public static GaPoTNumRotorsSequence CreateFromOrthonormalFrames(GaPoTNumFrame sourceFrame, GaPoTNumFrame targetFrame)
{
Debug.Assert(targetFrame.Count == sourceFrame.Count);
Debug.Assert(sourceFrame.IsOrthonormal() && targetFrame.IsOrthonormal());
Debug.Assert(sourceFrame.HasSameHandedness(targetFrame));
var rotorsSequence = new GaPoTNumRotorsSequence();
var sourceFrameVectors = new GaPoTNumVector[sourceFrame.Count];
for (var i = 0; i < sourceFrame.Count; i++)
{
sourceFrameVectors[i] = sourceFrame[i];
}
for (var i = 0; i < sourceFrame.Count - 1; i++)
{
var sourceVector = sourceFrameVectors[i];
var targetVector = targetFrame[i];
var rotor =
sourceVector.GetRotorToVector(targetVector);
rotorsSequence.AppendRotor(rotor);
for (var j = i + 1; j < sourceFrame.Count; j++)
{
sourceFrameVectors[j] = sourceFrameVectors[j].ApplyRotor(rotor);
}
}
return(rotorsSequence);
}
public static GaPoTNumFrame CreateFromColumns(double[,] matrix)
{
var rowsCount = matrix.GetLength(0);
var colsCount = matrix.GetLength(1);
var frame = new GaPoTNumFrame();
for (var j = 0; j < colsCount; j++)
{
var vector = new GaPoTNumVector();
for (var i = 0; i < rowsCount; i++)
{
var value = matrix[i, j];
if (value == 0)
{
continue;
}
vector.AddTerm(i + 1, value);
}
frame.AppendVector(vector);
}
return(frame);
}
public static GaPoTNumFrame CreateFbdFrame4D()
{
var c = Math.Sqrt(0.75d);
var frame = new GaPoTNumFrame();
var v1 = new GaPoTNumVector(
c * Math.Sqrt(8.0d / 9.0d),
0.0d,
c / 3.0d
);
var v2 = new GaPoTNumVector(
c * -Math.Sqrt(2.0d / 9.0d),
c * Math.Sqrt(2.0d / 3.0d),
c / 3.0d
);
var v3 = new GaPoTNumVector(
-c * Math.Sqrt(2.0d / 9.0d),
c * -Math.Sqrt(2.0d / 3.0d),
c / 3.0d
);
var v4 = new GaPoTNumVector(
0.0d,
0.0d,
-c
);
frame.AppendVectors(v1, v2, v3, v4);
return(frame);
}
public static GaPoTNumFrame CreateBasisFrame(int vectorsCount)
{
var frame = new GaPoTNumFrame();
for (var i = 0; i < vectorsCount; i++)
{
var vector = new GaPoTNumVector().AddTerm(i + 1, 1.0d);
frame.AppendVector(vector);
}
return(frame);
}
public GaPoTNumVector GetProjectionOnFrame(GaPoTNumFrame frame)
{
var vector = new GaPoTNumVector();
foreach (var term in _termsDictionary.Values)
{
var i = term.TermId - 1;
var v = term.Value;
vector += v * frame[i];
}
return(vector);
}
public static GaPoTNumFrame CreateFbdFrame3D()
{
var frame = new GaPoTNumFrame();
var v1 = new GaPoTNumVector(
1.0d,
0.0d
);
var v2 = new GaPoTNumVector(
-0.5d,
0.5d * Math.Sqrt(3.0d)
);
var v3 = new GaPoTNumVector(
-0.5d,
-0.5d * Math.Sqrt(3.0d)
);
frame.AppendVectors(v1, v2, v3);
return(frame);
}
public static GaPoTNumFrame CreateFbdFrame(int vectorsCount, out GaPoTNumFrame kirchhoffFrame)
{
//var uPseudoScalar = new GaPoTNumMultivector()
// .SetTerm(
// (1 << vectorsCount) - 1,
// 1.0d
// );
//kirchhoffFrame = CreateKirchhoffFrame(vectorsCount, vectorsCount - 1);
//kirchhoffFrame = CreateBasisFrame(vectorsCount)
// .GetProjectionOnFrame(kirchhoffFrame)
// .GetSubFrame(0, vectorsCount - 1);
//var cFrame = kirchhoffFrame.GetOrthogonalFrame(true);
//cFrame.AppendVector(
// -GaPoTNumUtils
// .OuterProduct(cFrame)
// .Gp(uPseudoScalar.CliffordConjugate())
