static MultidimensionalArray NodalPatchRecovery(int jCell, double[] Nodes, DGField Phi, out AffineTrafo Trafilein)
{
GridData GridData = (GridData)Phi.GridDat;
int[] Neighbours, Edges;
GridData.GetCellNeighbours(jCell, GetCellNeighbours_Mode.ViaVertices, out Neighbours, out Edges);
if (Neighbours.Length != 8)
{
throw new NotSupportedException();
}
int[] JS = Neighbours;
jCell.AddToArray(ref JS);
MultidimensionalArray CellCoordinates = MultidimensionalArray.Create(JS.Length, 4, 2); // 1st index: jcell, top, bottom, left, right
var Kref = GridData.iGeomCells.RefElements[0];
if (GridData.iGeomCells.RefElements.Length != 1 || Kref.GetType() != typeof(BoSSS.Foundation.Grid.RefElements.Square))
{
throw new NotImplementedException();
}
for (int f = 0; f < JS.Length; f++)
{
GridData.TransformLocal2Global(Kref.Vertices, CellCoordinates.ExtractSubArrayShallow(f, -1, -1), JS[f]);
}
double xMin = CellCoordinates.ExtractSubArrayShallow(-1, -1, 0).Min();
double xMax = CellCoordinates.ExtractSubArrayShallow(-1, -1, 0).Max();
double yMin = CellCoordinates.ExtractSubArrayShallow(-1, -1, 1).Min();
double yMax = CellCoordinates.ExtractSubArrayShallow(-1, -1, 1).Max();
int N = Nodes.Length;
double[] xNodes = new double[N];
double[] yNodes = new double[N];
for (int i = 0; i < N; i++)
{
xNodes[i] = (xMax - xMin) * 0.5 * (Nodes[i] + 1) + xMin;
yNodes[i] = (yMax - yMin) * 0.5 * (Nodes[i] + 1) + yMin;
}
var TrChey2Glob = new AffineTrafo(2);
TrChey2Glob.Matrix[0, 0] = (xMax - xMin) * 0.5; TrChey2Glob.Affine[0] = (xMax - xMin) * 0.5 + xMin;
TrChey2Glob.Matrix[1, 1] = (yMax - yMin) * 0.5; TrChey2Glob.Affine[1] = (yMax - yMin) * 0.5 + yMin;
MultidimensionalArray[] NodeSets_global = new MultidimensionalArray[JS.Length];
NodeSet[] NodeSets = new NodeSet[JS.Length];
List <double> xNodesCell = new List <double>();
List <double> yNodesCell = new List <double>();
int[][] MapTo_i = new int[JS.Length][];
int[][] MapTo_j = new int[JS.Length][];
for (int f = 0; f < JS.Length; f++)
{
MultidimensionalArray CellCoords = CellCoordinates.ExtractSubArrayShallow(f, -1, -1);
double xMinCell = CellCoords.ExtractSubArrayShallow(-1, 0).Min();
double xMaxCell = CellCoords.ExtractSubArrayShallow(-1, 0).Max();
double yMinCell = CellCoords.ExtractSubArrayShallow(-1, 1).Min();
double yMaxCell = CellCoords.ExtractSubArrayShallow(-1, 1).Max();
int iMin = xNodes.FirstIndexWhere(x => x >= xMinCell);
int iMax = xNodes.LastIndexWhere(x => x < xMaxCell);
int jMin = yNodes.FirstIndexWhere(y => y >= yMinCell);
int jMax = yNodes.LastIndexWhere(y => y < yMaxCell);
int NxCell = iMax - iMin + 1;
int NyCell = jMax - jMin + 1;
int K = NxCell * NyCell;
NodeSets_global[f] = MultidimensionalArray.Create(K, 2);
MapTo_i[f] = new int[K];
MapTo_j[f] = new int[K];
int k = 0;
for (int i = iMin; i <= iMax; i++)
{
for (int j = jMin; j <= jMax; j++)
{
MapTo_i[f][k] = i;
MapTo_j[f][k] = j;
NodeSets_global[f][k, 0] = xNodes[i];
NodeSets_global[f][k, 1] = yNodes[j];
Debug.Assert(GridData.Cells.IsInCell(new double[] { xNodes[i], yNodes[j] }, JS[f], null));
k++;
}
}
NodeSets[f] = new NodeSet(GridData.Cells.GetRefElement(jCell), NxCell * NyCell, 2);
