public static Quadratic From3Coordinate2(IVector2 <double> A, IVector2 <double> B, IVector2 <double> C)
{
//Convert the 3 points to quadratic equations.
var equation1 = new Quadratic(A.X, A.Y);
var equation2 = new Quadratic(B.X, B.Y);
var equation3 = new Quadratic(C.X, C.Y);
//Cancel out "C"
var equation4 = equation1.MakeSubject(equation1.C).Subtract(equation2.MakeSubject(equation1.C));
var equation5 = equation2.MakeSubject(equation2.C).Subtract(equation3.MakeSubject(equation3.C));
//Cancel out "B"
var equation6 = equation4.MakeSubject(equation4.B).Subtract(equation5.MakeSubject(equation5.B));
//Solve for A then B then C
var a = equation6.MakeSubject(equation6.A).Result; //Substitute into EQ 6
var b = (equation4.Result - equation4.A * a) / equation4.B; //Into EQ 4
var c = (A.Y) - (a * (A.X) * (A.X)) - (b * (A.X)); //Into EQ 1
//Create new Quadratic solver based on A, B and C.
var output = new Quadratic
{
A = a,
B = b,
C = c
};
return(output);
}