public CubicSpline(Point[] inputPoints)
{
buildRanges(inputPoints);
splines = new Polynomial[ranges.Length];
double[] h = new double[points.Length];
for (int i = 1; i < points.Length; i++)
{
h[i] = points[i].getX() - points[i - 1].getX();
}
TriDiagonalMatrix matrix = new TriDiagonalMatrix(points.Length - 2);
double[] F = new double[points.Length - 2];
// Построение системы динейных уравнений относительно coeff_c[i], коэффициент при x^2
for (int i = 2; i < points.Length; i++)
{
matrix[i - 2].a = h[i - 1];
matrix[i - 2].c = 2 * (h[i] + h[i - 1]);
matrix[i - 2].b = h[i];
F[i - 2] = 3 * ((points[i].getY() - points[i - 1].getY()) / h[i] -
(points[i - 1].getY() - points[i - 2].getY()) / h[i - 1]);
}
matrix[0].a = 0;
matrix[matrix.Length - 1].b = 0;
// Находим коэффициенты 'с'
double[] c = new double[points.Length + 1];
c[0] = 0;
c[1] = 0;
double[] t = matrix.solve(F);
Array.Copy(t, 0, c, 2, t.Length);
c[c.Length - 1] = 0;
// Вычисляем оставшмеся коэффициетны и создаем сплайны
for (int i = 1; i < c.Length - 1; i++)
{
double a = points[i - 1].getY(); // свободный коэффициент
double d = (c[i + 1] - c[i]) / (3 * h[i]); // коэффициент при x^3
double b = (points[i].getY() - points[i - 1].getY()) / h[i] - (2 * c[i] + c[i + 1]) * h[i] / 3; // коэффициент при x^1
splines[i - 1] = new Polynomial(new double[] { a, b, c[i], d });
}
}
/// <summary>
/// Compute spline coefficients for the specified x,y points.
/// This does the "natural spline" style for ends.
/// This can extrapolate off the ends of the splines.
/// You must provide points in X sort order.
/// </summary>
/// <param name="x">Input. X coordinates to fit.</param>
/// <param name="y">Input. Y coordinates to fit.</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>
public void Fit(float[] x, float[] y, float startSlope = float.NaN, float endSlope = float.NaN, bool debug = false)
{
if (Single.IsInfinity(startSlope) || Single.IsInfinity(endSlope))
{
throw new Exception("startSlope and endSlope cannot be infinity.");
}
// Save x and y for eval
this.xOrig = x;
this.yOrig = y;
int n = x.Length;
float[] r = new float[n]; // the right hand side numbers: wikipedia page overloads b
var m = new TriDiagonalMatrix(n);
float dx1, dx2, dy1, dy2;
// First row is different (equation 16 from the article)
if (float.IsNaN(startSlope))
{
dx1 = x[1] - x[0];
m.C[0] = 1.0f / dx1;
m.B[0] = 2.0f * m.C[0];
r[0] = 3 * (y[1] - y[0]) / (dx1 * dx1);
}
else
{
m.B[0] = 1;
r[0] = startSlope;
}
// Body rows (equation 15 from the article)
for (int i = 1; i < n - 1; i++)
{
dx1 = x[i] - x[i - 1];
dx2 = x[i + 1] - x[i];
m.A[i] = 1.0f / dx1;
m.C[i] = 1.0f / dx2;
m.B[i] = 2.0f * (m.A[i] + m.C[i]);
dy1 = y[i] - y[i - 1];
dy2 = y[i + 1] - y[i];
r[i] = 3 * (dy1 / (dx1 * dx1) + dy2 / (dx2 * dx2));
}
// Last row also different (equation 17 from the article)
if (float.IsNaN(endSlope))
{
dx1 = x[n - 1] - x[n - 2];
dy1 = y[n - 1] - y[n - 2];
m.A[n - 1] = 1.0f / dx1;
m.B[n - 1] = 2.0f * m.A[n - 1];
r[n - 1] = 3 * (dy1 / (dx1 * dx1));
}
else
{
m.B[n - 1] = 1;
r[n - 1] = endSlope;
}
//if (debug) Console.WriteLine("Tri-diagonal matrix:\n{0}", m.ToDisplayString(":0.0000", " "));
//if (debug) Console.WriteLine("r: {0}", ArrayUtil.ToString<float>(r));
// k is the solution to the matrix
float[] k = m.Solve(r);
//if (debug) Console.WriteLine("k = {0}", ArrayUtil.ToString<float>(k));
// a and b are each spline's coefficients
this.a = new float[n - 1];
this.b = new float[n - 1];
for (int i = 1; i < n; i++)
{
dx1 = x[i] - x[i - 1];
dy1 = y[i] - y[i - 1];
a[i - 1] = k[i - 1] * dx1 - dy1; // equation 10 from the article
b[i - 1] = -k[i] * dx1 + dy1; // equation 11 from the article
}
//if (debug) Console.WriteLine("a: {0}", ArrayUtil.ToString<float>(a));
//if (debug) Console.WriteLine("b: {0}", ArrayUtil.ToString<float>(b));
}
