WPF 拉格朗日插值法简单实现

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拉格朗日插值法，解释起来差不多就是，【有很多点，我不知道构造这些点的具体函数，但是我可以尝试在每个点的时让其他点的纵坐标都为零，这个点为纵坐标为1，此时得到一个点的函数，后续每个点重复操作，最后相加即可】

先上截图

xaml的具体代码：主要是对canvas的绘图绑定

 <Grid >
        <Grid.RowDefinitions>
            <RowDefinition Height="*"/>
            <RowDefinition Height="auto"/>
        </Grid.RowDefinitions>
        <ItemsControl Background="White" x:Name="T1" ItemsSource="{Binding    EP }" PreviewMouseLeftButtonUp="T1_PreviewMouseLeftButtonUp">
            <ItemsControl.ItemsPanel>
                <ItemsPanelTemplate>
                    <Canvas   />
                </ItemsPanelTemplate>
            </ItemsControl.ItemsPanel>
            <ItemsControl.ItemTemplate>
                <DataTemplate>
                    <ContentControl Content="{Binding UI}"/>
                </DataTemplate>
            </ItemsControl.ItemTemplate>
            <ItemsControl.ItemContainerStyle>
                <Style >
                    <Setter Property="Canvas.Top" Value="{Binding Y}"/>
                    <Setter Property="Canvas.Left" Value="{Binding X}"/>
                </Style>
            </ItemsControl.ItemContainerStyle>
        </ItemsControl>
        <Button Height="40" Grid.Row="1" Click="Button_Click" Content="draw"/>
    </Grid>

后台代码

namespace 拉格朗日插值
{
    public class EPS
    {
        private double _x;

        public double X
        {
            get { return _x; }
            set { _x = value; }
        }

        private double _y;

        public double Y
        {
            get { return _y; }
            set { _y = value; }
        }

        private Ellipse ellipse;

        public Ellipse UI
        {
            get { return ellipse; }
            set { ellipse = value; }
        }
        public EPS(Point point,bool b=true)
        {
            UI = new Ellipse
            {
                Stroke = new SolidColorBrush(Colors.Silver),
                Fill = new SolidColorBrush(b ? Colors.Red : Colors.Blue),
                Height = b ? 15 : 5,
                Width = b ? 15 : 5
            };
            Y = point.Y;
            X = point.X;
        }
        public EPS()
        {

        }
    }
    /// <summary>
    /// MainWindow.xaml 的交互逻辑
    /// </summary>
    public partial class MainWindow : Window
    {
        public ObservableCollection<EPS> EP { get; set; }
        public MainWindow()
        {
            InitializeComponent();
            EP = new ObservableCollection<EPS>();
            DataContext = this;
        }

        private void T1_PreviewMouseLeftButtonUp(object sender, MouseButtonEventArgs e)
        {
            if (CanDraw)
            {
                EP.Clear();
                CanDraw = false;
            }
            EP.Add(new EPS(e.GetPosition(T1)));
            //两点基画法
            //if (EP.Count > 3)
            //{
            //    EP.Clear();
                
            //}
            //if (EP.Count == 2)
            //{
            //    for (double i = EP[0].X; i < EP[1].X; i+=1)
            //    {
            //        EP.Add(new EPS(new Point(i,Towpoint(i)),false));
            //    }
            //}
           
        }
        double Towpoint(double x)
        {
            var b=
                (EP[0].Y * ((x - EP[1].X) /( EP[0].X - EP[1].X)) )
                + 
                (EP[1].Y * ((x - EP[0].X) /( EP[1].X - EP[0].X)));
            return b;
        }
        double MultiPoint(List<EPS> Points,double x)
        {
            var k = (from item in Points
                    let l1 = item.Y
                    * (Points.Where(c => c != item).Select(p => x - p.X).Aggregate((a, b) => a * b))
                    / (Points.Where(c => c != item).Select(p => item.X - p.X).Aggregate((a, b) => a * b))
                    select l1).Sum();
                return k;
        }
        bool CanDraw;
        private void Button_Click(object sender, RoutedEventArgs e)
        {
            var k = new EPS[EP.Count];
            EP.CopyTo(k, 0);
            var items = k.ToList();
            for (double  i = EP[0].X; i < items.Last().X; i+=5)
            {
                  EP.Add(new EPS(new Point(i, MultiPoint(items, i)), false));
            }
            CanDraw = true;
        }
    }
}