private static List <System.Windows.Point> Spline(List <System.Windows.Point> point_vector, int splits)
{
List <System.Windows.Point> temp1 = new List <System.Windows.Point>();
General.Vector Y = new General.Vector(point_vector.Count);
General.Vector a = new General.Vector(point_vector.Count);
General.Matrix A = new General.Matrix(point_vector.Count);
double[] x = new double[splits];
double[] y = new double[splits];
for (int i = 0; i < point_vector.Count; i++)
{
double temp = point_vector[i].X;
y[i] = point_vector[i].Y;
for (int j = 0; j < point_vector.Count; j++)
{
A[i, j] = System.Math.Pow(temp, j);
}
}
a = A.InverceMatrix() * Y;
for (int k = 0; k < splits; k++)
{
var max = (search_max(point_vector, XorY.X) - search_min(point_vector, XorY.X));
x[k] = max * k / splits;
}
for (int k = 0; k < splits; k++)
{
for (int i = 0; i < point_vector.Count; i++)
{
y[k] += a[i] * System.Math.Pow(x[k], i);
}
}
for (int k = 0; k < splits; ++k)
{
System.Windows.Point temp = new System.Windows.Point(x[k], y[k]);
temp1.Add(temp);
}
return(temp1);
}
public static List <System.Windows.Point> SplineInterpolation(List <System.Windows.Point> point_vector, int _splits)
{
int n = point_vector.Count - 1;
var splits = _splits / n;
double[] ax = new double[n + 1];
double[] bx = new double[n + 1];
double[] cx = new double[n + 1];
double[] dx = new double[n + 1];
double[] ay = new double[n + 1];
double[] by = new double[n + 1];
double[] cy = new double[n + 1];
double[] dy = new double[n + 1];
double[] u = new double[splits];
General.Matrix A = new General.Matrix(n + 1);
General.Vector vec_bx = new General.Vector(n + 1);
General.Vector vec_cx = new General.Vector(n + 1);
General.Vector vec_by = new General.Vector(n + 1);
General.Vector vec_cy = new General.Vector(n + 1);
List <System.Windows.Point> new_list = new List <System.Windows.Point>();
for (int i = 0; i < n + 1; i++)
{
ax[i] = point_vector[i].X;
ay[i] = point_vector[i].Y;
}
A[0, 0] = 1;
A[n, n] = 1;
for (int i = 1; i < n; i++)
{
A[i, i - 1] = 1;
A[i, i] = 4;
A[i, i + 1] = 1;
}
vec_bx[0] = 0;
vec_bx[n] = 0;
vec_by[0] = 0;
vec_by[n] = 0;
for (int i = 1; i < n; i++)
{
vec_bx[i] = 3 * (ax[i + 1] - 2 * ax[i] + ax[i - 1]);
vec_by[i] = 3 * (ay[i + 1] - 2 * ay[i] + ay[i - 1]);
}
//cx = (A.InverceMatrix() * vec_bx).ToDoubleArray();
//cy = (A.InverceMatrix() * vec_by).ToDoubleArray();
General.Solvers.JacobiMethod jSolver1 = new Solvers.JacobiMethod(A.GetArray(), vec_bx.ToDoubleArray());
General.Solvers.JacobiMethod jSolver2 = new Solvers.JacobiMethod(A.GetArray(), vec_by.ToDoubleArray());
jSolver1.Error = 1E-15;
jSolver2.Error = 1E-15;
jSolver1.CheckInterval = 10;
jSolver2.CheckInterval = 10;
jSolver1.Solve();
jSolver2.Solve();
cx = jSolver1.Solution;
cy = jSolver2.Solution;
for (int i = 0; i < n; i++)
{
bx[i] = (ax[i + 1] - ax[i]) - (cx[i + 1] + 2 * cx[i]) / 3;
dx[i] = (cx[i + 1] - cx[i]) / 3;
by[i] = (ay[i + 1] - ay[i]) - (cy[i + 1] + 2 * cy[i]) / 3;
dy[i] = (cy[i + 1] - cy[i]) / 3;
}
//Generate x point
for (int k = 0; k < splits; k++)
{
u[k] = (double)k / (double)splits;
}
for (int i = 0; i < n; i++)
{
for (int k = 0; k < splits; k++)
{
var x = ax[i] + bx[i] * u[k] + cx[i] * System.Math.Pow(u[k], 2) + dx[i] * System.Math.Pow(u[k], 3);
var y = ay[i] + by[i] * u[k] + cy[i] * System.Math.Pow(u[k], 2) + dy[i] * System.Math.Pow(u[k], 3);
new_list.Add(new System.Windows.Point(x, y));
}
}
new_list.Add(point_vector[n]);
return(new_list);
}
