/// <summary>
/// Evaluates the <see cref="SpatialDimension"/>-dimensional
/// coordinate of the point with parameter value t.
/// </summary>
/// <param name="t"></param>
/// <returns></returns>
public double[] GetPointOnSegment(double t)
{
Debug.Assert(
t.Abs() <= 1.0,
"Point out of range");
double[] result = new double[SpatialDimension];
for (int d = 0; d < SpatialDimension; d++)
{
result[d] = 0.5 * ((End[d] - Start[d]) * t + Start[d] + End[d]);
}
return(result);
}
private static IEnumerable <GradientStop> ScaleGradientStops(IEnumerable <GradientStop> gradientStops, Point startPoint, Point endPoint, Size targetSize)
{
if (startPoint.X == endPoint.X)
{
return(startPoint.Y < endPoint.Y ?
ScaleGradientStops(gradientStops, startPoint.Y / targetSize.Height, endPoint.Y / targetSize.Height) :
ScaleGradientStops(gradientStops, 1 - startPoint.Y / targetSize.Height, 1 - endPoint.Y / targetSize.Height));
}
if (startPoint.Y == endPoint.Y)
{
return(startPoint.X < endPoint.X ?
ScaleGradientStops(gradientStops, startPoint.X / targetSize.Width, endPoint.X / targetSize.Width) :
ScaleGradientStops(gradientStops, 1 - startPoint.X / targetSize.Width, 1 - endPoint.X / targetSize.Width));
}
Point direction = endPoint - startPoint;
double directionLength = direction.GetLength();
double sin = direction.Y / directionLength;
double cos = direction.X / directionLength;
// generated gradient image size
double generatedImageWidth = cos.Abs() * targetSize.Width + sin.Abs() * targetSize.Height;
double generatedImageHeight = sin.Abs() * targetSize.Width + cos.Abs() * targetSize.Height;
// transformation from a unit square to the generated gradient image rectangle
Matrix matrix =
Matrix.TranslationMatrix(-0.5, -0.5) * // translate the unit square center to the origin
Matrix.ScalingMatrix(generatedImageWidth, generatedImageHeight) * // scale to the generated gradient image size
new Matrix(cos, sin, -sin, cos, 0, 0) * // rotate to the generated gradient image angle
Matrix.TranslationMatrix(targetSize.Width / 2, targetSize.Height / 2); // translate to the target rectangle center
Point relativeStart = startPoint * matrix.Inverse;
Point relativeEnd = endPoint * matrix.Inverse;
return(ScaleGradientStops(gradientStops, relativeStart.X, relativeEnd.X));
}
private bool Animate(double targetValue)
{
double diff = targetValue - percentOffset;
if (diff.Abs() > MinimalValueDelta ||
velocity.Abs() > MinimalVelocityDelta)
{
velocity = velocity * (1 - Dampening);
velocity += diff * AttractionFator;
if (velocity.Abs() > TerminalVelocity)
{
velocity *= TerminalVelocity / velocity.Abs();
}
percentOffset = percentOffset + velocity;
return(true);
}
percentOffset = targetValue;
velocity = 0;
return(false);
}
public static void ScaleFromPoint_Scales_Shape(double scale,
double expectedCentroid_x, double expectedCentroid_y)
{
List <CartesianCoordinate> bowTieNonCrossingSegmentsScaled = new List <CartesianCoordinate>()
{
new CartesianCoordinate(4, 3.5),
new CartesianCoordinate(3, 5),
new CartesianCoordinate(3, 2),
new CartesianCoordinate(4, 3.5),
new CartesianCoordinate(5, 2),
new CartesianCoordinate(5, 5),
new CartesianCoordinate(4, 3.5),
};
Polygon polygon = new Polygon(bowTieNonCrossingSegmentsScaled);
// Check shape position
CartesianCoordinate originalCentroid = polygon.Centroid;
Assert.AreEqual(4, originalCentroid.X);
Assert.AreEqual(3.5, originalCentroid.Y);
CartesianCoordinate referencePoint = new CartesianCoordinate(2, 1);
Polygon polygonScaled = polygon.ScaleFromPoint(scale, referencePoint) as Polygon;
// Check shape scale
PointExtents extents = polygonScaled.Extents();
Assert.AreEqual(2 * scale.Abs(), extents.Width);
Assert.AreEqual(3 * scale.Abs(), extents.Height);
// Check scaled centroid position
CartesianCoordinate scaledCentroid = polygonScaled.Centroid;
Assert.AreEqual(expectedCentroid_x, scaledCentroid.X);
Assert.AreEqual(expectedCentroid_y, scaledCentroid.Y);
}
private void GetCornerD(DragDeltaEventArgs e, out double dx, out double dy, double invert)
{
var multiplier = GetScaleMultiplier();
dx = e.HorizontalChange * Viewbox.Scale.Width * multiplier;
dy = e.VerticalChange * Viewbox.Scale.Height * multiplier;
if (dx.Abs() > dy.Abs())
{
dx = invert.Sign() * dy * _model.TargetWidth / _model.TargetHeight;
}
else
{
dy = invert.Sign() * dx * _model.TargetHeight / _model.TargetWidth;
}
}
// Reset this spring to its initial state
public void Reset()
{
double mass = 0;
if (Element?.Geometry != null)
{
if (Element.Family != null)
{
Stiffness = Element.Family.GetAxialStiffness();
mass = Element.Family.GetArea();
mass *= Element.Family.GetPrimaryMaterial()?.Density ?? 0;
}
else
{
Stiffness = 0;
}
}
if (Element.StartNode != null)
{
StartParticle = Element.StartNode.GetData <Particle>();
}
if (Element.EndNode != null)
{
EndParticle = Element.EndNode.GetData <Particle>();
}
RestLength = Element.EndNode.Position.DistanceTo(Element.StartNode.Position);
mass *= RestLength;
// Lump stiffness at nodes:
Vector dir = EndParticle.Position - StartParticle.Position;
double length = dir.Magnitude();
dir /= length;
double extension = length - RestLength;
double T = extension * Stiffness;
double Ke = Stiffness / RestLength;
double Kg = T.Abs() / length;
double K = 0.5 * (Ke + Kg);
Vector Kv = dir.Abs() * K;
// Hmmm... do we need to worry about signs?
