public static MultiVector CreatePoint(MultiVector v)
{
if (IPNS.GetGeometricEntity(v) != GeometricEntity.Vector)
{
throw new InvalidEntityException();
}
return(v + 0.5 * MultiVector.ScalarProduct(v, v) * Basis.E8 + Basis.E0);
}
public static void GetSphereParams(MultiVector obj, out MultiVector c, out double r)
{
if (!obj.ContainsOnly(1) || obj.E0 == 0.0)
{
throw new InvalidEntityException();
}
obj /= obj.E0;
c = MultiVector.Vector(obj.E1, obj.E2, obj.E3);
r = Math.Sqrt(Math.Abs(2 * obj.E8 - (double)MultiVector.ScalarProduct(c, c)));
// HACK
if (Math.Abs(r) < 1E-3)
{
r = 0.0;
}
}
public static void GetCircleParams(MultiVector obj, out MultiVector n, out MultiVector c, out double r)
{
if (!obj.ContainsOnly(2))
{
throw new InvalidEntityException();
}
// c cross n
MultiVector ccd = MultiVector.Vector(
-obj[Basis.E23],
obj[Basis.E13],
-obj[Basis.E12]);
// c dot n
double d = obj[Basis.EPLANE];
n = MultiVector.Vector(
obj[Basis.E1 ^ Basis.E0],
obj[Basis.E2 ^ Basis.E0],
obj[Basis.E3 ^ Basis.E0]);
c = MultiVector.CrossProduct(n, ccd) + n * d;
c /= (double)MultiVector.ScalarProduct(n, n);
double x;
if (n.E1 != 0)
{
x = (obj[Basis.E1 ^ Basis.E8] + (double)d * c.E1) / n.E1;
}
else if (n.E2 != 0)
{
x = (obj[Basis.E2 ^ Basis.E8] + (double)d * c.E2) / n.E2;
}
else if (n.E3 != 0)
{
x = (obj[Basis.E3 ^ Basis.E8] + (double)d * c.E3) / n.E3;
}
else
{
throw new InvalidEntityException();
}
r = Math.Sqrt((double)MultiVector.ScalarProduct(c, c) - 2 * x);
n /= n.Length;
}
public static MultiVector CreateCircle(MultiVector n, MultiVector c, double r)
{
double d = (double)MultiVector.ScalarProduct(c, n);
return(IPNS.CreatePlane(n, d) ^ IPNS.CreateSphere(c, r));
}
public static MultiVector CreatePoint(double e1, double e2, double e3)
{
MultiVector v = MultiVector.Vector(e1, e2, e3);
return(v + 0.5 * MultiVector.ScalarProduct(v, v) * Basis.E8 + Basis.E0);
}
