param eft: Element field template nodes are stored for in element.
    :return: List of 8 local node identifiers.
    '''
    elementbasis = eft.getElementbasis()
    basisNodesCount = elementbasis.getNumberOfNodes()
    assert basisNodesCount == 8, 'getElementNodeIdentifiers8Node:  Element ' + str(element.getIdentifier()) + ' is not using an 8 node basis'
    nodeIdentifiers = []
    fn = 1
    for n in range(basisNodesCount):
        ln = eft.getTermLocalNodeIndex(fn, 1)
        nodeIdentifiers.append(element.getNode(eft, ln).getIdentifier())
        fn += elementbasis.getNumberOfFunctionsPerNode(n + 1)
    return nodeIdentifiers

def getMaximumNodeIdentifier(nodeset):
    """
    :return: Maximum node identifier in nodeset or -1 if none.
    """
    maximumNodeId = -1
    nodeiterator = nodeset.createNodeiterator()
    node = nodeiterator.next()
    while node.isValid():
        id = node.getIdentifier()
        if id > maximumNodeId:
            maximumNodeId = id
        node = nodeiterator.next()
    return maximumNodeId

def getMaximumElementIdentifier(mesh):
    """
    :return: Maximum element identifier in mesh or -1 if none.
    """
    maximumElementId = -1
    elementiterator = mesh.createElementiterator()
    element = elementiterator.next()
    while element.isValid():
        id = element.getIdentifier()
        if id > maximumElementId:
            maximumElementId = id
        element = elementiterator.next()
    return maximumElementId

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 = 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 = interpolateCubicHermite(v1, d1, v2, d2, xi)
    dx_ds = 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 computeNodeDerivativeHermiteLagrange(cache, coordinates, node1, derivative1, scale1, node2, scale2):
    """
    Computes the derivative at node2 from quadratic Hermite-Lagrange interpolation of
    node1 value and derivative1 to node2 value.
    :param cache: Field cache to evaluate in.
    :param coordinates: Coordinates field.
    :param node1, node2: Start and end nodes.
    :param derivative1: Node value label for derivative at node1.
    :param scale1, scale2: Scaling to apply to derivatives at nodes, e.g. -1.0 to reverse.
    :return: dx_dxi at node2
    """
    cache.setNode(node1)
    result, v1 = coordinates.getNodeParameters(cache, -1, Node.VALUE_LABEL_VALUE, 1, 3 )
    result, d1 = coordinates.getNodeParameters(cache, -1, derivative1, 1, 3 )
    d1 = [ d*scale1 for d in d1 ]
    cache.setNode(node2)
    result, v2 = coordinates.getNodeParameters(cache, -1, Node.VALUE_LABEL_VALUE, 1, 3 )
    d2 = interpolateHermiteLagrangeDerivative(v1, d1, v2, 1.0)
    d2 = [ d*scale2 for d in d2 ]
    return d2

Utility functions for easing use of Zinc API. Created on Jan 4, 2018  @author: <NAME> Finds or creates a rectangular cartesian coordinate field.     New field has component names, 'x', 'y', 'z'.     Raises exception if existing field of name is not finite element type or has incorrect attributes.     :param fieldmodule:  Zinc fieldmodule to find or create field in.     :param name:  Name of field to find or create.     :param componentsCount: Number of components / dimension of field. Finds or creates a stored mesh location field for storing locations in the     supplied mesh e.g. for defining on annotation points with mesh locations.     Raises exception if existing field of name is not stored mesh location type.     Note can't currently verify existing field stores locations in the supplied mesh.     :param fieldmodule:  Zinc fieldmodule to find or create field in.     :param name:  Name of field to find or create.     :param mesh:  Mesh to store locations in. Finds or creates a stored string field for defining labels on nodes, e.g. annotation points.     Raises exception if existing field of name is not string-valued.     Note can't currently distinguish stored string from constant string fields.     :param fieldmodule:  Zinc fieldmodule to find or create field in.     :param name:  Name of field to find or create. Get identifiers of all nodes used by eft in element. Get 4 node identifiers for an element with 4 basis nodes, handling     collapses e.g. where eft has fewer nodes. Asserts basis has 4 nodes.     :param element: Element to query.     :param eft: Element field template nodes are stored for in element.     :return: List of 4 local node identifiers. Get 8 node identifiers for an element with 8 basis nodes, handling     collapses e.g. where eft has fewer nodes. Asserts basis has 8 nodes.     :param element: Element to query.     :param eft: Element field template nodes are stored for in element.     :return: List of 8 local node identifiers. :return: Maximum node identifier in nodeset or -1 if none. :return: Maximum element identifier in mesh or -1 if none. 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 Computes the derivative at node2 from quadratic Hermite-Lagrange interpolation of     node1 value and derivative1 to node2 value.     :param cache: Field cache to evaluate in.     :param coordinates: Coordinates field.     :param node1, node2: Start and end nodes.     :param derivative1: Node value label for derivative at node1.     :param scale1, scale2: Scaling to apply to derivatives at nodes, e.g. -1.0 to reverse.     :return: dx_dxi at node2