public static void GetLineParams(MultiVector obj, out MultiVector t, out MultiVector d)
{
if (!obj.ContainsOnly(2))
{
throw new InvalidEntityException();
}
d = MultiVector.Vector(
-obj[Basis.E23],
obj[Basis.E13],
-obj[Basis.E12]);
double norm = d.Length;
if (norm == 0.0)
{
throw new InvalidEntityException();
}
d /= norm;
// d cross t
MultiVector dct = MultiVector.Vector(
obj[Basis.E1 ^ Basis.E8],
obj[Basis.E2 ^ Basis.E8],
obj[Basis.E3 ^ Basis.E8]) / norm;
t = MultiVector.CrossProduct(dct, d);
}
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 CreateLine(MultiVector t, MultiVector d)
{
return(d * Basis.E123 + (MultiVector.CrossProduct(d, t) ^ Basis.E8));
}