GridData.TransformGlobal2Local(NodeSets_global[f], NodeSets[f], JS[f], null);
NodeSets[f].LockForever();
}
var TrGl2Loc = AffineTrafo.FromPoints(NodeSets_global.Last().ExtractSubArrayShallow(new int[] { 0, 0 }, new int[] { 2, 1 }), NodeSets.Last().ExtractSubArrayShallow(new int[] { 0, 0 }, new int[] { 2, 1 }));
Trafilein = (TrGl2Loc * TrChey2Glob).Invert();
var Return = MultidimensionalArray.Create(N, N);
for (int f = 0; f < JS.Length; f++)
{
int K = NodeSets[f].GetLength(0);
var Result = MultidimensionalArray.Create(1, K);
Phi.Evaluate(JS[f], 1, NodeSets[f], Result);
for (int k = 0; k < K; k++)
{
//double x_i = xNodes[MapTo_i[f][k]];
//double y_j = yNodes[MapTo_j[f][k]];
//double val = (x_i*0.3).Pow2() - (y_j*0.3).Pow2();
Debug.Assert(Return[MapTo_i[f][k], MapTo_j[f][k]] == 0.0);
Return[MapTo_i[f][k], MapTo_j[f][k]] = Result[0, k];
}
}
// ----------------------------------
return(Return);
}
/// <summary>
/// Constructs suitable quadrature rules cells in
/// <paramref name="mask"/>.
/// </summary>
/// <param name="mask">
/// Cells for which quadrature rules shall be created
/// </param>
/// <param name="order">
/// Desired order of the moment-fitting system. Assuming that
/// <see cref="surfaceRuleFactory"/> integrates the basis polynomials
/// exactly over the zero iso-contour (which it usually
/// doesn't!), the resulting quadrature rules will be exact up to this
/// order.
/// </param>
/// <returns>A set of quadrature rules</returns>
/// <remarks>
/// Since the selected level set is generally discontinuous across cell
/// boundaries, this method does not make use of the fact that
/// neighboring cells share edges. That is, the optimization will be
/// performed twice for each inner edge in <paramref name="mask"/>.
/// </remarks>
public IEnumerable <IChunkRulePair <QuadRule> > GetQuadRuleSet(ExecutionMask mask, int order)
{
using (var tr = new FuncTrace()) {
CellMask cellMask = mask as CellMask;
if (cellMask == null)
{
throw new ArgumentException("Mask must be a volume mask", "mask");
}
// Note: This is a parallel call, so do this early to avoid parallel confusion
localCellIndex2SubgridIndex = new SubGrid(cellMask).LocalCellIndex2SubgridIndex;
int maxLambdaDegree = order + 1;
int noOfLambdas = GetNumberOfLambdas(maxLambdaDegree);
int noOfEdges = LevelSetData.GridDat.Grid.RefElements[0].NoOfFaces;
int D = RefElement.SpatialDimension;
// Get the basis polynomials and integrate them analytically
Polynomial[] basePolynomials = RefElement.GetOrthonormalPolynomials(order).ToArray();
Polynomial[] polynomials = new Polynomial[basePolynomials.Length * D];
for (int i = 0; i < basePolynomials.Length; i++)
{
Polynomial p = basePolynomials[i];
for (int d = 0; d < D; d++)
{
Polynomial pNew = p.CloneAs();
for (int j = 0; j < p.Coeff.Length; j++)
{
pNew.Exponents[j, d]++;
pNew.Coeff[j] /= pNew.Exponents[j, d];
pNew.Coeff[j] /= D; // Make sure divergence is Phi again
}
polynomials[i * D + d] = pNew;
}
}
// basePolynomials[i] == div(polynomials[i*D], ... , polynomials[i*D + D - 1])
lambdaBasis = new PolynomialList(polynomials);
if (RestrictNodes)
{
trafos = new AffineTrafo[mask.NoOfItemsLocally];
foreach (Chunk chunk in mask)
{
