Connected.Components/Components/Chart/Interpolation/EndSlopeSpline.cs

/*
 *  Work in this file is derived from code originally written by Hans-Peter Moser:
 *  http://www.mosismath.com/AngleSplines/EndSlopeSplines.html
 */

namespace Connected.Components;

public class EndSlopeSpline : SplineInterpolator
{
   public EndSlopeSpline(double[] xs, double[] ys,
      int resolution = 10, double firstSlopeDegrees = 0, double lastSlopeDegrees = 0) :
      base(xs, ys, resolution)
   {
      m = new Matrix(n);
      gauss = new MatrixSolver(n, m);

      a = new double[n];
      b = new double[n];
      c = new double[n];
      d = new double[n];
      h = new double[n];

      CalcParameters(firstSlopeDegrees, lastSlopeDegrees);
      Integrate();
      Interpolate();
   }

   public void CalcParameters(double alpha, double beta)
   {
      for (int i = 0; i < n; i++)
         a[i] = GivenYs[i];

      for (int i = 0; i < n - 1; i++)
         h[i] = GivenXs[i + 1] - GivenXs[i];

      m.a[0, 0] = 2.0 * h[0];
      m.a[0, 1] = h[0];
      m.y[0] = 3 * ((a[1] - a[0]) / h[0] - Math.Tan(alpha * Math.PI / 180));

      for (int i = 0; i < n - 2; i++)
      {
         m.a[i + 1, i] = h[i];
         m.a[i + 1, i + 1] = 2.0 * (h[i] + h[i + 1]);
         if (i < n - 2)
            m.a[i + 1, i + 2] = h[i + 1];

         if ((h[i] != 0.0) && (h[i + 1] != 0.0))
            m.y[i + 1] = ((a[i + 2] - a[i + 1]) / h[i + 1] - (a[i + 1] - a[i]) / h[i]) * 3.0;
         else
            m.y[i + 1] = 0.0;
      }

      m.a[n - 1, n - 2] = h[n - 2];
      m.a[n - 1, n - 1] = 2.0 * h[n - 2];
      m.y[n - 1] = 3.0 * (Math.Tan(beta * Math.PI / 180) - (a[n - 1] - a[n - 2]) / h[n - 2]);

      if (gauss.Eliminate() == false)
         throw new InvalidOperationException();

      gauss.Solve();

      for (int i = 0; i < n; i++)
      {
         c[i] = m.x[i];
      }
      for (int i = 0; i < n; i++)
      {
         if (h[i] != 0.0)
         {
            d[i] = 1.0 / 3.0 / h[i] * (c[i + 1] - c[i]);
            b[i] = 1.0 / h[i] * (a[i + 1] - a[i]) - h[i] / 3.0 * (c[i + 1] + 2 * c[i]);
         }
      }
   }
}