StartParticle.LumpedK += Kv;
EndParticle.LumpedK += Kv;
// Lump mass at nodes:
StartParticle.Mass += mass / 2;
EndParticle.Mass += mass / 2;
}
private static void GetPoints(double angle, out Point startPoint, out Point endPoint)
{
double radians = Math.PI * angle / 180;
double x = Math.Cos(radians);
double y = Math.Sin(radians);
double scale = 1 / x.Abs().Max(y.Abs());
x *= scale;
y *= scale;
Point offset = new Point(x.Min(0), y.Min(0));
startPoint = -offset;
endPoint = new Point(x, y) - offset;
}
public bool Animate(
double currentValue, double currentVelocity, double targetValue,
double attractionFator, double dampening,
double terminalVelocity, double minValueDelta, double minVelocityDelta,
out double newValue, out double newVelocity)
{
Debug.Assert(currentValue.IsValid());
Debug.Assert(currentVelocity.IsValid());
Debug.Assert(targetValue.IsValid());
Debug.Assert(dampening.IsValid());
Debug.Assert(dampening > 0 && dampening < 1);
Debug.Assert(attractionFator.IsValid());
Debug.Assert(attractionFator > 0);
Debug.Assert(terminalVelocity > 0);
Debug.Assert(minValueDelta > 0);
Debug.Assert(minVelocityDelta > 0);
double diff = targetValue - currentValue;
if (diff.Abs() > minValueDelta || currentVelocity.Abs() > minVelocityDelta)
{
newVelocity = currentVelocity * (1 - dampening);
newVelocity += diff * attractionFator;
if (currentVelocity.Abs() > terminalVelocity)
{
newVelocity *= terminalVelocity / currentVelocity.Abs();
}
newValue = currentValue + newVelocity;
return(true);
}
else
{
newValue = targetValue;
newVelocity = 0;
return(false);
}
}
/// <summary>
///
/// </summary>
/// <param name="Lab"></param>
/// <param name="Observer"></param>
/// <param name="Illuminant"></param>
public Lch(Lab Lab, ObserverAngle Observer = ObserverAngle.Two, Illuminant Illuminant = Illuminant.Default) : this(0, 0, 0, Observer, Illuminant)
{
double l, c, h = Math.Atan2(Lab.B, Lab.A);
if (h > 0d)
{
h = (h / Math.PI) * 180d;
}
else
{
h = 360d - (h.Abs() / Math.PI) * 180d;
}
l = Lab.L;
c = Math.Sqrt(Math.Pow(Lab.A, 2d) + Math.Pow(Lab.B, 2d));
L = l;
C = c;
H = h;
}
private Pen GetPen()
{
double strokeThickness = StrokeThickness;
if (Stroke == null ||
strokeThickness.IsNaNValue() ||
strokeThickness.IsEqualOrCloseToZero())
{
return(null);
}
if (strokePen != null)
{
return(strokePen);
}
double thickness = strokeThickness.Abs();
strokePen = new Pen
{
Thickness = thickness,
Brush = Stroke,
StartLineCap = StrokeStartLineCap,
EndLineCap = StrokeEndLineCap,
DashCap = StrokeDashCap,
LineJoin = StrokeLineJoin,
MiterLimit = StrokeMiterLimit
};
if (StrokeDashArray != null ||
!StrokeDashOffset.IsEqualOrCloseToZero())
{
strokePen.DashStyle = new DashStyle(StrokeDashArray, StrokeDashOffset);
}
strokePen.Freeze();
return(strokePen);
}
static double DistanceByHeightAndAngle(double heigth, double angle)
{
var a = angle.Abs();
return(a >= 90 ? heigth * a / 90 : heigth / Math.Sin(a.Radians()));
}
public static double AutoRound2(this double d, int digits)
{
var digitsReal = Math.Log10(d.Abs()).Floor() + 1;
return(d.Round((digits - digitsReal).Max(0)));
}
static bool IsTresholdAbsOk(double value, double treshold)
{
return(treshold >= 0 ? value.Abs() >= treshold : value.Abs() < -treshold);
}
/// <summary>
/// Usually used after <see cref="MergeLogically(GridCommons, GridCommons)"/>; this method finds element boundaries
/// which intersect geometrically, but not logically and inserts a <see cref="CellFaceTag"/> which connects those cells.
/// </summary>
/// <param name="g"></param>
/// <param name="upsampling"></param>
/// <returns></returns>
public static GridCommons Seal(GridCommons g, int upsampling = 4)
{
GridCommons R = g.CloneAs();
g = null;
GridData gdat = new GridData(R);
int D = gdat.SpatialDimension;
int J = gdat.Cells.NoOfLocalUpdatedCells;
if (R.CellPartitioning.MpiSize > 1)
{
throw new NotSupportedException("Not supported in MPI-parallel mode.");
}
//NodeSet[] TestNodes = gdat.Edges.EdgeRefElements.Select(KrefEdge => KrefEdge.GetSubdivisionTree(upsampling).GlobalVertice).ToArray();
NodeSet[] TestNodes = gdat.Edges.EdgeRefElements.Select(KrefEdge => KrefEdge.GetBruteForceQuadRule(upsampling, 1).Nodes).ToArray();
// Its better to use vertices in the interior of the element; if we use vertices at the corners, we might get
// intersection of edges that just share one point.