foreach (var cell in chunk.Elements.AsSmartEnumerable())
{
CellMask singleElementMask = new CellMask(
LevelSetData.GridDat, Chunk.GetSingleElementChunk(cell.Value));
LineAndPointQuadratureFactory.LineQRF lineFactory = this.edgeRuleFactory as LineAndPointQuadratureFactory.LineQRF;
if (lineFactory == null)
{
throw new Exception();
}
var lineRule = lineFactory.GetQuadRuleSet(singleElementMask, order).Single().Rule;
var pointRule = lineFactory.m_Owner.GetPointFactory().GetQuadRuleSet(singleElementMask, order).Single().Rule;
// Also add point rule points since line rule points
// are constructed from Gauss rules that do not include
// the end points
BoundingBox box = new BoundingBox(lineRule.Nodes);
box.AddPoints(pointRule.Nodes);
int noOfRoots = pointRule.Nodes.GetLength(0);
if (noOfRoots <= 1)
{
// Cell is considered cut because the level set
// is very close, but actually isn't. Note that
// we can NOT omit the cell (as in the surface
// case) as it will be missing in the list of
// uncut cells, i.e. this cell would be ignored
// completely
trafos[localCellIndex2SubgridIndex[cell.Value]] =
AffineTrafo.Identity(RefElement.SpatialDimension);
continue;
}
else if (noOfRoots == 2)
{
// Go a bit into the direction of the normal
// from the center between the nodes in order
// not to miss regions with strong curvature
double[] center = box.Min.CloneAs();
center.AccV(1.0, box.Max);
center.ScaleV(0.5);
NodeSet centerNode = new NodeSet(RefElement, center);
centerNode.LockForever();
MultidimensionalArray normal = LevelSetData.GetLevelSetReferenceNormals(centerNode, cell.Value, 1);
MultidimensionalArray dist = LevelSetData.GetLevSetValues(centerNode, cell.Value, 1);
double scaling = Math.Sqrt(LevelSetData.GridDat.Cells.JacobiDet[cell.Value]);
double[] newPoint = new double[D];
for (int d = 0; d < D; d++)
{
newPoint[d] = center[d] - normal[0, 0, d] * dist[0, 0] / scaling;
}
box.AddPoint(newPoint);
// Make sure points stay in box
for (int d = 0; d < D; d++)
{
box.Min[d] = Math.Max(box.Min[d], -1);
box.Max[d] = Math.Min(box.Max[d], 1);
}
}
MultidimensionalArray preImage = RefElement.Vertices.ExtractSubArrayShallow(
new int[] { 0, 0 }, new int[] { D, D - 1 });
MultidimensionalArray image = MultidimensionalArray.Create(D + 1, D);
image[0, 0] = box.Min[0]; // Top left
image[0, 1] = box.Max[1];
image[1, 0] = box.Max[0]; // Top right
image[1, 1] = box.Max[1];
image[2, 0] = box.Min[0]; // Bottom left;
image[2, 1] = box.Min[1];
AffineTrafo trafo = AffineTrafo.FromPoints(preImage, image);
trafos[localCellIndex2SubgridIndex[cell.Value]] = trafo;
}
}
}
LambdaCellBoundaryQuadrature cellBoundaryQuadrature =
new LambdaCellBoundaryQuadrature(this, edgeRuleFactory, cellMask);
cellBoundaryQuadrature.Execute();
LambdaLevelSetSurfaceQuadrature surfaceQuadrature =
new LambdaLevelSetSurfaceQuadrature(this, surfaceRuleFactory, cellMask);
surfaceQuadrature.Execute();
// Must happen _after_ all parallel calls (e.g., definition of
// the sub-grid or quadrature) in order to avoid problems in
// parallel runs
if (mask.NoOfItemsLocally == 0)
{
var empty = new ChunkRulePair <QuadRule> [0];
return(empty);
}
if (cachedRules.ContainsKey(order))
{
