public static Vector3 Solve(QFCoefficient coefficient)
{
//https://www.value-at-risk.net/minimizing-a-quadratic-polynomial/
//Minimize x' c x + b x + a
//c:
//x^2 xy xz
// y^2 yz
// z^2
var vv = coefficient.Values;
Matrix4x4 c = new Matrix4x4(
vv[0], vv[3] / 2, vv[5] / 2, 0,
vv[3] / 2, vv[1], vv[4] / 2, 0,
vv[5] / 2, vv[4] / 2, vv[2], 0,
0, 0, 0, 1);
if (!Matrix4x4.Invert(c, out var ic))
{
throw new Exception("Internal error");
}
var b = new Vector4(vv[6], vv[7], vv[8], 0);
var ret = Vector4.Transform(b, Matrix4x4.Transpose(ic)) * -0.5f;
return(new Vector3(ret.X, ret.Y, ret.Z));
}
public QFCoefficient Clone()
{
var c = new QFCoefficient();
var ret = c.Values;
Array.Copy(Values, 0, ret, 0, Values.Length);
return(c);
}