// Define all edges that will be tested (set to boundary edges)
// ============================================================
int[] UnknownEdges = gdat.BoundaryEdges.ItemEnum.ToArray();
int L = UnknownEdges.Sum(iEdg => TestNodes[gdat.Edges.GetRefElementIndex(iEdg)].NoOfNodes);
// Transform nodes on edges (that should be tested) to global coordinates
// ======================================================================
MultidimensionalArray TestNodesGlobal = MultidimensionalArray.Create(L, D);
MultidimensionalArray NormalsGlobal = MultidimensionalArray.Create(L, D);
int[] NodeToEdge = new int[L]; // pointer l -> Edge index, where l is the first index into 'TestNodesGlobal' & 'NormalsGlobal'
int[,] E2C = gdat.Edges.CellIndices;
int cnt = 0;
foreach (int iEdg in UnknownEdges)
{
int iKref = gdat.Edges.GetRefElementIndex(iEdg);
NodeSet Ns = TestNodes[iKref];
int K = Ns.NoOfNodes;
int[] I0 = new int[] { cnt, 0 };
int[] IE = new int[] { cnt + K - 1, D - 1 };
MultidimensionalArray TN = gdat.GlobalNodes.GetValue_EdgeSV(Ns, iEdg, 1);
TestNodesGlobal.SetSubArray(TN.ExtractSubArrayShallow(0, -1, -1), I0, IE);
MultidimensionalArray N1 = gdat.Edges.NormalsCache.GetNormals_Edge(Ns, iEdg, 1);
NormalsGlobal.SetSubArray(N1.ExtractSubArrayShallow(0, -1, -1), I0, IE);
for (int i = cnt; i < cnt + K; i++)
{
NodeToEdge[i] = iEdg;
}
cnt += K;
}
// binary tree to speed up point localization
int[] pl_Permutation = new int[L];
PointLocalization pl = new PointLocalization(TestNodesGlobal, 0.01, pl_Permutation);
Debug.Assert(!object.ReferenceEquals(pl.Points, TestNodesGlobal));
// compare search edges to all other nodes
// =======================================
// mapping: cell --> Neighbour cell index, face index
// 1st index: Cell index;
// 2nd index: enumeration
List <Tuple <int, int> >[] FoundPairings = new List <Tuple <int, int> > [gdat.Cells.NoOfCells];
int[][] C2E = gdat.Cells.Cells2Edges;
byte[,] E2F = gdat.Edges.FaceIndices;
int cnt2 = 0;
for (int iEdgC = 0; iEdgC < UnknownEdges.Length; iEdgC++) // loop over edges that may get sealed
{
int iEdg = UnknownEdges[iEdgC];
int iKref = gdat.Edges.GetRefElementIndex(iEdg);
NodeSet Ns = TestNodes[iKref];
int K = Ns.NoOfNodes;
int jCell1 = E2C[iEdg, 0];
Debug.Assert(E2C[iEdg, 1] < 0);
int iFace1 = E2F[iEdg, 0];
Debug.Assert(E2F[iEdg, 1] == byte.MaxValue);
int[] I0 = new int[] { cnt2, 0 };
int[] IE = new int[] { cnt2 + K - 1, D - 1 };
MultidimensionalArray TN = TestNodesGlobal.ExtractSubArrayShallow(I0, IE);
//MultidimensionalArray N1 = NormalsGlobal.ExtractSubArrayShallow(I0, IE);
// find bounding box for edge
BoundingBox bbEdge = new BoundingBox(TN);
if (bbEdge.h_min / bbEdge.h_max < 1.0e-5)
{
// very thin bounding box, thicken slightly
double delta = bbEdge.h_max * 1.0e-5;
for (int d = 0; d < D; d++)
{
bbEdge.Min[d] -= delta;
bbEdge.Max[d] += delta;
}
}
bbEdge.ExtendByFactor(0.01);
// determine binary code for bounding box
int bbEdgeSigBits;
GeomBinTreeBranchCode bbEdgeCode = GeomBinTreeBranchCode.Combine(
GeomBinTreeBranchCode.CreateFormPoint(pl.PointsBB, bbEdge.Min),
GeomBinTreeBranchCode.CreateFormPoint(pl.PointsBB, bbEdge.Max),
out bbEdgeSigBits);
// determine all points in bounding box
int iP0, Len;
pl.GetPointsInBranch(bbEdgeCode, bbEdgeSigBits, out iP0, out Len);
// determine all edged which potentially overlap with edge 'iEdg'
HashSet <int> PotOvrlap = new HashSet <int>(); // a set of edge indices
for (int n = 0; n < Len; n++)
{
int l = iP0 + n;
int iPt = pl_Permutation[l];
Debug.Assert(GenericBlas.L2DistPow2(pl.Points.GetRow(l), TestNodesGlobal.GetRow(iPt)) <= 0);
int iOvlpEdge = NodeToEdge[iPt];
if (iOvlpEdge != iEdg)
{
PotOvrlap.Add(iOvlpEdge);
}
}
//int[] PotOvrlap = UnknownEdges.CloneAs();
// determine actually overlapping boundary edges:
foreach (int iOvrlapEdge in PotOvrlap)
{
int jCell2 = E2C[iOvrlapEdge, 0];
Debug.Assert(E2C[iOvrlapEdge, 1] < 0);
if (jCell2 == jCell1)
{
continue;
}
int iFace2 = E2F[iOvrlapEdge, 0];
Debug.Assert(E2F[iOvrlapEdge, 1] == byte.MaxValue);
int AllreadyFound = FoundPairings[jCell1] == null ?
0 : FoundPairings[jCell1].Where(tp => tp.Item1 == jCell2 && tp.Item2 == iFace1).Count();
if (AllreadyFound > 1)
{
throw new ApplicationException("Error in algorithmus.");
}
if (AllreadyFound > 0)
{
continue;
}
var Kref_j2 = gdat.Cells.GetRefElement(jCell2);
double h = Kref_j2.GetMaxDiameter();
MultidimensionalArray LocVtx_j2 = MultidimensionalArray.Create(K, D);
bool[] NewtonConvervence = new bool[K];
gdat.TransformGlobal2Local(TN, LocVtx_j2, jCell2, NewtonConvervence);
for (int k = 0; k < K; k++) // loop over all transformed points
{
if (!NewtonConvervence[k])
{
continue;
}
double[] pt = LocVtx_j2.GetRow(k);
double[] ptClose = new double[D];
double dist = Kref_j2.ClosestPoint(pt, ptClose);
if (dist > h * 1.0e-8)
{
continue;
}
AffineManifold Face = Kref_j2.GetFacePlane(iFace2);
double FaceDist = Face.PointDistance(pt);
if (FaceDist.Abs() > 1.0e-8 * h)
{
continue;
}
NodeSet Ns2 = new NodeSet(Kref_j2, pt);
MultidimensionalArray Normals2 = MultidimensionalArray.Create(1, D);
gdat.Edges.GetNormalsForCell(Ns2, jCell2, iFace2, Normals2);
double[] N1d = NormalsGlobal.GetRow(cnt2 + k);
double[] N2d = Normals2.GetRow(0);
//Check if face normals points exactly in the opposite direction, 2 ways:
// 1) calculate angle between both normals -> bad choice because of Math.Acos
// 2) inner product of two opposite vectors is -1
//if (Math.Abs(Math.Abs(Math.Acos(GenericBlas.InnerProd(N1d, N2d))) - Math.PI) > 1.0e-8)
if (Math.Abs(GenericBlas.InnerProd(N1d, N2d) + 1.0) > 1.0e-8)
{
continue;
}
// if we reach this point, jCell1 should match with jCell2/iFace2
if (FoundPairings[jCell1] == null)
{
FoundPairings[jCell1] = new List <Tuple <int, int> >();
}
if (FoundPairings[jCell2] == null)
{
FoundPairings[jCell2] = new List <Tuple <int, int> >();
}
