用OxyPlot在WPF中演示正演磁异常的变化规律

为了在展示实验成果时动态演示理论球体磁异常随其埋深、磁化倾角的变化规律，我用WPF写了一个小程序来作演示。

MatLab计算磁异常数据

首先是计算理论球体磁异常数据，在Matlab中可以很方便地计算。
为了在展示时能够同时改变磁化倾角（is)、埋深（Deep），计算数据时套了两层循环，外层是is从0到90°，内层是Deep从10到100m，里面计算一条剖面上的Za和Hax磁异常数据。实现代码如下：

function Za=sphere_deeps()
    % 测点分布范围
    dx=5; % X方向测点间距
    nx=81; % X方向测点数
    xmin=-200; % X方向起点
    x=xmin:dx:(xmin+(nx-1)*dx); % X方向范围

    u=4*pi*10^(-7);  %磁导率
    i=pi/2;  %有效磁化倾角is
    a=0; %剖面磁方位角
    T=50000;%地磁场T=50000nT

    % 球体参数
    R1=10; % 球体半径 m
    %D1=30; % 球体埋深 m
    v1=4*pi*R1^3;
    k=0.2; %磁化率
    M1=k*T/u;  %磁化强度 A/m
    m1=M1*v1;   %磁矩

    % 球体 理论磁异常主剖面
    %(x-0),(y-0)
    y=0;
    Za=zeros(46,nx);
    Hax=zeros(46,nx);

    fp=fopen('za_all.out','w');
    for ii=0:90
        i=ii*pi/180;
        for j=0:45
            D1=10+j*2;
            Za0=(u*m1*((2*D1.^2-x.^2-y.^2)*sin(i)-3*D1*x.*cos(i)*cos(a)-3*D1*y.*cos(i)*sin(a)))./(4*pi*(x.^2+y.^2+D1.^2).^(5/2));
            for k=1:nx
                fprintf(fp,'%g ',Za0(k));
            end
            fprintf(fp,'\n');
        end
    end
    fclose(fp);

    fp=fopen('hax_all.out','w');
    for ii=0:90
        i=ii*pi/180;
        for j=0:45
            D1=10+j*2;
            Hax0=(u*m1*((2*x.^2-y.^2-D1.^2)*cos(i)*cos(a)-3*D1*x.*sin(i)+3*x.*y.*cos(i)*sin(a)))./(4*pi*(x.^2+y.^2+D1.^2).^(5/2));
            for k=1:nx
                fprintf(fp,'%g ',Hax0(k));
            end
            fprintf(fp,'\n');
        end
    end
    fclose(fp);

最后是将所有数据都输出至za_all.out以及hax_all.out文件中，其中有91（is从0-90°）*46（Deep从10-100m，间隔2m）行数据，每一行中都有nx（81，测线上的点数）个数据。

C#处理数据文件

首先将之前的za_all.out以及hax_all.out文件复制到WPF项目中，并且对其设置属性为“内容”，并“始终复制”。
将数据读取后分别存储在一个三维数组中，即倾角*深度*测点这样的结构。

    using System;
    using System.Collections.Generic;
    using System.Linq;
    using System.Text;
    using System.Threading.Tasks;
    using System.IO;
    using System.Resources;
    using System.Windows;
    using System.Windows.Resources;

    namespace GeoMag_Viewer
    {
        class Values
        {
            private int iNum = 91;
            private int jNum = 81;
            public double[, ,] Za3D
            {
                get;
                private set;
            }
            public double[, ,] Hax3D
            {
                get;
                private set;
            }

            public Values()
            {
                StreamResourceInfo za3DInfo = Application.GetContentStream(new Uri("Resources/za_all.out", UriKind.Relative));
                var za3DStreamReader = new StreamReader(za3DInfo.Stream);
                string content = za3DStreamReader.ReadToEnd();
                string[] lines = content.Split(new string[] { " \n" }, StringSplitOptions.None);
                Za3D = new Double[91, 46, jNum];
                for (int l = 0; l < 91; l++)
                {
                    for (int i = 0; i < 46; i++)
                    {
                        int index = l * 46 + i;
                        string[] words = lines[index].Split(new string[] { " " }, StringSplitOptions.None);
                        for (int j = 0; j < jNum; j++)
                        {
                            Za3D[l, i, j] = Double.Parse(words[j]);
                        }
                    }
                }

                StreamResourceInfo hax3DInfo = Application.GetContentStream(new Uri("Resources/hax_all.out", UriKind.Relative));
                var hax3DStreamReader = new StreamReader(hax3DInfo.Stream);
                content = hax3DStreamReader.ReadToEnd();
                lines = content.Split(new string[] { " \n" }, StringSplitOptions.None);
                Hax3D = new Double[91, 46, jNum];
                for (int l = 0; l < 91; l++)
                {
                    for (int i = 0; i < 46; i++)
                    {
                        int index = l * 46 + i;
                        string[] words = lines[index].Split(new string[] { " " }, StringSplitOptions.None);
                        for (int j = 0; j < jNum; j++)
                        {
                            Hax3D[l, i, j] = Double.Parse(words[j]);
                        }
                    }
                }
            }
        }
    }

使用OxyPlot组件

为了在WPF中绘制曲线图，通过搜索找到了OxyPlot这个开源库，可以方便地绘制我想要的图形。
创建WPF项目后，打开NUGet程序包管理器，搜索OxyPlot，安装OxyPlot for wpf。

