double polynomialInterpolation (double x, vector<Vector> points) throw(CoincidentPointsException) {
size_t n = points.size();
double px = 0.0;
vector<double> lagrangian(n, 1.0);
for (size_t i=0; i < n; i++)
for (size_t j=0; j < n; j++)
if (i != j)
lagrangian[i] *= ( (x - points[j][0]) / (points[i][0] - points[j][0]) );
for (size_t i=0; i < n; i++)
px += (points[i][1] * lagrangian[i]);
return px;
}
Force3 force(unsigned i, Parameters ps, Configurations c, Length dx)
{
Configurations cx = c;
Configurations cy = c;
Configurations cz = c;
cx.position[i] = c.position[i] + dx * ex;
cy.position[i] = c.position[i] + dx * ey;
cz.position[i] = c.position[i] + dx * ez;
Force fx = (lagrangian(i, ps, cx) - lagrangian(i, ps, c)) / dx;
Force fy = (lagrangian(i, ps, cy) - lagrangian(i, ps, c)) / dx;
Force fz = (lagrangian(i, ps, cz) - lagrangian(i, ps, c)) / dx;
Force3 f = fx * ex + fy * ey + fz * ez;
return f;
}