order = cachedRules.Keys.Where(cachedOrder => cachedOrder >= order).Min();
CellMask cachedMask = new CellMask(mask.GridData, cachedRules[order].Select(p => p.Chunk).ToArray());
if (cachedMask.Equals(mask))
{
return(cachedRules[order]);
}
else
{
throw new NotImplementedException(
"Case not yet covered yet in combination with caching; deactivate caching to get rid of this message");
}
}
double[,] quadResults = cellBoundaryQuadrature.Results;
foreach (Chunk chunk in mask)
{
for (int i = 0; i < chunk.Len; i++)
{
int iSubGrid = localCellIndex2SubgridIndex[chunk.i0 + i];
switch (jumpType)
{
case JumpTypes.Heaviside:
for (int k = 0; k < noOfLambdas; k++)
{
quadResults[iSubGrid, k] -= surfaceQuadrature.Results[iSubGrid, k];
}
break;
case JumpTypes.OneMinusHeaviside:
for (int k = 0; k < noOfLambdas; k++)
{
quadResults[iSubGrid, k] += surfaceQuadrature.Results[iSubGrid, k];
}
break;
case JumpTypes.Sign:
for (int k = 0; k < noOfLambdas; k++)
{
quadResults[iSubGrid, k] -= 2.0 * surfaceQuadrature.Results[iSubGrid, k];
}
break;
default:
throw new NotImplementedException();
}
}
}
BitArray voidCellsArray = new BitArray(LevelSetData.GridDat.Cells.NoOfLocalUpdatedCells);
BitArray fullCellsArray = new BitArray(LevelSetData.GridDat.Cells.NoOfLocalUpdatedCells);
foreach (Chunk chunk in cellMask)
{
foreach (var cell in chunk.Elements)
{
double rhsL2Norm = 0.0;
for (int k = 0; k < noOfLambdas; k++)
{
double entry = quadResults[localCellIndex2SubgridIndex[cell], k];
rhsL2Norm += entry * entry;
}
if (rhsL2Norm < 1e-14)
{
// All integrals are zero => cell not really cut
// (level set is tangent) and fully in void region
voidCellsArray[cell] = true;
continue;
}
double l2NormFirstIntegral = quadResults[localCellIndex2SubgridIndex[cell], 0];
l2NormFirstIntegral *= l2NormFirstIntegral;
double rhsL2NormWithoutFirst = rhsL2Norm - l2NormFirstIntegral;
// Beware: This check is only sensible if basis is orthonormal on RefElement!
if (rhsL2NormWithoutFirst < 1e-14 &&
Math.Abs(l2NormFirstIntegral - RefElement.Volume) < 1e-14)
{
// All integrals are zero except integral over first integrand
// If basis is orthonormal, this implies that cell is uncut and
// fully in non-void region since then
// \int_K \Phi_i dV = \int_A \Phi_i dV = \delta_{0,i}
// However, we have to compare RefElement.Volume since
// integration is performed in reference coordinates!
fullCellsArray[cell] = true;
}
}
}
var result = new List <ChunkRulePair <QuadRule> >(cellMask.NoOfItemsLocally);
CellMask emptyCells = new CellMask(LevelSetData.GridDat, voidCellsArray);
foreach (Chunk chunk in emptyCells)
{
foreach (int cell in chunk.Elements)
{
QuadRule emptyRule = QuadRule.CreateEmpty(RefElement, 1, RefElement.SpatialDimension);
emptyRule.Nodes.LockForever();
result.Add(new ChunkRulePair <QuadRule>(
Chunk.GetSingleElementChunk(cell), emptyRule));
}
}
CellMask fullCells = new CellMask(LevelSetData.GridDat, fullCellsArray);
foreach (Chunk chunk in fullCells)
{
foreach (int cell in chunk.Elements)
{
QuadRule fullRule = RefElement.GetQuadratureRule(order);
result.Add(new ChunkRulePair <QuadRule>(
Chunk.GetSingleElementChunk(cell), fullRule));
}
}