// .GetVectorPart()
//);
//Debug.Assert(
// cFrame.IsOrthonormal()
//);
//Debug.Assert(
// CreateBasisFrame(vectorsCount).HasSameHandedness(cFrame)
//);
//return cFrame;
var basisFrame = CreateBasisFrame(vectorsCount);
var diffFrame = CreateKirchhoffFrame(vectorsCount);
var projFrame = basisFrame.GetProjectionOnFrame(diffFrame);
var projMatrix = projFrame.GetMatrix(vectorsCount);
var rowsCount = projMatrix.GetLength(0);
var colsCount = projMatrix.GetLength(1);
for (var j = 0; j < colsCount; j++)
{
var djj = projMatrix[j, j];
for (var j1 = j + 1; j1 < colsCount; j1++)
{
var d = projMatrix[0, j1] / djj;
for (var i = 0; i <= j1; i++)
{
projMatrix[i, j1] = 0;
}
for (var i = j1; i < rowsCount; i++)
{
projMatrix[i, j1] = projMatrix[i, j1] - d * projMatrix[i, j];
}
}
}
kirchhoffFrame = diffFrame;
var fbdFrame = GaPoTNumFrame.CreateFromColumns(projMatrix).Normalize();
return(fbdFrame);
if (vectorsCount == 3)
{
return(CreateFbdFrame3D());
}
if (vectorsCount == 4)
{
return(CreateFbdFrame4D());
}
throw new InvalidOperationException();
}
public static GaPoTNumFrame CreateGramSchmidtFrame(int vectorsCount, int refVectorIndex, out GaPoTNumFrame kirchhoffFrame)
{
kirchhoffFrame = CreateKirchhoffFrame(vectorsCount, refVectorIndex);
var uPseudoScalar = new GaPoTNumMultivector()
.SetTerm(
(1 << vectorsCount) - 1,
1.0d
);
var cFrame = kirchhoffFrame.GetOrthogonalFrame(true);
cFrame.AppendVector(
-GaPoTNumUtils
.OuterProduct(cFrame)
.Gp(uPseudoScalar.CliffordConjugate())
.GetVectorPart()
);
Debug.Assert(
cFrame.IsOrthonormal()
);
Debug.Assert(
CreateBasisFrame(vectorsCount).HasSameHandedness(cFrame)
);
return(cFrame);
}
public static GaPoTNumFrame CreateGramSchmidtFrame(int vectorsCount, out GaPoTNumFrame kirchhoffFrame)
{
return(CreateGramSchmidtFrame(vectorsCount, 0, out kirchhoffFrame));
}
public static GaPoTNumRotorsSequence CreateFromFrames(int baseSpaceDimensions, GaPoTNumFrame sourceFrame, GaPoTNumFrame targetFrame)
{
Debug.Assert(targetFrame.Count == sourceFrame.Count);
//Debug.Assert(IsOrthonormal() && targetFrame.IsOrthonormal());
Debug.Assert(sourceFrame.HasSameHandedness(targetFrame));
var rotorsSequence = new GaPoTNumRotorsSequence();
var pseudoScalar =
GaPoTNumMultivector
.CreateZero()
.SetTerm((1 << baseSpaceDimensions) - 1, 1.0d);
var sourceFrameVectors = new GaPoTNumVector[sourceFrame.Count];
var targetFrameVectors = new GaPoTNumVector[targetFrame.Count];
for (var i = 0; i < sourceFrame.Count; i++)
{
sourceFrameVectors[i] = sourceFrame[i];
targetFrameVectors[i] = targetFrame[i];
}
for (var i = 0; i < sourceFrame.Count - 1; i++)
{
var sourceVector = sourceFrameVectors[i];
var targetVector = targetFrameVectors[i];
var rotor =
sourceVector.GetRotorToVector(targetVector);
rotorsSequence.AppendRotor(rotor);
pseudoScalar = targetVector.ToMultivector().Lcp(pseudoScalar.Inverse());
for (var j = i + 1; j < sourceFrame.Count; j++)
{
sourceFrameVectors[j] =
sourceFrameVectors[j].ApplyRotor(rotor).GetProjectionOnBlade(pseudoScalar);
targetFrameVectors[j] =
targetFrameVectors[j].GetProjectionOnBlade(pseudoScalar);
}
}
return(rotorsSequence);
}
