Example: SplineData Chart

using System;
using System.Collections;
using System.ComponentModel;
using System.Drawing;
using System.Data;
using System.Windows.Forms;
using Imsl.Math;
using Imsl.Chart2D;
using Random = Imsl.Stat.Random;

public class SplineDataEx1 : FrameChart 
{

    private const int nData = 21;
    private const int nSpline = 100;

    public SplineDataEx1() 
    {

        Chart chart = this.Chart;
        AxisXY axis = new AxisXY(chart);

        chart.ChartTitle.SetTitle(new Text("Smoothed Spline"));
        
        Legend legend = chart.Legend;
        legend.SetTitle(new Text("Legend"));
        legend.SetViewport(0.7, 0.9, 0.1, 0.3);
        legend.IsVisible = true;
        
        // Original data
        double[] xData = grid(nData);
        double[] yData = new double[nData];
        for (int k = 0; k < nData; k++)
        {
            yData[k] = f(xData[k]);
        }
        
        Data data = new Data(axis, xData, yData);
        data.DataType = Imsl.Chart2D.Data.DATA_TYPE_MARKER;
        data.MarkerType = Data.MARKER_TYPE_HOLLOW_CIRCLE;
        data.MarkerColor = System.Drawing.Color.Red;
        data.SetTitle("Original Data");
        
        // Noisy data
        Random random = new Random(123457);
        double[] yNoisy = new double[nData];
        for (int k = 0; k < nData; k++)
        {
            yNoisy[k] = yData[k] + (2.0 * random.NextDouble() - 1.0);
        }
        data = new Data(axis, xData, yNoisy);
        data.DataType = Imsl.Chart2D.Data.DATA_TYPE_MARKER;
        data.MarkerType = Data.MARKER_TYPE_FILLED_SQUARE;
        data.MarkerSize = 0.75;
        data.MarkerColor = System.Drawing.Color.Blue;
        data.SetTitle("Noisy Data");
        
        chartSpline(axis, new CsSmooth(xData, yData), System.Drawing.Color.Red,
         "CsSmooth");
        chartSpline(axis, new CsSmoothC2(xData, yData, nData),
         System.Drawing.Color.Orange, "CsSmoothC2");
    }

    static private void chartSpline(AxisXY axis, Imsl.Math.Spline spline,
      System.Drawing.Color color, System.String title)
    {
        Data data = new SplineData(axis, spline);
        data.DataType = Imsl.Chart2D.Data.DATA_TYPE_LINE;
        data.LineColor = color;
        data.SetTitle(title);
    }

    static private double[] grid(int nData)
    {
        double[] xData = new double[nData];
        for (int k = 0; k < nData; k++)
        {
            xData[k] = 3.0 * k / (double) (nData - 1);
        }
        return xData;
    }
    
    static private double f(double x)
    {
        return 1.0 / (0.1 + System.Math.Pow(3.0 * (x - 1.0), 4));
    }

    public static void Main(string[] argv) 
    {
        System.Windows.Forms.Application.Run(new SplineDataEx1());
    }
}

Output

Link to C# source.