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 GaPoTNumMultivector Sp(GaPoTNumMultivector mv2)
{
var result = new GaPoTNumMultivector();
foreach (var term1 in _termsDictionary.Values)
{
if (!mv2._termsDictionary.TryGetValue(term1.IDsPattern, out var term2))
{
continue;
}
var value = term1.Value * term2.Value;
if (value == 0)
{
continue;
}
if (GaPoTNumUtils.ComputeIsNegativeEGp(term1.IDsPattern, term2.IDsPattern))
{
value = -value;
}
result.AddTerm(new GaPoTNumMultivectorTerm(0, value));
}
return(result);
}
public GaPoTNumMultivector ApplyRotor(GaPoTNumMultivector rotor)
{
var r1 = rotor;
var r2 = rotor.Reverse();
return(r1.Gp(this).Gp(r2));
}
public GaPoTNumVector ApplyRotor(GaPoTNumMultivector rotor)
{
var r1 = rotor;
var r2 = rotor.Reverse();
var v = ToMultivector();
var mv = r1.Gp(v).Gp(r2);
return(mv.GetVectorPart());
}
/// <summary>
/// Assuming this multivector is a simple rotor, this extracts its angle and 2-blade of rotation
/// </summary>
/// <returns></returns>
public Tuple <double, GaPoTNumMultivector> GetSimpleRotorAngleBlade()
{
var scalarPart = GetTermValue(0);
var bivectorPart = new GaPoTNumMultivector(GetTermsOfGrade(2));
var halfAngle = Math.Acos(scalarPart);
var angle = 2.0d * halfAngle;
var blade = bivectorPart / Math.Sin(halfAngle);
return(new Tuple <double, GaPoTNumMultivector>(angle, blade));
}
public static GaPoTNumMultivector operator -(GaPoTNumMultivector v)
{
var result = new GaPoTNumMultivector();
foreach (var term in v._termsDictionary.Values)
{
result.AddTerm(term.IDsPattern, -term.Value);
}
return(result);
}
/// <summary>
/// Create a simple rotor from an angle and a blade
/// </summary>
/// <param name="rotationAngle"></param>
/// <param name="rotationBlade"></param>
/// <returns></returns>
public static GaPoTNumMultivector CreateSimpleRotor(double rotationAngle, GaPoTNumMultivector rotationBlade)
{
var cosHalfAngle = Math.Cos(rotationAngle / 2.0d);
var sinHalfAngle = Math.Sin(rotationAngle / 2.0d);
var rotationBladeScalar =
sinHalfAngle /
Math.Sqrt(Math.Abs(rotationBlade.Gp(rotationBlade).GetTermValue(0)));
var rotor =
cosHalfAngle + rotationBladeScalar * rotationBlade;
//rotor.IsSimpleRotor();
return(rotor);
}
public static GaPoTNumMultivector operator /(GaPoTNumMultivector v, double s)
{
s = 1.0d / s;
var result = new GaPoTNumMultivector();
foreach (var term in v._termsDictionary.Values)
{
result.AddTerm(
term.IDsPattern,
term.Value * s
);
}
return(result);
}
public static GaPoTNumMultivector operator +(double v2, GaPoTNumMultivector v1)
{
var result = new GaPoTNumMultivector();
foreach (var term in v1._termsDictionary.Values)
{
result.AddTerm(
term.IDsPattern,
term.Value
);
}
result.AddTerm(0, v2);
return(result);
}
public GaPoTNumMultivector Gp(GaPoTNumMultivector mv2)
{
var result = new GaPoTNumMultivector();
foreach (var term1 in _termsDictionary.Values)
{
foreach (var term2 in mv2._termsDictionary.Values)
{
var term = term1.Gp(term2);
if (term.Value != 0)
{
result.AddTerm(term);
}
}
}
return(result);
}
public static GaPoTNumMultivector operator *(GaPoTNumMultivector v1, GaPoTNumMultivector v2)
{
var result = new GaPoTNumMultivector();
foreach (var term1 in v1._termsDictionary.Values)
{
foreach (var term2 in v2._termsDictionary.Values)
{
var term = term1.Gp(term2);
if (term.Value != 0)
{
result.AddTerm(term);
}
}
}
return(result);
}
public GaPoTNumMultivector Subtract(GaPoTNumMultivector v)
{
return(this - v);
}
public GaPoTNumMultivector Add(GaPoTNumMultivector v)
{
return(this + v);
}
public GaPoTNumVector GetProjectionOnBlade(GaPoTNumMultivector blade)
{
return(ToMultivector().Lcp(blade).Lcp(blade.Inverse()).GetVectorPart());
}
public GaPoTNumMultivector GetRotorToVector(GaPoTNumVector v2)
{
return(GaPoTNumMultivector.CreateSimpleRotor(this, v2));
}
public GaPoTNumMultivector Gp(GaPoTNumMultivector v)
{
return(ToMultivector().Gp(v));
}