static Vector ComputeIntersection(Vector S, Vector E, AffineManifold clipEdge)
{
var SE = AffineManifold.FromPoints(S, E);
var I = AffineManifold.Intersect2D(SE, clipEdge);
//var D = S - E;
//D.Normalize();
//var N1 = new Vector(D.y, -D.x);
//double inner = N1 * clipEdge.Normal;
Debug.Assert(!double.IsNaN(I.x));
Debug.Assert(!double.IsInfinity(I.x));
Debug.Assert(!double.IsNaN(I.y));
Debug.Assert(!double.IsInfinity(I.y));
return(I);
}
/// <summary>
/// Intersection of line <paramref name="S1"/>--<paramref name="S2"/> and <paramref name="E1"/>--<paramref name="E2"/>
/// </summary>
/// <param name="S1"></param>
/// <param name="S2"></param>
/// <param name="E1"></param>
/// <param name="E2"></param>
/// <param name="alpha1">
/// coordinate of <paramref name="I"/> on the line <paramref name="S1"/>--<paramref name="S2"/>
/// </param>
/// <param name="alpha2">
/// coordinate of <paramref name="I"/> on the line <paramref name="E1"/>--<paramref name="E2"/>
/// </param>
/// <param name="I"></param>
/// <returns></returns>
public static bool ComputeIntersection(Vector S1, Vector S2, Vector E1, Vector E2, out double alpha1, out double alpha2, out Vector I)
{
if (S1.Dim != 2)
{
throw new ArgumentException("spatial dimension mismatch.");
}
if (S2.Dim != 2)
{
throw new ArgumentException("spatial dimension mismatch.");
}
if (E1.Dim != 2)
{
throw new ArgumentException("spatial dimension mismatch.");
}
if (E2.Dim != 2)
{
throw new ArgumentException("spatial dimension mismatch.");
}
Vector S12 = S2 - S1;
Vector E12 = E2 - E1;
var P_S12 = AffineManifold.FromPoints(S1, S2);
var P_E12 = AffineManifold.FromPoints(E1, E2);
double parallel = S12[0] * E12[1] - S12[1] * E12[0];
double relParallel = parallel * parallel / (S12.AbsSquare() * E12.AbsSquare());
if (Math.Abs(relParallel) <= 1e-20)
{
alpha1 = P_S12.PointDistance(E1);
alpha1 /= E12.Abs();
alpha2 = double.PositiveInfinity;
I = new Vector(double.PositiveInfinity, double.PositiveInfinity);
return(false);
}
//S12.Normalize();
//E12.Normalize();
I = AffineManifold.Intersect2D(P_S12, P_E12);
Vector IS1 = I - S2;
Vector IE1 = I - E2;
Vector IS2 = I - S1;
Vector IE2 = I - E1;
Vector IS;
bool flip_1;
if (IS1.AbsSquare() > IS2.AbsSquare())
{
IS = IS1;
flip_1 = true;
}
else
{
IS = IS2;
flip_1 = false;
}
Vector IE;
bool flip_2;
if (IE1.AbsSquare() > IE2.AbsSquare())
{
IE = IE1;
flip_2 = true;
}
else
{
IE = IE2;
flip_2 = false;
}
Debug.Assert((S12.AngleTo(IS).Abs() <= 1.0e-5) || ((S12.AngleTo(IS).Abs() - Math.PI).Abs() <= 1.0e-5));
Debug.Assert((E12.AngleTo(IE).Abs() <= 1.0e-5) || ((E12.AngleTo(IE).Abs() - Math.PI).Abs() <= 1.0e-5));
alpha1 = (S12 * IS) / S12.AbsSquare();
alpha2 = (E12 * IE) / E12.AbsSquare();
if (flip_1)
{
alpha1 = 1 + alpha1;
}
if (flip_2)
{
alpha2 = 1 + alpha2;
}
return(true);
}
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 )
}
}
}