/// <summary>
/// Create a derived frame system where the derived frame is the reciprocal of the base frame
/// </summary>
/// <param name="baseFrame"></param>
/// <returns></returns>
public static DerivedFrameSystem CreateReciprocalCbmFrameSystem(GaFrame baseFrame)
{
if (baseFrame.IsOrthogonal)
{
var cbmat = baseFrame.Ipm.Inverse();
var b2DOm = GaOuterMorphismFull.Create(baseFrame.Ipm);
var d2BOm = GaOuterMorphismFull.Create(cbmat);
var derivedFrame = CreateOrthogonal(cbmat.GetDiagonal());
return(new DerivedFrameSystem(baseFrame, derivedFrame, d2BOm, b2DOm));
}
var cbmArray = new MathematicaScalar[baseFrame.VSpaceDimension, baseFrame.VSpaceDimension];
var mv2 = baseFrame.CreateInverseUnitPseudoScalar();
for (var i = 0; i < baseFrame.VSpaceDimension; i++)
{
var id = (1 << i) ^ baseFrame.MaxBasisBladeId;
var mv1 = GaMultivector.CreateTerm(baseFrame.GaSpaceDimension, id, SymbolicUtils.Constants.One);
var mv = baseFrame.Lcp(mv1, mv2);
foreach (var term in mv)
{
var j = term.Key.BasisBladeIndex();
if ((i & 1) == 1)
{
cbmArray[i, j] = term.Value;
}
else
{
cbmArray[i, j] = -term.Value;
}
}
}
var cbm = MathematicaMatrix.CreateFullMatrix(SymbolicUtils.Cas, cbmArray);
return(CreateDerivedCbmFrameSystem(baseFrame, cbm));
}
public GaMultivector CreateInverseUnitPseudoScalar()
{
//TODO: Review this computation
return(GaMultivector.CreateTerm(GaSpaceDimension, MaxBasisBladeId, UnitPseudoScalarCoef));
}
internal static GMacValueMultivector CreateTerm(GMacFrameMultivector mvType, int id, MathematicaScalar coef)
{
var mvCoefs = GaMultivector.CreateTerm(mvType.ParentFrame.GaSpaceDimension, id, coef);
return(new GMacValueMultivector(mvType, mvCoefs));
}