// Linear Interp.
real Maths::LinearValue(real a, real b, real amount) {
    return a + amount * (b-a);
}

// Monomial Interp.
real Maths::MonomialValue(real a, real b, real power, real amount) {
    return pow(LinearValue(a,b,amount), power);
}

// Hermite Interp.
real _sc_h00(real s) { // 2*s^3 - 3*s^2 + 1
    return (real) ((real)2.0 * pow(s,(real)3.0) - (real)3.0 * pow(s,(real)2.0) + 1.0); }
real _sc_h10(real s) { // s^3 - 2*s^2 + s
    return (real) (pow(s,(real)3.0) - (real)2.0 * pow(s,(real)2.0) + s); }
real _sc_h01(real s) { // -2*s^3 + 3*s^2
    return (real) ((real)-2.0 * pow(s,(real)3.0) + (real)3.0 * pow(s,(real)2.0)); }
real _sc_h11(real s) { // s^3 - s^2
    return (real) (pow(s,(real)3.0) - pow(s,(real)2.0)); }

real Maths::HermiteValue(real a, real atan, real b, real btan, real t) {
    return (_sc_h00(t)*a + _sc_h10(t)*atan + _sc_h01(t)*b + _sc_h11(t)*btan);
}

// Bezier Interp.
real Maths::Bezier2Value(real p0, real p1, real p2, real t) {
    real p01 = LinearValue(p0,p1,t);
    real p12 = LinearValue(p1,p2,t);
    return LinearValue(p01,p12,t);
}

real Maths::Bezier3Value(real p0, real p1, real p2, real p3, real t) {
    real p01 = LinearValue(p0,p1,t);
    real p12 = LinearValue(p1,p2,t);
    real p23 = LinearValue(p2,p3,t);
    real p0112 = LinearValue(p01,p12,t);
    real p1223 = LinearValue(p12,p23,t);
    return LinearValue(p0112,p1223,t);
}