/// <summary>
/// Evaluation of complete interpolating function. Note that since each curve
/// segment is controlled by four points, the end points will not be
/// interpolated. If extra control points are not desirable, the end points
/// can simply be repeated to ensure interpolation. Note also that points of
/// non-differentiability and discontinuity can be introduced by repeating
/// points
/// </summary>
/// <param name="f0_base"></param>
/// <param name="p0"></param>
/// <param name="pn"></param>
/// <param name="plotter"></param>
/// <param name="res"></param>
public void interpolate(int[][] f0_base, int p0, int pn, PointPlotter plotter, double res)
{
double k1, k2;
// Set up points for first curve segment.
int p1 = p0;
++p1;
int p2 = p1;
++p2;
int p3 = p2;
++p3;
// Draw each curve segment.
for (; p2 != pn; ++p0, ++p1, ++p2, ++p3)
{
// p1 and p2 equal; single point.
if (x(f0_base, p1) == x(f0_base, p2))
{
continue;
}
// Both end points repeated; straight line.
if (x(f0_base, p0) == x(f0_base, p1) && x(f0_base, p2) == x(f0_base, p3))
{
k1 = k2 = (y(f0_base, p2) - y(f0_base, p1)) / (x(f0_base, p2) - x(f0_base, p1));
}
// p0 and p1 equal; use f''(x1) = 0.
else if (x(f0_base, p0) == x(f0_base, p1))
{
k2 = (y(f0_base, p3) - y(f0_base, p1)) / (x(f0_base, p3) - x(f0_base, p1));
k1 = (3 * (y(f0_base, p2) - y(f0_base, p1)) / (x(f0_base, p2) - x(f0_base, p1)) - k2) / 2;
}
// p2 and p3 equal; use f''(x2) = 0.
else if (x(f0_base, p2) == x(f0_base, p3))
{
k1 = (y(f0_base, p2) - y(f0_base, p0)) / (x(f0_base, p2) - x(f0_base, p0));
k2 = (3 * (y(f0_base, p2) - y(f0_base, p1)) / (x(f0_base, p2) - x(f0_base, p1)) - k1) / 2;
}
// Normal curve.
else
{
k1 = (y(f0_base, p2) - y(f0_base, p0)) / (x(f0_base, p2) - x(f0_base, p0));
k2 = (y(f0_base, p3) - y(f0_base, p1)) / (x(f0_base, p3) - x(f0_base, p1));
}
#if SPLINE_BRUTE_FORCE
{
interpolate_brute_force(x(f0_base, p1), y(f0_base, p1), x(f0_base, p2), y(f0_base, p2), k1, k2, plotter, res);
}
#else
{
interpolate_forward_difference(x(f0_base, p1), y(f0_base, p1), x(f0_base, p2), y(f0_base, p2), k1, k2, plotter, res);
}
#endif
}
}
/// <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;
}
}
/// <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);
}
}