CellMask realCutCells = cellMask.Except(emptyCells).Except(fullCells);
if (RestrictNodes)
{
foreach (Chunk chunk in realCutCells)
{
foreach (int cell in chunk.Elements)
{
CellMask singleElementMask = new CellMask(
LevelSetData.GridDat, Chunk.GetSingleElementChunk(cell));
AffineTrafo trafo = trafos[localCellIndex2SubgridIndex[cell]];
Debug.Assert(Math.Abs(trafo.Matrix.Determinant()) > 1e-10);
NodeSet nodes = GetNodes(noOfLambdas).CloneAs();
NodeSet mappedNodes = new NodeSet(RefElement, trafo.Transform(nodes));
mappedNodes.LockForever();
// Remove nodes in negative part
MultidimensionalArray levelSetValues = LevelSetData.GetLevSetValues(mappedNodes, cell, 1);
List <int> nodesToBeCopied = new List <int>(mappedNodes.GetLength(0));
for (int n = 0; n < nodes.GetLength(0); n++)
{
if (levelSetValues[0, n] >= 0.0)
{
nodesToBeCopied.Add(n);
}
}
NodeSet reducedNodes = new NodeSet(
this.RefElement, nodesToBeCopied.Count, D);
for (int n = 0; n < nodesToBeCopied.Count; n++)
{
for (int d = 0; d < D; d++)
{
reducedNodes[n, d] = mappedNodes[nodesToBeCopied[n], d];
}
}
reducedNodes.LockForever();
QuadRule optimizedRule = GetOptimizedRule(
cell,
trafo,
reducedNodes,
quadResults,
order);
result.Add(new ChunkRulePair <QuadRule>(
singleElementMask.Single(), optimizedRule));
}
}
}
else
{
// Use same nodes in all cells
QuadRule[] optimizedRules = GetOptimizedRules(
realCutCells, GetNodes(noOfLambdas), quadResults, order);
int ruleIndex = 0;
foreach (Chunk chunk in realCutCells)
{
foreach (var cell in chunk.Elements)
{
result.Add(new ChunkRulePair <QuadRule>(
Chunk.GetSingleElementChunk(cell), optimizedRules[ruleIndex]));
ruleIndex++;
}
}
}
cachedRules[order] = result.OrderBy(p => p.Chunk.i0).ToArray();
return(cachedRules[order]);
}
}
public void CreateWithMatlab()
{
// ================================
// generate voronoi graph in matlab
// ================================
int J = this.DelaunayVertices.NoOfRows;
int D = this.DelaunayVertices.NoOfCols;
if (D != 2)
{
throw new NotSupportedException("todo");
}
int[][] OutputVertexIndex = new int[J * 5][];
MultidimensionalArray VertexCoordinates;
{
var Matlab = new BatchmodeConnector();
Matlab.PutMatrix(this.DelaunayVertices, "X");
// create mirror points
Matlab.Cmd("[J, D] = size(X);");
Matlab.Cmd("Xneg = [-X(:, 1), X(:, 2)];");
Matlab.Cmd("Yneg = [X(:, 1), -X(:, 2)];");
Matlab.Cmd("X2 = [ones(J, 1) * 2, zeros(J, 1)];");
Matlab.Cmd("Y2 = [zeros(J, 1), ones(J, 1) * 2];");
Matlab.Cmd("Xm = X;");
Matlab.Cmd("Xm = [Xm; Xneg]; % mirror at x = 0");
Matlab.Cmd("Xm = [Xm; X2 + Xneg]; % mirror at x = 1");
Matlab.Cmd("Xm = [Xm; Yneg]; % mirror at x = 0");
Matlab.Cmd("Xm = [Xm; Y2 + Yneg]; % mirror at x = 1");
// compute Voronoi diagramm
Matlab.Cmd("[V, C] = voronoin(Xm);");
// output (export from matlab)
Matlab.GetStaggeredIntArray(OutputVertexIndex, "C");
Matlab.GetMatrix(null, "V");
// run matlab
Matlab.Execute(false);
// import here
VertexCoordinates = (MultidimensionalArray)(Matlab.OutputObjects["V"]);
// correct indices (1-based index to 0-based index)
foreach (int[] cell in OutputVertexIndex)
{
int K = cell.Length;
for (int k = 0; k < K; k++)
{
cell[k]--;
}
}
}
// ===============
// record internal