FoundPairings[jCell1].Add(new Tuple <int, int>(jCell2, iFace1));
FoundPairings[jCell2].Add(new Tuple <int, int>(jCell1, iFace2));
break; // no need to test jCell1 vs. jCell2 anymore
}
}
cnt2 += K;
}
// add the newly found pairings to the grid
for (int j = 0; j < J; j++)
{
var fp = FoundPairings[j];
if (fp != null)
{
foreach (var t in fp)
{
ArrayTools.AddToArray(new CellFaceTag()
{
EdgeTag = 0,
FaceIndex = t.Item2,
ConformalNeighborship = false,
NeighCell_GlobalID = gdat.CurrentGlobalIdPermutation.Values[t.Item1]
}, ref R.Cells[j].CellFaceTags);
}
}
}
return(R);
}
public void DoAbs(double value, double expectedValue)
{
Assert.Equal(expectedValue, value.Abs());
}
public static int IteratonSequenceNextStep(int count, double power = 1, int loop = 0)
{
var p = count / 100.0 * Math.Pow(count, power.Abs()) / Math.Pow(2, loop.Abs());
return(p.Ceiling() * power.Sign() * ((double)loop).SignUp());
}
public static double Abs_Double(double value)
{
return(value.Abs());
}
public bool LocalSolve(int jCell, BitArray AcceptedMask, SinglePhaseField Phi, double _sign, out double Min, out double Max)
{
Debug.Assert(_sign.Abs() == 1);
// find all accepted neighbors
// ===========================
var NeighCells = this.GridDat.GetCellNeighboursViaEdges(jCell);
int iKref = this.GridDat.Cells.GetRefElementIndex(jCell);
int NN = NeighCells.Length;
var NeighCellsK = new Tuple <int, int, int> [NN];
int NNK = 0;
for (int nn = 0; nn < NN; nn++)
{
if (AcceptedMask[NeighCells[nn].Item1] == true)
{
NeighCellsK[NNK] = NeighCells[nn];
NNK++;
}
}
// evaluate accepted neighbors
// ============================
Min = double.MaxValue;
Max = double.MinValue;
var TrafoIdx = this.GridDat.Edges.Edge2CellTrafoIndex;
int K = this.PhiEvalBuffer[0].GetLength(1); // Nodes per edge
for (int nnk = 0; nnk < NNK; nnk++) // loop over accepted neighbours
{
int jNC = NeighCellsK[nnk].Item1;
int iEdg = NeighCellsK[nnk].Item2;
int InOrOut = NeighCellsK[nnk].Item3;
int iTrafo = TrafoIdx[iEdg, InOrOut];
this.PhiEvalBuffer[nnk].Clear();
Phi.Evaluate(jNC, 1, this.EdgeNodes.GetVolumeNodeSet(this.GridDat, iTrafo), this.PhiEvalBuffer[nnk]);
this.GridDat.TransformLocal2Global(this.EdgeNodes.GetVolumeNodeSet(this.GridDat, iTrafo), this.CellNodesGlobal[nnk], jNC);
Max = Math.Max(Max, PhiEvalBuffer[nnk].Max());
Min = Math.Min(Min, PhiEvalBuffer[nnk].Min());
}
var _QuadNodesGlobal = this.QuadNodesGlobal[iKref];
this.GridDat.TransformLocal2Global(this.DaRuleS[iKref].Nodes, _QuadNodesGlobal, jCell);
if (_sign > 0)
{
Max += this.GridDat.Cells.h_max[jCell];
}
else
{
Min -= this.GridDat.Cells.h_max[jCell];
}
// perform projection of geometric reinit
// ======================================
// temp storage
double[] Y = new double[2];
double[] X = new double[2];
double[] X1 = new double[2];
double[] X2 = new double[2];
// basis values at cell quadrature nodes
var BasisValues = this.LevelSetBasis_Geometric.CellEval(this.DaRuleS[iKref].Nodes, jCell, 1).ExtractSubArrayShallow(0, -1, -1);
int NoOfQn = BasisValues.GetLength(0); // number of quadrature nodes
// result at quadrature nodes
var PhiAtQuadNodes = MultidimensionalArray.Create(NoOfQn);
for (int iQn = NoOfQn - 1; iQn >= 0; iQn--) // loop over all quadrature nodes
{
Y[0] = _QuadNodesGlobal[iQn, 0];
Y[1] = _QuadNodesGlobal[iQn, 1];
double _dist_min1 = double.MaxValue, _phi_min1 = double.NaN;
int _nnk_Min1 = int.MinValue, _k_min1 = int.MinValue;
double _dist_min2 = double.MaxValue, _phi_min2 = double.NaN;
int _nnk_Min2 = int.MinValue, _k_min2 = int.MinValue;
// find closest point: brute force approach
for (int nnk = 0; nnk < NNK; nnk++) // loop over all edges with known values
{
double dist_min1 = double.MaxValue, phi_min1 = double.NaN;
int nnk_Min1 = int.MinValue, k_min1 = int.MinValue;
double dist_min2 = double.MaxValue, phi_min2 = double.NaN;
int nnk_Min2 = int.MinValue, k_min2 = int.MinValue;
for (int k = 0; k < K; k++) // loop over all nodes on this edge
{
X[0] = this.CellNodesGlobal[nnk][k, 0];
X[1] = this.CellNodesGlobal[nnk][k, 1];
double phi = this.PhiEvalBuffer[nnk][0, k];
phi *= _sign;
double dist = GenericBlas.L2Dist(X, Y) + phi;
bool NoBlock = true;
if (dist < dist_min1)
{
nnk_Min2 = nnk_Min1;
k_min2 = k_min1;
dist_min2 = dist_min1;
phi_min2 = phi_min1;
dist_min1 = dist;
nnk_Min1 = nnk;
k_min1 = k;
phi_min1 = phi;
NoBlock = false;
}
if (dist >= dist_min1 && dist < dist_min2 && NoBlock)
{
dist_min2 = dist;
nnk_Min2 = nnk;
k_min2 = k;
phi_min2 = phi;
}
}
if (dist_min1 < _dist_min1)
{
_dist_min1 = dist_min1;
_k_min1 = k_min1;
_nnk_Min1 = nnk_Min1;
_phi_min1 = phi_min1;
_dist_min2 = dist_min2;
_k_min2 = k_min2;
_nnk_Min2 = nnk_Min2;
_phi_min2 = phi_min2;
}
}
{
Debug.Assert(_nnk_Min1 == _nnk_Min2);
Debug.Assert(_k_min1 != _k_min2);
double PhiMin1 = this.PhiEvalBuffer[_nnk_Min1][0, _k_min1];
double PhiMin2 = this.PhiEvalBuffer[_nnk_Min2][0, _k_min2];
X1[0] = this.CellNodesGlobal[_nnk_Min1][_k_min1, 0];
X1[1] = this.CellNodesGlobal[_nnk_Min1][_k_min1, 1];
X2[0] = this.CellNodesGlobal[_nnk_Min2][_k_min2, 0];
X2[1] = this.CellNodesGlobal[_nnk_Min2][_k_min2, 1];
}
_dist_min1 *= _sign;
PhiAtQuadNodes[iQn] = _dist_min1 * this.DaRuleS[iKref].Weights[iQn];
}
// finalize projection & return
// ============================
if (this.GridDat.Cells.IsCellAffineLinear(jCell))
{
int N = this.LevelSetBasis_Geometric.GetLength(jCell);
int N2 = Phi.Basis.GetLength(jCell);
MultidimensionalArray Phi_1 = MultidimensionalArray.Create(N);
double scale = this.GridDat.Cells.JacobiDet[jCell];
Phi_1.Multiply(scale, BasisValues, PhiAtQuadNodes, 0.0, "m", "km", "k");
for (int n = 0; n < N; n++)
{
Phi.Coordinates[jCell, n] = Phi_1[n];
}
for (int n = N; n < N2; n++)
{
Phi.Coordinates[jCell, n] = 0;
}
}
else
{
throw new NotImplementedException("not implemented for curved cells");
}
return(true);
}
/// <summary>
/// Quadrangulate this mesh by merging adjacent tris into quads.
