public static Blade InnerProduct(Basis e1, Basis e2)
{
int hashPair = Basis.GetHashPair(e1, e2);
if (innerProductCache.ContainsKey(hashPair))
{
return(innerProductCache[hashPair]);
}
Blade result;
if (e1.IsNullMetric || e2.IsNullMetric)
{
MultiVector m1 = e1.ToMinkowskiMetric();
MultiVector m2 = e2.ToMinkowskiMetric();
result = (Blade)MultiVector.InnerProduct(m1, m2).ToNullMetric();
}
else
{
if ((e1.bitMask & ~e2.bitMask) == 0)
{
result = (Blade)(e1 * e2);
}
else
{
result = Blade.Zero;
}
}
innerProductCache.Add(hashPair, result);
return(result);
}
public static void GetPointPairParams(MultiVector obj, out MultiVector p1, out MultiVector p2)
{
if (!obj.ContainsOnly(3))
{
throw new InvalidEntityException();
}
obj = obj.Dual;
double delta = Math.Sqrt(Math.Abs((double)MultiVector.InnerProduct(obj, obj)));
try
{
MultiVector temp = MultiVector.InnerProduct(Basis.E8, obj);
p1 = (+delta + obj) / temp;
p2 = (-delta + obj) / temp;
}
catch (InvalidOperationException)
{
throw new InvalidEntityException();
}
}
public static GeometricEntity GetGeometricEntity(MultiVector obj)
{
if (obj.ContainsOnly(0))
{
return(GeometricEntity.Scalar);
}
if (obj.ContainsOnly(1))
{
if (obj.E0 == 0 && obj.E8 == 0)
{
return(GeometricEntity.Vector);
}
if (obj.E0 == 0)
{
return(GeometricEntity.Plane);
}
MultiVector center; double radius;
GetSphereParams(obj, out center, out radius);
if (radius == 0)
{
return(GeometricEntity.Point);
}
return(GeometricEntity.Sphere);
}
if (obj.ContainsOnly(2))
{
if (obj.ContainsOnly(Basis.E12, Basis.E13, Basis.E23))
{
return(GeometricEntity.Bivector);
}
if (MultiVector.InnerProduct(Basis.E8, obj) == 0.0)
{
return(GeometricEntity.Line);
}
return(GeometricEntity.Circle);
}
if (obj.ContainsOnly(3))
{
if (obj.ContainsOnly(Basis.E123))
{
return(GeometricEntity.Trivector);
}
try
{
MultiVector p1, p2;
GetPointPairParams(obj, out p1, out p2);
return(GeometricEntity.PointPair);
}
catch (InvalidEntityException)
{
return(GeometricEntity.Unknown);
}
}
return(GeometricEntity.Unknown);
}