/// <summary>
/// Fit the input x,y points using the parametric approach, so that y does not have to be an explicit
/// function of x, meaning there does not need to be a single value of y for each x.
/// </summary>
/// <param name="x">Input x coordinates.</param>
/// <param name="y">Input y coordinates.</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>
/// <param name="firstDx">Optionally specifies the first point's slope in combination with firstDy. Together they
/// are a vector describing the direction of the parametric spline of the starting point. The vector does
/// not need to be normalized. If either is NaN then neither is used.</param>
/// <param name="firstDy">See description of dx0.</param>
/// <param name="lastDx">Optionally specifies the last point's slope in combination with lastDy. Together they
/// are a vector describing the direction of the parametric spline of the last point. The vector does
/// not need to be normalized. If either is NaN then neither is used.</param>
/// <param name="lastDy">See description of dxN.</param>
public static void FitParametric(float[] x, float[] y, int nOutputPoints, out float[] xs, out float[] ys,
float firstDx = Single.NaN, float firstDy = Single.NaN, float lastDx = Single.NaN, float lastDy = Single.NaN)
{
// Compute distances
int n = x.Length;
float[] dists = new float[n]; // cumulative distance
dists[0] = 0;
float totalDist = 0;
for (int i = 1; i < n; i++)
{
float dx = x[i] - x[i - 1];
float dy = y[i] - y[i - 1];
float dist = (float)Math.Sqrt(dx * dx + dy * dy);
totalDist += dist;
dists[i] = totalDist;
}
// Create 'times' to interpolate to
float dt = totalDist / (nOutputPoints - 1);
float[] times = new float[nOutputPoints];
times[0] = 0;
for (int i = 1; i < nOutputPoints; i++)
{
times[i] = times[i - 1] + dt;
}
// Normalize the slopes, if specified
NormalizeVector(ref firstDx, ref firstDy);
NormalizeVector(ref lastDx, ref lastDy);
// Spline fit both x and y to times
CubicSpline xSpline = new CubicSpline();
xs = xSpline.FitAndEval(dists, x, times, firstDx / dt, lastDx / dt);
CubicSpline ySpline = new CubicSpline();
ys = ySpline.FitAndEval(dists, y, times, firstDy / dt, lastDy / dt);
}
/// <summary>
/// Static all-in-one method to fit the splines and evaluate at X coordinates.
/// </summary>
/// <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 float[] Compute(float[] x, float[] y, float[] xs, float startSlope = float.NaN, float endSlope = float.NaN, bool debug = false)
{
CubicSpline spline = new CubicSpline();
return spline.FitAndEval(x, y, xs, startSlope, endSlope, debug);
}