/// The algorithm will prioritise merging the longest edges first
/// </summary>
public void Quadrangulate()
{
var sortedPairs = new SortedList <double, Pair <MeshFace, MeshFace> >(Count);
// Find adjacent pairs of tris and sort by resultant face 'squareness'
for (int i = 0; i < Count - 1; i++)
{
MeshFace faceA = this[i];
if (faceA.IsTri)
{
for (int j = i + 1; j < Count; j++)
{
MeshFace faceB = this[j];
if (faceB.IsTri)
{
double squareness = faceA.SharedEdgeSquareness(faceB);
if (!squareness.IsNaN() && squareness.Abs() < 0.8)
{
sortedPairs.AddSafe(squareness, Pair.Create(faceA, faceB));
}
}
}
}
}
// Reverse through pairs and join:
for (int i = 0; i < sortedPairs.Count; i++)
{
var pair = sortedPairs.Values[i];
if (Contains(pair.First.GUID) && Contains(pair.Second.GUID))
{
Remove(pair.First);
Remove(pair.Second);
Add(pair.First.MergeWith(pair.Second));
}
}
// Version 0.2: also deprecated
/*var sortedPairs = new SortedList<double, Pair<MeshFace, MeshFace>>(Count);
* // Find adjacent pairs of tris and sort by edge length
* for (int i = 0; i < Count - 1; i++)
* {
* MeshFace faceA = this[i];
* if (faceA.IsTri)
* {
* for (int j = i + 1; j < Count; j++)
* {
* MeshFace faceB = this[j];
* if (faceB.IsTri)
* {
* double length = faceA.SharedEdgeLengthSquared(faceB);
* if (length > 0)
* sortedPairs.AddSafe(length, Pair.Create(faceA, faceB));
* }
* }
* }
* }
*
* // Reverse through pairs and join:
* for (int i = sortedPairs.Count - 1; i >= 0; i--)
* {
* var pair = sortedPairs.Values[i];
* if (Contains(pair.First.GUID) && Contains(pair.Second.GUID))
* {
* Remove(pair.First);
* Remove(pair.Second);
* Add(pair.First.MergeWith(pair.Second));
* }
* }*/
// Version 0.1: Deprecated:
/*
* // Populate lists:
* var sortedLists = new SortedList<double, IList<MeshFace>>(Count / 2);
*
* foreach (MeshFace face in this)
* {
* if (face.IsTri)
* {
* double longEdge = face.LongestEdgeLengthSquared();
*
* if (!sortedLists.ContainsKey(longEdge))
* sortedLists.Add(longEdge, new MeshFaceCollection());
*
* sortedLists[longEdge].Add(face);
* }
* }
*
* foreach (IList<MeshFace> faceSet in sortedLists.Values)
* {
* for (int i = 0; i < faceSet.Count - 1; i++)
* {
* MeshFace faceA = faceSet[i];
* for (int j = i + 1; j < faceSet.Count; j++)
* {
* MeshFace faceB = faceSet[j];
* if (faceA.SharedVertexCount(faceB) == 2) // Has a shared edge
* {
* // Merge faces and replace:
* Remove(faceA);
* Remove(faceB);
* Add(faceA.MergeWith(faceB));
*
* faceSet.RemoveAt(j);
* j = faceSet.Count;
* }
* }
* }
* }
*/
}
public static double AbsoluteValue(double val)
{
return(val.Abs());
}
public NormalsClustering(V3d[] normalArray, double delta)
{
var count = normalArray.Length;
Alloc(count);
var ca = m_indexArray;
var sa = new int[count].Set(1);
var suma = SumArray;
var kdTree = normalArray.CreateRkdTreeDistDotProduct(0);
var query = kdTree.CreateClosestToPointQuery(delta, 0);
for (int i = 0; i < count; i++)
{
int ci = ca[i]; if (ca[ci] != ci)
{
do
{
ci = ca[ci];
} while (ca[ci] != ci); ca[i] = ci;
}
int si = sa[ci];
V3d avgNormali = suma[ci].Normalized;
kdTree.GetClosest(query, avgNormali);
kdTree.GetClosest(query, avgNormali.Negated);
foreach (var id in query.List)
{
int j = (int)id.Index;
int cj = ca[j]; if (ca[cj] != cj)
{
do
{
cj = ca[cj];
} while (ca[cj] != cj); ca[j] = cj;
}
if (ci == cj)
{
continue;
}
int sj = sa[cj];
V3d avgNormalj = suma[cj].Normalized;
double avgDot = avgNormali.Dot(avgNormalj);
if (avgDot.Abs() < 1.0 - 2.0 * delta)
{
continue;
}
V3d sum = suma[ci] + (avgDot > 0 ? suma[cj] : suma[cj].Negated);
if (si < sj)
{
ca[ci] = cj; ca[i] = cj; ci = cj;
}
else
{
ca[cj] = ci; ca[j] = ci;
}
si += sj; sa[ci] = si; suma[ci] = sum;
}
query.Clear();
}
Init();
}
private void MassCorrection()
{
double[] Qnts_old = ComputeBenchmarkQuantities();
CorrectionLevSet.Clear();
CorrectionLevSet.Acc(1.0, phi);
this.CorrectionLsTrk.UpdateTracker(0.0);
double[] Qnts = ComputeBenchmarkQuantities();
double massDiff = Qnts_old[0] - Qnts[0];
// we assume the current phasefield is close to the equilibrium tangenshyperbolicus form
SinglePhaseField phiNew = new SinglePhaseField(phi.Basis);
GridData GridDat = (GridData)(phi.GridDat);
double mass_uc = Qnts[0];
int i = 0;
while (massDiff.Abs() > 1e-6)
{
// calculated for a cone, one could include the shape e.g. by using the circularity
// correction guess
double correction = Math.Sign(massDiff) * 1e-10;//-Qnts[1] / (4 * Qnts[0] * Math.PI) * massDiff * 1e-5;