// ===============
{
// define Cell data
{
this.m_CellData = new CellData();
this.m_CellData.m_Owner = this;
this.m_VertexData = new VertexData();
this.m_LogEdges = new LogEdgeData();
this.m_VertexData.Coordinates = VertexCoordinates;
this.m_CellData.CellVertices = OutputVertexIndex.GetSubVector(0, J);
this.m_CellData.InfoFlags = new CellInfo[J];
ArrayTools.SetAll(this.m_CellData.InfoFlags, CellInfo.CellIsAffineLinear | CellInfo.IsAggregate);
}
// decomposition of Voronoi cells to triangles/tetrahedrons
{
m_CellData.AggregateCellToParts = new int[J][];
if (D == 2)
{
var Tri = RefElements.Triangle.Instance;
m_CellData.RefElements = new RefElement[] { Tri };
int cnt = 0;
for (int j = 0; j < J; j++)
{
int[] VtxIndices = m_CellData.CellVertices[j];
int[] PartIdx = new int[VtxIndices.Length - 2];
for (int i = 0; i < PartIdx.Length; i++)
{
PartIdx[i] = cnt;
cnt++;
}
m_CellData.AggregateCellToParts[j] = PartIdx;
}
int NoOfParts = cnt;
m_CellData.PartTransformation = MultidimensionalArray.Create(NoOfParts, D, D);
m_CellData.PartCenter = MultidimensionalArray.Create(NoOfParts, D);
MultidimensionalArray TriangleVtx = MultidimensionalArray.Create(3, D);
for (int j = 0; j < J; j++)
{
int[] VtxIndices = m_CellData.CellVertices[j];
int[] PartIdx = m_CellData.AggregateCellToParts[j];
for (int i = 0; i < PartIdx.Length; i++)
{
int iV0 = VtxIndices[0];
int iV1 = VtxIndices[i + 1];
int iV2 = VtxIndices[i + 2];
TriangleVtx[0, 0] = m_VertexData.Coordinates[iV0, 0];
TriangleVtx[0, 1] = m_VertexData.Coordinates[iV0, 1];
TriangleVtx[1, 0] = m_VertexData.Coordinates[iV1, 0];
TriangleVtx[1, 1] = m_VertexData.Coordinates[iV1, 1];
TriangleVtx[2, 0] = m_VertexData.Coordinates[iV2, 0];
TriangleVtx[2, 1] = m_VertexData.Coordinates[iV2, 1];
var TR = AffineTrafo.FromPoints(Tri.Vertices, TriangleVtx);
m_CellData.PartTransformation.ExtractSubArrayShallow(PartIdx[i], -1, -1).Set(TR.Matrix);
m_CellData.PartCenter.ExtractSubArrayShallow(PartIdx[i], -1).SetVector(TR.Affine);
}
}
}
else if (D == 3)
{
throw new NotImplementedException("todo");
}
else
{
throw new NotSupportedException("Unknown spatial dimension.");
}
}
// bounding boxes, transformations
{
BoundingBox BB = new BoundingBox(D);
m_CellData.BoundingBoxTransformation = MultidimensionalArray.Create(J, D, D);
m_CellData.BoundingBoxCenter = MultidimensionalArray.Create(J, D);
for (int j = 0; j < J; j++)
{
m_CellData.GetCellBoundingBox(j, BB);
for (int d = 0; d < D; d++)
{
double lo = BB.Min[d];
double hi = BB.Max[d];
m_CellData.BoundingBoxCenter[j, d] = 0.5 * (lo + hi);
m_CellData.BoundingBoxTransformation[j, d, d] = 0.5 * (hi - lo);
}
}
}
// mapping: vertex to cell
{
List <int>[] VertexToCell = new List <int> [VertexCoordinates.Length];
for (int j = 0; j < J; j++)
{
foreach (int iVtx in OutputVertexIndex[j])
{
if (VertexToCell[iVtx] == null)
{
VertexToCell[iVtx] = new List <int>();
}
if (!VertexToCell[iVtx].Contains(j))
{
VertexToCell[iVtx].Add(j);
}
}
}
m_VertexData.VerticeToCell = new int[VertexToCell.Length][];
for (int i = 0; i < VertexToCell.Length; i++)
{
if (VertexToCell[i] == null)
{
m_VertexData.VerticeToCell[i] = new int[0];
}
else
{
m_VertexData.VerticeToCell[i] = VertexToCell[i].ToArray();
