- inline std::pair<Real,Real> SolveQuadratic(const Real & a, const Real & b, const Real & c)
- {
- Real x0((-b + Sqrt(b*b - Real(4)*a*c))/(Real(2)*a));
- Real x1((-b - Sqrt(b*b - Real(4)*a*c))/(Real(2)*a));
- return std::pair<Real,Real>(x0,x1);
- }
-
- inline std::vector<Real> SolveCubic(const Real & a, const Real & b, const Real & c, const Real & d)
- {
- // This is going to be a big one...
- // See http://en.wikipedia.org/wiki/Cubic_function#General_formula_for_roots
-
- // delta = 18abcd - 4 b^3 d + b^2 c^2 - 4ac^3 - 27 a^2 d^2
-
- Real discriminant = Real(18) * a * b * c * d - Real(4) * (b * b * b) * d
- + (b * b) * (c * c) - Real(4) * a * (c * c * c)
- - Real(27) * (a * a) * (d * d);
-
- Debug("Trying to solve %fx^3 + %fx^2 + %fx + %f (Discriminant: %f)", a,b,c,d, discriminant);
- // discriminant > 0 => 3 distinct, real roots.
- // discriminant = 0 => a multiple root (1 or 2 real roots)
- // discriminant < 0 => 1 real root, 2 complex conjugate roots
-
- Real delta0 = (b*b) - Real(3) * a * c;
- Real delta1 = Real(2) * (b * b * b) - Real(9) * a * b * c + Real(27) * (a * a) * d;
-
- std::vector<Real> roots;