/// <summary>
/// Setup interpolation for all nodes in the mesh.
/// </summary>
public void Setup(SMeshData mesh)
{
var nodeInterpData = new Interpolator.InterPData[mesh.NumberOfNodes];
for (int i = 0; i < mesh.NumberOfNodes; i++)
{
nodeInterpData[i] = SetupNodeInterpolation(mesh, i);
}
_nodeInterpolator = new Interpolator(nodeInterpData);
}
/// <summary>
/// Setup interpolation for all nodes in the mesh.
/// </summary>
public void Setup()
{
var nodeInterpData = new Interpolator.InterPData[_mesh.Nodes.Count];
for (int i = 0; i < _mesh.Nodes.Count; i++)
{
MeshNode node = _mesh.Nodes[i];
nodeInterpData[i] = SetupNodeInterpolation(node);
}
_nodeInterpolator = new Interpolator(nodeInterpData);
}
/// <summary>
/// Calculate interpolation weights for interpolating a value at the provided <paramref name="node"/>
/// from the surrounding element center values.
/// </summary>
/// <param name="node">Node to setup interpolation for</param>
public Interpolator.InterPData SetupNodeInterpolation(MeshNode node)
{
Interpolator.InterPData interpData = new Interpolator.InterPData()
{
Indices = new int[node.Elements.Count],
Weights = new double[node.Elements.Count],
};
double Ixx = 0;
double Iyy = 0;
double Ixy = 0;
double Rx = 0;
double Ry = 0;
double omegaTot = 0;
for (int i = 0; i < node.Elements.Count; i++)
{
MeshElement element = node.Elements[i];
double dx = element.XCenter - node.X;
double dy = element.YCenter - node.Y;
Ixx += dx * dx;
Iyy += dy * dy;
Ixy += dx * dy;
Rx += dx;
Ry += dy;
interpData.Indices[i] = element.Index;
}
double lambda = Ixx * Iyy - Ixy * Ixy;
if (lambda > 1e-10 * (Ixx * Iyy))
{
// Standard case - Pseudo Laplacian
for (int i = 0; i < node.Elements.Count; i++)
{
MeshElement element = node.Elements[i];
double dx = element.XCenter - node.X;
double dy = element.YCenter - node.Y;
double lambda_x = (Ixy * Ry - Iyy * Rx) / lambda;
double lambda_y = (Ixy * Rx - Ixx * Ry) / lambda;
double omega = 1.0 + lambda_x * dx + lambda_y * dy;
if (!_allowExtrapolation)
{
if (omega < 0)
{
omega = 0;
}
else if (omega > 2)
{
omega = 2;
}
}
interpData.Weights[i] = omega;
omegaTot += omega;
}
}
if (omegaTot <= 0)
{
// We did not succeed using pseudo laplace procedure,
// use inverse distance instead
omegaTot = 0;
for (int i = 0; i < node.Elements.Count; i++)
{
MeshElement element = node.Elements[i];
double dx = element.XCenter - node.X;
double dy = element.YCenter - node.Y;
// Inverse distance weighted interpolation weight
double omega = 1 / Math.Sqrt(dx * dx + dy * dy);
interpData.Weights[i] = omega;
omegaTot += omega;
}
}
// Scale to 1
if (omegaTot != 0)
{
for (int i = 0; i < interpData.Weights.Length; i++)
{
interpData.Weights[i] /= omegaTot;
}
}
else
{
for (int i = 0; i < interpData.Weights.Length; i++)
{
interpData.Weights[i] = 0;
}
}
//double sum = 0;
//for (int i = 0; i < interpData.Weights.Length; i++)
//{
// sum += interpData.Weights[i];
//}
//if (Math.Abs(sum - 1) > 1e-12)
// Console.Out.WriteLine("Duh!!!: "+node.Index);
return(interpData);
}
/// <summary>
/// Calculate interpolation weights for interpolating a value at the node <paramref name="nodeIndex"/>
/// from the surrounding element center values.
/// </summary>
/// <param name="mesh">Mesh object</param>
/// <param name="nodeIndex">Index of node to setup interpolation for</param>
public Interpolator.InterPData SetupNodeInterpolation(SMeshData mesh, int nodeIndex)
{
List <int> nodeElements = mesh.NodesElmts[nodeIndex];
Interpolator.InterPData interpData = new Interpolator.InterPData()
{
Indices = new int[nodeElements.Count],
Weights = new double[nodeElements.Count],
};
double omegaTot = 0;
// Pseudo-Laplacian only works in case of more than 3 elements connected to the node.
if (nodeElements.Count >= 3)
{
double Ixx = 0;
double Iyy = 0;
double Ixy = 0;
double Rx = 0;
double Ry = 0;
for (int i = 0; i < nodeElements.Count; i++)
{
int elementIndex = nodeElements[i];
double dx = mesh.ElementXCenter[elementIndex] - mesh.X[nodeIndex];
double dy = mesh.ElementYCenter[elementIndex] - mesh.Y[nodeIndex];
Ixx += dx * dx;
Iyy += dy * dy;
Ixy += dx * dy;
Rx += dx;
Ry += dy;
interpData.Indices[i] = elementIndex;
}
double lambda = Ixx * Iyy - Ixy * Ixy;
if (lambda > 1e-10 * (Ixx * Iyy))
{
// Standard case - Pseudo Laplacian
double lambda_x = (Ixy * Ry - Iyy * Rx) / lambda;
double lambda_y = (Ixy * Rx - Ixx * Ry) / lambda;
for (int i = 0; i < nodeElements.Count; i++)
{
int elementIndex = nodeElements[i];
double dx = mesh.ElementXCenter[elementIndex] - mesh.X[nodeIndex];
double dy = mesh.ElementYCenter[elementIndex] - mesh.Y[nodeIndex];
double omega = 1.0 + lambda_x * dx + lambda_y * dy;
if (!_allowExtrapolation)
{
if (omega < 0)
{
omega = 0;
}
else if (omega > 2)
{
omega = 2;
}
}
interpData.Weights[i] = omega;
omegaTot += omega;
}
}
}
if (omegaTot <= 1e-10)
{
// We did not succeed using pseudo laplace procedure,
// use inverse distance instead
omegaTot = 0;
for (int i = 0; i < nodeElements.Count; i++)
{
int elementIndex = nodeElements[i];
double dx = mesh.ElementXCenter[elementIndex] - mesh.X[nodeIndex];
double dy = mesh.ElementYCenter[elementIndex] - mesh.Y[nodeIndex];
// Inverse distance weighted interpolation weight
double omega = 1 / Math.Sqrt(dx * dx + dy * dy);
interpData.Indices[i] = elementIndex;
interpData.Weights[i] = omega;
omegaTot += omega;
}
}
// Scale to 1
if (omegaTot != 0)
{
for (int i = 0; i < interpData.Weights.Length; i++)
{
interpData.Weights[i] /= omegaTot;
}
}
else
{
for (int i = 0; i < interpData.Weights.Length; i++)
{
interpData.Weights[i] = 0;
}
}
//double sum = 0;
//for (int i = 0; i < interpData.Weights.Length; i++)
//{
// sum += interpData.Weights[i];
//}
//if (Math.Abs(sum - 1) > 1e-12)
// Console.Out.WriteLine("Duh!!!: "+node.Index);
return(interpData);
}
