public bool IntersectionWith(Line line2, out Vector Intersection)
{
Intersection = new Vector(Dimensions);
// Lösen der Gleichung n*Direction + P1 = m*Direction2 + P2
// => P2 - P1 = n*Direction - m*Direction2
// => P2 - P1 = [Direction | Direction2] * (n, m)t
// => (n,m)t = [Direction | Direction2]^-1 * P2 - P1
Vector Pdiff = line2.P1 - P1;
Transformations.Matrix M = new Transformations.Matrix(Dimensions, 2);
M.SetColumn(0, Direction);
M.SetColumn(1, line2.Direction);
Transformations.Matrix Minv;
if (!M.Invert(out Minv))
{
return(false);
}
Vector nm = Minv.RightMul(Pdiff);
Intersection.Set((nm[0] * Direction + P1).coordinates);
return(true);
}
/// <summary>
/// Invertierung nach Austauschverfahren (Pivot)
/// y = M x -> x = MInv y
/// </summary>
/// <param name="Minv"></param>
/// <returns></returns>
public bool Invert(out Matrix Minv)
{
Minv = new Matrix(this);
int[] ixX = IndexGenerator(Dimensions).ToArray();
bool[] Xchanged = BoolFieldGenerator(false, Dimensions).ToArray();
int[] ixY = IndexGenerator(CountLines).ToArray();
bool[] Ychanged = BoolFieldGenerator(false, Dimensions).ToArray();
int pivotC = 0, pivotL = 0;
try
{
// Tauschen aller x gegen alle y
for (pivotC = 0; pivotC < Math.Min(this.Dimensions, this.CountLines); pivotC++)
{
// Suchen in aktueller Spalte nach einem Koeff für eine Zeile, deren y noch nicht getauscht wurde
pivotL = ColAsTriple(Minv, pivotC, Ychanged).Where(line => line.Item2 != 0 && !line.Item3).First().Item1;
// x und y tauschen. Tausch protokollieren
int tausch = ixX[pivotC];
ixX[pivotC] = ixY[pivotL];
ixY[pivotL] = tausch;
Xchanged[pivotC] = Ychanged[pivotL] = true;
// Inversion in Hilfsmatrix durchführen
Matrix M2 = new Matrix(Minv);
double p = Minv[pivotC, pivotL];
M2.SetLine(pivotL, Minv.Line(pivotL) * (-1 / p));
M2.SetColumn(pivotC, Minv.Column(pivotC) * (1 / p));
M2[pivotL, pivotC] = 1 / p;
for (int line = 0; line < Dimensions; line++)
{
if (line != pivotL)
{
for (int col = 0; col < Dimensions; col++)
{
if (col != pivotC)
{
M2[line, col] = Minv[line, col] + -Minv[line, pivotC] * Minv[pivotL, col] / p;
}
}
}
}
// Hilfsmatrix zur neuen gültigen erklären
Minv = M2;
}
// Umsortieren der Zeilen
Matrix M3 = new Matrix(Minv.CountLines, Minv.Dimensions);
for (int line = 0; line < CountLines; line++)
{
M3.SetLine(ixY[line], Minv.Line(line));
}
Matrix M4 = new Matrix(Minv.CountLines, Minv.Dimensions);
for (int col = 0; col < Dimensions; col++)
{
M4.SetColumn(ixX[col], M3.Column(col));
}
Minv = M4;
}
catch (Exception)
{
return(false);
}
// Reihenfolge wiederherstellen
return(true);
}