// take the correction guess and calculate a forward difference to approximate the derivative
phiNew.ProjectField(
(ScalarFunctionEx) delegate(int j0, int Len, NodeSet NS, MultidimensionalArray result)
{ // ScalarFunction2
Debug.Assert(result.Dimension == 2);
Debug.Assert(Len == result.GetLength(0));
int K = result.GetLength(1); // number of nodes
// evaluate Phi
// -----------------------------
phi.Evaluate(j0, Len, NS, result);
// compute the pointwise values of the new level set
// -----------------------------
result.ApplyAll(x => 0.5 * Math.Log(Math.Max(1 + x, 1e-10) / Math.Max(1 - x, 1e-10)) * Math.Sqrt(2) * this.Control.cahn);
result.ApplyAll(x => Math.Tanh((x + correction) / (Math.Sqrt(2) * this.Control.cahn)));
}
);
// update LsTracker
CorrectionLevSet.Clear();
CorrectionLevSet.Acc(1.0, phiNew);
this.CorrectionLsTrk.UpdateTracker(0.0);
Qnts = ComputeBenchmarkQuantities();
correction = -(massDiff) / ((Qnts_old[0] - Qnts[0] - massDiff) / (correction));
double initial = massDiff;
bool finished = false;
int k = 0;
//while (massDiff.Abs() - initial.Abs() >= 0.0 && step > 1e-12)
while (!finished)
{
double step = Math.Pow(0.5, k);
// compute and project
// step one calculate distance field phiDist = 0.5 * log(Max(1+c, eps)/Max(1-c, eps)) * sqrt(2) * Cahn
// step two project the new phasefield phiNew = tanh((cDist + correction)/(sqrt(2) * Cahn))
// ===================
phiNew.ProjectField(
(ScalarFunctionEx) delegate(int j0, int Len, NodeSet NS, MultidimensionalArray result)
{ // ScalarFunction2
Debug.Assert(result.Dimension == 2);
Debug.Assert(Len == result.GetLength(0));
int K = result.GetLength(1); // number of nodes
// evaluate Phi
// -----------------------------
phi.Evaluate(j0, Len, NS, result);
// compute the pointwise values of the new level set
// -----------------------------
result.ApplyAll(x => 0.5 * Math.Log(Math.Max(1 + x, 1e-10) / Math.Max(1 - x, 1e-10)) * Math.Sqrt(2) * this.Control.cahn);
result.ApplyAll(x => Math.Tanh((x + correction * step) / (Math.Sqrt(2) * this.Control.cahn)));
}
);
// update LsTracker
CorrectionLevSet.Clear();
CorrectionLevSet.Acc(1.0, phiNew);
this.CorrectionLsTrk.UpdateTracker(0.0);
Qnts = ComputeBenchmarkQuantities();
massDiff = Qnts_old[0] - Qnts[0];
if (massDiff.Abs() < (1 - 1e-4 * step) * initial.Abs())
{
finished = true;
// update field
phi.Clear();
phi.Acc(1.0, phiNew);
// update LsTracker
CorrectionLevSet.Clear();
CorrectionLevSet.Acc(1.0, phi);
this.CorrectionLsTrk.UpdateTracker(0.0);
Console.WriteLine($"" +
$"converged with stepsize: {step}, correction: {correction}\n" +
$" dM: {massDiff}");
if (k > 0)
{
Console.WriteLine($"Finished Linesearch in {k} iterations");
}
}
else if (Math.Abs(correction * step) < 1e-15)
{
// reset LsTracker
CorrectionLevSet.Clear();
CorrectionLevSet.Acc(1.0, phi);
this.CorrectionLsTrk.UpdateTracker(0.0);
Qnts = ComputeBenchmarkQuantities();
massDiff = Qnts_old[0] - Qnts[0];
Console.WriteLine($" Linesearch failed after {k} iterations");
goto Failed;
}
else
{
k++;
}
}
i++;
}
Failed:
Console.WriteLine($"Performed Mass Correction in {i} iteratins: \n" +
$"\told mass: {Qnts_old[0]:N4}\n" +
$"\tuncorrected mass: {mass_uc:N4}\n" +
$"\tcorrected mass: {Qnts[0]:N4}");
}
/// <summary>
/// Solution of the extension problem on a single cell in the far-region
/// </summary>
/// <param name="Phi">Input;</param>
/// <param name="GradPhi">Input;</param>
/// <param name="ExtProperty"></param>
/// <param name="ExtPropertyMin">Input/Output: lower threshold.</param>
/// <param name="ExtPropertyMax">Input/Output: upper threshold.</param>
/// <param name="jCell"></param>
/// <param name="Accepted"></param>
/// <param name="signMod"></param>
public void ExtVelSolve_Far(SinglePhaseField Phi, VectorField <SinglePhaseField> GradPhi, ConventionalDGField ExtProperty, ref double ExtPropertyMin, ref double ExtPropertyMax, int jCell, CellMask Accepted, double signMod)
{
GridData gDat = (GridData)(Phi.GridDat);
Debug.Assert(signMod.Abs() == 1.0);
Debug.Assert(ExtPropertyMin <= ExtPropertyMax);
// define cell- and edge-mask for re-compute
// =========================================
CellMask cM = new CellMask(gDat, Chunk.GetSingleElementChunk(jCell));
int[] Edges = gDat.iLogicalCells.Cells2Edges[jCell].CloneAs();
for (int i = 0; i < Edges.Length; i++)
{
Edges[i] = Math.Abs(Edges[i]) - 1;
}
EdgeMask eM = new EdgeMask(gDat, FromIndEnum(Edges, gDat.iLogicalEdges.Count)); // won't scale.