}
}
VertexToCell = null;
}
// cell neighbors, edges
{
m_CellData.CellNeighbours = new int[J][];
var tmpCells2Edges = new List <int> [J];
Dictionary <int, int> ShareCount = new Dictionary <int, int>(); // key: cell index; value: number of vertices shared with this cell
var EdgesTemp = new List <EdgeTemp>();
List <int> Neighs = new List <int>();
List <int> EdgeVtx = new List <int>();
List <int> IdedEdgsAtOneCell = new List <int>();
for (int jCell = 0; jCell < J; jCell++) // loop over cells
{
ShareCount.Clear();
Neighs.Clear();
IdedEdgsAtOneCell.Clear();
// determine how many vertices 'jCell' shares with other cells
foreach (int iVtx in m_CellData.CellVertices[jCell])
{
foreach (int jOtherCell in m_VertexData.VerticeToCell[iVtx])
{
if (jOtherCell != jCell)
{
if (!ShareCount.ContainsKey(jOtherCell))
{
ShareCount.Add(jOtherCell, 1);
}
else
{
ShareCount[jOtherCell]++;
}
}
}
}
// find faces
int[][] FaceIdx = ConvexHullFaces(m_VertexData.Coordinates, m_CellData.CellVertices[jCell]);
// determine cell neighbors and edges
int NoOfFacesFound = 0;
foreach (var kv in ShareCount)
{
int jCellNeigh = kv.Key;
int NoOfSharedVtx = kv.Value;
if (NoOfSharedVtx >= D)
{
// +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// cells 'jCell' and 'jCellNeigh' share more than 'D' vertices - this is an edge to another cell,
// resp. a face of 'jCell'.
// +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Debug.Assert(jCellNeigh != jCell);
Debug.Assert(!Neighs.Contains(jCellNeigh));
Neighs.Add(jCellNeigh);
NoOfFacesFound++;
EdgeVtx.Clear();
foreach (int iVtx in m_CellData.CellVertices[jCell])
{
if (Array.IndexOf(m_VertexData.VerticeToCell[iVtx], jCellNeigh) >= 0)
{
EdgeVtx.Add(iVtx);
}
}
if (jCell < jCellNeigh)
{
// the pairing 'jCell'/'jCellNeigh' will be discovered twice;
// we only want to record once
var Etmp = new EdgeTemp()
{
jCell1 = jCell,
jCell2 = jCellNeigh,
Vertices = EdgeVtx.ToArray()
};
EdgesTemp.Add(Etmp);
IdedEdgsAtOneCell.Add(EdgesTemp.Count - 1);
if (tmpCells2Edges[jCell] == null)
{
tmpCells2Edges[jCell] = new List <int>();
}
if (tmpCells2Edges[jCellNeigh] == null)
{
tmpCells2Edges[jCellNeigh] = new List <int>();
}
tmpCells2Edges[jCell].Add(EdgesTemp.Count); // the funky convention for edges-to-cell: the index is
tmpCells2Edges[jCellNeigh].Add(-EdgesTemp.Count); // shifted by 1, out-cell is negative
}
else
{
Debug.Assert(jCellNeigh < jCell);
int MatchCount = 0;
foreach (int i in tmpCells2Edges[jCellNeigh])
{
int iEdge = Math.Abs(i) - 1;
if (EdgesTemp[iEdge].jCell1 == jCellNeigh && EdgesTemp[iEdge].jCell2 == jCell)
{
MatchCount++;
IdedEdgsAtOneCell.Add(iEdge);
}
}
Debug.Assert(MatchCount == 1);
}
#if DEBUG
if (D == 2)
{
Debug.Assert(EdgeVtx.Count == 2);
}
else if (D == 3)
{
// verify that all vertices of the edge are geometrically in one plane
Debug.Assert(EdgeVtx.Count >= 3);
var FacePlane = AffineManifold.FromPoints(
m_VertexData.Coordinates.GetRowPt(EdgeVtx[0]),
m_VertexData.Coordinates.GetRowPt(EdgeVtx[1]),
m_VertexData.Coordinates.GetRowPt(EdgeVtx[2])
);
BoundingBox BB = new BoundingBox(D);
m_CellData.GetCellBoundingBox(jCell, BB);
double h = BB.Diameter;
