/// <summary>
/// Evaluation of cubic polynomial by brute force
/// </summary>
/// <param name="x1"></param>
/// <param name="y1"></param>
/// <param name="x2"></param>
/// <param name="y2"></param>
/// <param name="k1"></param>
/// <param name="k2"></param>
/// <param name="plotter"></param>
/// <param name="res"></param>
protected void interpolate_brute_force(double x1, double y1, double x2, double y2, double k1, double k2, PointPlotter plotter, double res)
{
Coefficients coeff = new Coefficients();
cubic_coefficients(x1, y1, x2, y2, k1, k2, coeff);
// Calculate each point
for (double x = x1; x <= x2; x += res)
{
double y = ((coeff.a * x + coeff.b) * x + coeff.c) * x + coeff.d;
plotter.plot(x, y);
}
}
/// <summary>
/// Evaluation of cubic polynomial by forward differencing
/// </summary>
/// <param name="x1"></param>
/// <param name="y1"></param>
/// <param name="x2"></param>
/// <param name="y2"></param>
/// <param name="k1"></param>
/// <param name="k2"></param>
/// <param name="plotter"></param>
/// <param name="res"></param>
protected void interpolate_forward_difference(double x1, double y1, double x2, double y2, double k1, double k2, PointPlotter plotter, double res)
{
Coefficients coeff = new Coefficients();
cubic_coefficients(x1, y1, x2, y2, k1, k2, coeff);
double y = ((coeff.a * x1 + coeff.b) * x1 + coeff.c) * x1 + coeff.d;
double dy = (3 * coeff.a * (x1 + res) + 2 * coeff.b) * x1 * res + ((coeff.a * res + coeff.b) * res + coeff.c) * res;
double d2y = (6 * coeff.a * (x1 + res) + 2 * coeff.b) * res * res;
double d3y = 6 * coeff.a * res * res * res;
// Calculate each point
for (double x = x1; x <= x2; x += res)
{
plotter.plot(x, y);
y += dy;
dy += d2y;
d2y += d3y;
}
}