/// <summary>
/// QUAT.Mul : res = a * b
/// The geometric product.
/// </summary>
public static QUAT operator *(QUAT a, QUAT b)
{
QUAT res = new QUAT();
res[0] = b[0] * a[0] - b[1] * a[1] - b[2] * a[2] - b[3] * a[3];
res[1] = b[1] * a[0] + b[0] * a[1] + b[3] * a[2] - b[2] * a[3];
res[2] = b[2] * a[0] - b[3] * a[1] + b[0] * a[2] + b[1] * a[3];
res[3] = b[3] * a[0] + b[2] * a[1] - b[1] * a[2] + b[0] * a[3];
return(res);
}
/// <summary>
/// QUAT.Conjugate : res = a.Conjugate()
/// Clifford Conjugation
/// </summary>
public QUAT Conjugate()
{
QUAT res = new QUAT();
res[0] = this[0];
res[1] = -this[1];
res[2] = -this[2];
res[3] = -this[3];
return(res);
}
/// <summary>
/// QUAT.Involute : res = a.Involute()
/// Main involution
/// </summary>
public QUAT Involute()
{
QUAT res = new QUAT();
res[0] = this[0];
res[1] = -this[1];
res[2] = -this[2];
res[3] = this[3];
return(res);
}
/// <summary>
/// QUAT.Dual : res = !a
/// Poincare duality operator.
/// </summary>
public static QUAT operator !(QUAT a)
{
QUAT res = new QUAT();
res[0] = -a[3];
res[1] = -a[2];
res[2] = a[1];
res[3] = a[0];
return(res);
}
/// <summary>
/// QUAT.adds : res = a + b
/// multivector/scalar addition
/// </summary>
public static QUAT operator +(QUAT a, float b)
{
QUAT res = new QUAT();
res[0] = a[0] + b;
res[1] = a[1];
res[2] = a[2];
res[3] = a[3];
return(res);
}
/// <summary>
/// QUAT.sadd : res = a + b
/// scalar/multivector addition
/// </summary>
public static QUAT operator +(float a, QUAT b)
{
QUAT res = new QUAT();
res[0] = a + b[0];
res[1] = b[1];
res[2] = b[2];
res[3] = b[3];
return(res);
}
/// <summary>
/// QUAT.Sub : res = a - b
/// Multivector subtraction
/// </summary>
public static QUAT operator -(QUAT a, QUAT b)
{
QUAT res = new QUAT();
res[0] = a[0] - b[0];
res[1] = a[1] - b[1];
res[2] = a[2] - b[2];
res[3] = a[3] - b[3];
return(res);
}
/// <summary>
/// QUAT.Vee : res = a & b
/// The regressive product. (JOIN)
/// </summary>
public static QUAT operator &(QUAT a, QUAT b)
{
QUAT res = new QUAT();
res[3] = 1 * (a[3] * b[3]);
res[2] = -1 * (a[2] * -1 * b[3] + a[3] * b[2] * -1);
res[1] = 1 * (a[1] * b[3] + a[3] * b[1]);
res[0] = 1 * (a[0] * b[3] + a[1] * b[2] * -1 - a[2] * -1 * b[1] + a[3] * b[0]);
return(res);
}