// solve the linear extension problem for 'jCell', eventually increase
// diffusion until we are satisfied with the solution
// ===================================================================
bool MaximumPrincipleFulfilled = false;
double DiffusionCoeff = 0; // initially: try without diffusion
double mini = double.NaN, maxi = double.NaN;
int count = 0;
while (MaximumPrincipleFulfilled == false) // as long as we are satisfied with the solution
{
count++;
// compute operator in 'jCell'
// ---------------------------
int N = ExtProperty.Basis.GetLength(jCell);
int i0G = ExtProperty.Mapping.GlobalUniqueCoordinateIndex(0, jCell, 0);
int i0L = ExtProperty.Mapping.GlobalUniqueCoordinateIndex(0, jCell, 0);
for (int n = 0; n < N; n++)
{
this.m_ExtvelMatrix.ClearRow(i0G + n);
this.m_ExtvelAffine[i0L + n] = 0;
}
double penaltyBase = ((double)(ExtProperty.Basis.Degree + 1)).Pow2();
var Flux = new ExtensionVelocityForm(Accepted.GetBitMask(), signMod, penaltyBase, gDat.Cells.h_min, jCell, DiffusionCoeff);
var op = (Flux).Operator(DegreeOfNonlinearity: 2);
// increase diffusion coefficient for next cycle
if (DiffusionCoeff == 0)
{
DiffusionCoeff = 1.0e-3; // should this be minus or plus?
}
else
{
DiffusionCoeff *= 10;
}
op.ComputeMatrixEx(ExtProperty.Mapping, ArrayTools.Cat <DGField>(new DGField[] { ExtProperty, Phi }, GradPhi), ExtProperty.Mapping,
this.m_ExtvelMatrix, this.m_ExtvelAffine,
OnlyAffine: false,
volQuadScheme: (new CellQuadratureScheme(true, cM)),
edgeQuadScheme: (new EdgeQuadratureScheme(true, eM)),
ParameterMPIExchange: false);
// extract operator matrix and RHS
// -------------------------------
// the matrix must only have entries in the block-diagonal!
MultidimensionalArray Mtx = MultidimensionalArray.Create(N, N);
//MultidimensionalArray rhs = MultidimensionalArray.Create(N);
double[] rhs = new double[N];
for (int n = 0; n < N; n++)
{
#if DEBUG
int Lr;
int[] row_cols = null;
double[] row_vals = null;
Lr = this.m_ExtvelMatrix.GetRow(i0G + n, ref row_cols, ref row_vals);
for (int lr = 0; lr < Lr; lr++)
{
int ColIndex = row_cols[lr];
double Value = row_vals[lr];
Debug.Assert((ColIndex >= i0G && ColIndex < i0G + N) || (Value == 0.0), "Matrix is expected to be block-diagonal.");
}
#endif
for (int m = 0; m < N; m++)
{
Mtx[n, m] = this.m_ExtvelMatrix[i0G + n, i0G + m];
}
rhs[n] = -this.m_ExtvelAffine[i0L + n];
}
// Solve the system, i.e. the local extension-velocity equation
// ------------------------------------------------------------
double[] ep = new double[N];
Mtx.Solve(ep, rhs);
for (int n = 0; n < N; n++)
{
ExtProperty.Coordinates[jCell, n] = ep[n];
}
// detect violation of maximum principle
// -------------------------------------
ExtProperty.GetExtremalValuesInCell(out mini, out maxi, jCell);
// define relaxed bounds...
double compExtPropertyMin = ExtPropertyMin - (1.0e-8 + ExtPropertyMax - ExtPropertyMin) * 0.2;
double compExtPropertyMax = ExtPropertyMax + (1.0e-8 + ExtPropertyMax - ExtPropertyMin) * 0.2;
// test if extension velocity solution is within bounds
MaximumPrincipleFulfilled = (mini >= compExtPropertyMin) && (maxi <= compExtPropertyMax);
if (count > 5)
{
break;
}
}
if (count > 4)
{
Console.WriteLine(" ExtVel, cell #{0}, Diff coeff {1}, extremal p. holds? {2} (min/max soll = {3:e4}/{4:e4}, ist = {5:e4}/{6:e4})", jCell, DiffusionCoeff, MaximumPrincipleFulfilled, ExtPropertyMin, ExtPropertyMax, mini, maxi);
}
// record maxima and minima
// ========================
ExtPropertyMax = Math.Max(ExtPropertyMax, maxi);
ExtPropertyMin = Math.Min(ExtPropertyMin, mini);
}
static void JacobianTest(Cell cl, out bool PositiveJacobianFlag, out bool NegativeJacobianFlag, out bool Linear)
{
RefElement Kref = cl.Type.GetRefElement();
int D = 3; // for OpenFOAM, we assume 3D;
// get nodes within ref element, to test the Jacobian
int deg = Kref.GetInterpolationDegree(cl.Type);
if (deg > 1)
{
deg--;
}
deg *= 3;
NodeSet TestNodes = Kref.GetQuadratureRule(2 * deg).Nodes;
// evaluate derivatives of nodal polynomials for transformation
PolynomialList[] Deriv = Kref.GetInterpolationPolynomials1stDeriv(cl.Type);
MultidimensionalArray[] DerivEval = new MultidimensionalArray[D];
for (int d = 0; d < D; d++)
{
DerivEval[d] = Deriv[d].Values.GetValues(TestNodes);
}
// evaluate Jacobian matrix
MultidimensionalArray Jacobi = MultidimensionalArray.Create(TestNodes.NoOfNodes, D, D); // temporary storage for Jacobian matrix
Debug.Assert(cl.TransformationParams.Dimension == 2);
Debug.Assert(cl.TransformationParams.GetLength(1) == 3);
for (int d1 = 0; d1 < D; d1++)
{
Debug.Assert(cl.TransformationParams.GetLength(0) == Deriv[d1].Count);
MultidimensionalArray JacobiCol = Jacobi.ExtractSubArrayShallow(-1, -1, d1);
JacobiCol.Multiply(1.0, DerivEval[d1], cl.TransformationParams, 0.0, "kd", "kn", "nd");
}
// do the tests
NegativeJacobianFlag = false;
PositiveJacobianFlag = false;
double MinAbsJacobiDet = double.MaxValue;
double MaxAbsJacobiDet = 0.0;
for (int n = 0; n < TestNodes.NoOfNodes; n++)
{
double detJac = Jacobi.ExtractSubArrayShallow(n, -1, -1).Determinant();
