double Interpolate(double x, double y, double a)
{
double negA = 1.0 - a;
double negASqr = negA * negA;
double fac1 = 3.0 * (negASqr) - 2.0 * (negASqr * negA);
double aSqr = a * a;
double fac2 = 3.0 * aSqr - 2.0 * (aSqr * a);
return x * fac1 + y * fac2; //add the weighted factors
}