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 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);
}