if (detJac <= 0)
{
NegativeJacobianFlag = true;
}
if (detJac > 0)
{
PositiveJacobianFlag = true;
}
MinAbsJacobiDet = Math.Min(MinAbsJacobiDet, detJac.Abs());
MaxAbsJacobiDet = Math.Max(MaxAbsJacobiDet, detJac.Abs());
}
if ((MaxAbsJacobiDet - MinAbsJacobiDet) / MinAbsJacobiDet <= 1.0e-8)
{
Linear = true;
}
else
{
Linear = false;
}
}
/// <summary>
/// Uses a safe-guarded Newton method to find all roots on
/// <paramref name="segment"/>
/// </summary>
/// <param name="segment"></param>
/// <param name="levelSet"></param>
/// <param name="cell"></param>
/// <param name="iKref"></param>
/// <returns></returns>
public double[] GetRoots(LineSegment segment, ILevelSet levelSet, int cell, int iKref)
{
LevelSet levelSetField = levelSet as LevelSet;
if (levelSetField == null)
{
throw new NotImplementedException("Method currently only works for polynomial level sets");
}
int maxNoOfCoefficientsPerDimension = levelSetField.Basis.Degree + 1;
int noOfPolynomials = segment.ProjectedPolynomialCoefficients.GetLength(1);
double[] coefficients = new double[maxNoOfCoefficientsPerDimension];
for (int i = 0; i < noOfPolynomials; i++)
{
double dgCoefficient = levelSetField.Coordinates[cell, i];
for (int j = 0; j < maxNoOfCoefficientsPerDimension; j++)
{
coefficients[j] += dgCoefficient * segment.ProjectedPolynomialCoefficients[iKref, i, j];
}
}
//if(coefficients.L2NormPow2() < this.Tolerance) {
// // ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// // special case :
// // the zero-level-set is probably parallel to this line segment
// // ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// return new double[] { -1.0, 1.0 };
//}
double[] roots;
unsafe
{
fixed(double *pCoeff = &coefficients[coefficients.Length - 1])
{
double xLow = -1.0;
double xHigh = 1.0;
int NO_OF_BRACKETS = 8;
List <double> lowerBounds = new List <double>();
List <double> upperBounds = new List <double>();
double dx2 = 2.0 / NO_OF_BRACKETS;
double x = xLow;
double fOld = Eval(x, pCoeff, coefficients.Length);
for (int i = 0; i < NO_OF_BRACKETS; i++)
{
x += dx2;
double fNew = Eval(x, pCoeff, coefficients.Length);
if (i == 0 && fOld.Abs() < Tolerance)
{
lowerBounds.Add(x - dx2);
upperBounds.Add(x);
fOld = fNew;
continue;
}
else
{
if (fNew.Abs() < Tolerance)
{
lowerBounds.Add(x - dx2);
upperBounds.Add(x);
x += dx2;
fOld = Eval(x, pCoeff, coefficients.Length);
continue;
}
}
if (fNew * fOld <= 0.0)
{
lowerBounds.Add(x - dx2);
upperBounds.Add(x);
}
fOld = fNew;
}
// Actual Newton-Raphson
int MAX_ITERATIONS = 50;
roots = new double[lowerBounds.Count];
for (int j = 0; j < lowerBounds.Count; j++)
{
xLow = lowerBounds[j];
xHigh = upperBounds[j];
double fLeft = Eval(xLow, pCoeff, coefficients.Length);
double fRight = Eval(xHigh, pCoeff, coefficients.Length);
if (fLeft.Abs() < Tolerance)
{
roots[j] = xLow;
break;
}
if (fRight.Abs() < Tolerance)
{
roots[j] = xHigh;
break;
}
if (fLeft.Sign() == fRight.Sign())
{
throw new Exception();
}
if (fLeft > 0.0)
{
xLow = upperBounds[j];
xHigh = lowerBounds[j];
}
double root = 0.5 * (xLow + xHigh);
double f;
double df;
Eval(root, pCoeff, coefficients.Length, out f, out df);
double dxOld = (xHigh - xLow).Abs();
double dx = dxOld;
int i = 0;
while (true)
{
if (i > MAX_ITERATIONS)
{
throw new Exception("Max iterations exceeded");
}
double a = ((root - xHigh) * df - f) * ((root - xLow) * df - f);
if (a > 0.0 || 2.0 * Math.Abs(f) > Math.Abs(dxOld * df))
{
// Newton out of range or too slow -> Bisect
dxOld = dx;
dx = 0.5 * (xHigh - xLow);
root = xLow + dx;
}
else
{
// Take Newton step
dxOld = dx;
dx = -f / df;
//// Convergence acceleration according to Yao2014
//double fDelta = Eval(root + dx, pCoeff, coefficients.Length);
//dx = -(f + fDelta) / df;
root += dx;
}
Eval(root, pCoeff, coefficients.Length, out f, out df);
if (Math.Abs(f) <= Tolerance)
{
roots[j] = root;
break;
}
if (f < 0.0)
{
xLow = root;
}
else
{
xHigh = root;
}
i++;
}
}
}
}
return(roots);
}
/// <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>
internal 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;
if (S12.Abs() <= 0)
{
throw new ArgumentException();
}
if (E12.Abs() <= 0)
{
throw new ArgumentException();
}
var P_S12 = AffineManifold.FromPoints(S1, S2);
var P_E12 = AffineManifold.FromPoints(E1, E2);
Vector NS = P_S12.Normal; NS.Normalize();
Vector NE = P_E12.Normal; NE.Normalize();
double parallel = NS * NE;
if (parallel.Abs() >= 1.0)
{
alpha1 = double.PositiveInfinity;
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 Abs_ShouldBehaveAsMathAbs_IfDouble(double value) => Assert.Equal(Math.Abs(value), value.Abs());
public static int SignedRoundToInt(this double x)
{
return(x.Sign() * x.Abs().RoundToInt());
}
internal void OnAddMyTrade(string portfolio, string securityId, string orderId, double price, double amount, DateTime time, string tradeNo)
{
NewMyTrade.SafeInvoke(portfolio, securityId, orderId.To <long>(), price.ToDecimal(), amount.Abs().ToDecimal(), time, tradeNo.To <long>());
}
public static int Sign(this double v)
{
return(v.Abs() < Epsilon ? 0 : Math.Sign(v));
}