/// <summary>
/// Fit the input x,y points using a 'geometric' strategy so that y does not have to be a single-valued
/// function of x.
/// </summary>
/// <param name="x">Input x coordinates.</param>
/// <param name="y">Input y coordinates, do not need to be a single-valued function of x.</param>
/// <param name="nOutputPoints">How many output points to create.</param>
/// <param name="xs">Output (interpolated) x values.</param>
/// <param name="ys">Output (interpolated) y values.</param>
public static void FitGeometric(double[] x, double[] y, int nOutputPoints, out double[] xs, out double[] ys)
{
// Compute distances
int n = x.Length;
double[] dists = new double[n]; // cumulative distance
dists[0] = 0;
double totalDist = 0;
for (int i = 1; i < n; i++)
{
double dx = x[i] - x[i - 1];
double dy = y[i] - y[i - 1];
double dist = (double)Math.Sqrt(dx * dx + dy * dy);
totalDist += dist;
dists[i] = totalDist;
}
// Create 'times' to interpolate to
double dt = totalDist / (nOutputPoints - 1);
double[] times = new double[nOutputPoints];
times[0] = 0;
for (int i = 1; i < nOutputPoints; i++)
{
times[i] = times[i - 1] + dt;
}
// Spline fit both x and y to times
CubicSpline xSpline = new CubicSpline();
xs = xSpline.FitAndEval(x.Length, dists, x, times);
CubicSpline ySpline = new CubicSpline();
ys = ySpline.FitAndEval(x.Length, dists, y, times);
}
/// <summary>
/// Static all-in-one method to fit the splines and evaluate at X coordinates.
/// </summary>
/// <param name="num">Input. Real Lenth of X. Values in X must in ascend Order</param>
/// <param name="x">Input. X coordinates to fit.</param>
/// <param name="y">Input. Y coordinates to fit.</param>
/// <param name="xs">Input. X coordinates to evaluate the fitted curve at.</param>
/// <param name="startSlope">Optional slope constraint for the first point. Single.NaN means no constraint.</param>
/// <param name="endSlope">Optional slope constraint for the final point. Single.NaN means no constraint.</param>
/// <param name="debug">Turn on console output. Default is false.</param>
/// <returns>The computed y values for each xs.</returns>
public static double[] Compute(int num, double[] x, double[] y, double[] xs, double startSlope = double.NaN, double endSlope = double.NaN, bool debug = false)
{
CubicSpline spline = new CubicSpline();
return(spline.FitAndEval(num, x, y, xs, startSlope, endSlope, debug));
}