foreach (int iVtx in EdgeVtx)
{
double dist = Math.Abs(FacePlane.PointDistance(m_VertexData.Coordinates.GetRow(iVtx)));
Debug.Assert(dist < h * 1e-8);
}
}
else
{
throw new NotSupportedException("Unknown spatial dimension.");
}
#endif
}
}
m_CellData.CellNeighbours[jCell] = Neighs.ToArray();
Debug.Assert(NoOfFacesFound <= FaceIdx.Length);
Debug.Assert(NoOfFacesFound == IdedEdgsAtOneCell.Count);
// boundary edges
if (NoOfFacesFound == FaceIdx.Length)
{
// nothing to do - all faces/edges identified
#if DEBUG
for (int i = 0; i < NoOfFacesFound; i++)
{
int Matches = 0;
for (int l = 0; l < NoOfFacesFound; l++)
{
if (FaceIdx[i].SetEquals(EdgesTemp[IdedEdgsAtOneCell[l]].Vertices))
{
Matches++;
}
}
Debug.Assert(Matches == 1);
}
#endif
}
else
{
// missing boundary
for (int i = 0; i < FaceIdx.Length; i++)
{
int Matches = 0;
for (int l = 0; l < NoOfFacesFound; l++)
{
if (FaceIdx[i].SetEquals(EdgesTemp[IdedEdgsAtOneCell[l]].Vertices))
{
Matches++;
}
}
Debug.Assert(Matches <= 1);
if (Matches == 0)
{
// boundary edge found
var Etmp = new EdgeTemp()
{
jCell1 = jCell,
jCell2 = int.MinValue,
Vertices = EdgeVtx.ToArray()
};
EdgesTemp.Add(Etmp);
tmpCells2Edges[jCell].Add(EdgesTemp.Count); // index shifted by 1
}
}
}
}
// convert temporary data structures to the final ones
m_CellData.Cells2Edges = new int[J][];
var C2E = m_CellData.Cells2Edges;
for (int j = 0; j < J; j++)
{
C2E[j] = tmpCells2Edges[j] != null ? tmpCells2Edges[j].ToArray() : new int[0];
}
m_GeomEdges = new GeomEdgeData();
int NoOfEdges = EdgesTemp.Count;
m_GeomEdges.Info = new EdgeInfo[NoOfEdges];
m_LogEdges.CellIndices = new int[NoOfEdges, 2];
m_GeomEdges.VertexIndices = new int[NoOfEdges][];
var Evtx = m_GeomEdges.VertexIndices;
var E2C = m_LogEdges.CellIndices;
var Einf = m_GeomEdges.Info;
for (int iEdge = 0; iEdge < NoOfEdges; iEdge++)
{
var Etmp = EdgesTemp[iEdge];
E2C[iEdge, 0] = Etmp.jCell1;
E2C[iEdge, 1] = Etmp.jCell2;
Einf[iEdge] = EdgeInfo.EdgeIsAffineLinear | EdgeInfo.IsAggregate;
if (Etmp.jCell2 < 0)
{
Einf[iEdge] |= EdgeInfo.Boundary;
}
Evtx[iEdge] = Etmp.Vertices;
}
}
// edge metrics
{
if (D == 2)
{
m_GeomEdges.EdgeRefElements = new RefElement[] { Line.Instance };
}
else if (D == 3)
{
m_GeomEdges.EdgeRefElements = new RefElement[] { Triangle.Instance };
}
else
{
throw new NotSupportedException("Unknown spatial dimension.");
}
int[][] Evtx = m_GeomEdges.VertexIndices;
int NoOfParts = 0;
int NoOfEdges = m_GeomEdges.Count;
for (int iEdge = 0; iEdge < NoOfEdges; iEdge++)
{
NoOfParts += Evtx[iEdge].Length - D + 1;
}
Debug.Assert(D != 2 || NoOfParts == NoOfEdges);
m_GeomEdges.Edge2CellTrafoIndex = new int[NoOfParts, 2];
var tmpEdg2CellTrafo = new Dictionary <int, Tuple <int, AffineTrafo> >();
// unsolved problem:
// (D-1) -- dimensional tesselation of edge is given by D -- dimensional tesselation of adjacent cells
// * case D == 2: trivial
// * case D == 3: the problem is that two adjacent cells will induce _two different_ tesselations, which
// wont match in the general case.
MultidimensionalArray PreImage = m_GeomEdges.EdgeRefElements[0].Vertices;
MultidimensionalArray Image = MultidimensionalArray.Create(PreImage.NoOfRows, D);
//for(int iEdge )
}
}
}