Xaml代码如下：

 <Window x:Class="GeoMag_Viewer.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:oxy="http://oxyplot.org/wpf"
        xmlns:local="clr-namespace:GeoMag_Viewer"
        Title="GeoMag Viewer" Height="350" Width="525">
    <Grid Background="Gray">
        <Grid.RowDefinitions>
            <RowDefinition Height="*"/>
            <RowDefinition Height="Auto"/>
            <RowDefinition Height="Auto"/>
        </Grid.RowDefinitions>
        <Grid>
            <Grid.ColumnDefinitions>
                <ColumnDefinition Width="*"/>
                <ColumnDefinition Width="Auto"/>
                <ColumnDefinition Width="Auto"/>
            </Grid.ColumnDefinitions>
            <oxy:PlotView Grid.Column="0" Name="MyPlotView">
                <oxy:PlotView.Series>
                    <oxy:LineSeries Name="ZaLine"/>
                    <oxy:LineSeries Name="HaxLine"/>
                </oxy:PlotView.Series>
            </oxy:PlotView>
            <Image Grid.Column="0"
                Name="SphereImage"
               Source="Resources/ci.jpg"
                   HorizontalAlignment="Left"
                   Margin="150,0,0,0"
               Width="150"
               Height="150"
               />
            <Slider Grid.Column="1" Name="DeepSlider"
                    Orientation="Vertical"
                    Margin="5,10,5,10"
                    ValueChanged="DeepSlider_ValueChanged"
                    Maximum="45"
                    Minimum="0"
                    TickFrequency="1"
                    TickPlacement="TopLeft"
                    />
            <TextBlock Grid.Column="2"
                       Name="DeepText"
                       FontSize="20"
                       FontWeight="Bold"
                       TextWrapping="Wrap"
                       VerticalAlignment="Center"
                       />
        </Grid>

        <Slider Grid.Row="1"
                Name="angleSlider"
                ValueChanged="angleSlider_ValueChanged"
                Margin="10,5,10,5"
                Maximum="90"
                Minimum="0"
                TickFrequency="1"
                TickPlacement="TopLeft"/>
        <TextBlock Grid.Row="2"
                   Name="tickText"
                   FontSize="24"
                   FontWeight="Bold"
                   Margin="150,0,150,0"
                   HorizontalAlignment="Center"/>
        </Grid>
</Window>

MainWindow.xaml.cs：

OxyPlot绘制曲线是是将Line.ItemSource设置为List，在这儿使用一个列表的二维数组分别保存Za、Hax异常。数组的第一个下标表示角度，第二个下标表示深度。
当用于控制角度、深度的Slider值变化时，分别调用angleSlider_ValueChanged和DeepSlider_ValueChanged来改变所要呈现的曲线，即

ZaLine.ItemsSource = Za3DLists[angleIndex, deepIndex];
HaxLine.ItemsSource = Hax3DLists[angleIndex, deepIndex];

这样，拖动Slider滑块，异常曲线就能跟着动态变化了，达到了演示效果。

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
using System.Windows.Media.Imaging;
using System.Windows.Navigation;
using System.Windows.Shapes;
using OxyPlot;
using OxyPlot.Series;
using OxyPlot.Wpf;
using Microsoft.Win32;

namespace GeoMag_Viewer
{
    /// <summary>
    /// MainWindow.xaml 的交互逻辑
    /// </summary>
    public partial class MainWindow : Window
    {
        public MainWindow()
        {
            InitializeComponent();
            this.WindowState = WindowState.Maximized;
            Values v = new Values();
            MyPlotView.Title = "Za/Hax与磁化倾角的关系Demo";
            var valueAxis = new LinearAxis() { Title = "磁异常/nT" };
            MyPlotView.Axes.Add(valueAxis);
            MyPlotView.LegendFontSize = 20;
            ZaLine.Title = "Za异常";
            HaxLine.Title = "Hax异常";
            tickText.Text = "磁化倾角is=0";
            DeepText.Text = "球体埋深";

            double[, ,] Za3D = v.Za3D;
            double[, ,] Hax3D = v.Hax3D;
            int lNum = Za3D.GetLength(0);//角度数
            int iNum = Za3D.GetLength(1);//深度数
            int jNum = Za3D.GetLength(2);//单测线点数
            Za3DLists = new List<DataPoint>[lNum, iNum];
            Hax3DLists = new List<DataPoint>[lNum, iNum];
            for (int l = 0; l < lNum; l++)
            {

                for (int i = 0; i < iNum; i++)
                {
                    Za3DLists[l, i] = new List<DataPoint>();
                    Hax3DLists[l, i] = new List<DataPoint>();
                    for (int j = 0; j < jNum; j++)
                    {
                        int x = -200 + j * 5;
                        Za3DLists[l, i].Add(new DataPoint(x, Za3D[l, i, j]));
                        Hax3DLists[l, i].Add(new DataPoint(x, Hax3D[l, i, j]));
                    }
                }
            }
            angleIndex = 0;
            deepIndex = 0;
            ZaLine.ItemsSource = Za3DLists[angleIndex, deepIndex];
            HaxLine.ItemsSource = Hax3DLists[angleIndex, deepIndex];

            width = 100;
            height=100;
            RotateTransform rt = new RotateTransform(0,width/2,height/2);
            SphereImage.RenderTransform = rt;

        }
        double width;
        double height;
        private void angleSlider_ValueChanged(object sender, RoutedPropertyChangedEventArgs<double> e)
        {
            if (tickText == null)
            {
                return;
            }
            int angle = (int)e.NewValue;
            int iAngle = angle;
            angleIndex = iAngle;
            tickText.Text = "磁化倾角is=" + angle;
            ZaLine.ItemsSource = Za3DLists[angleIndex, deepIndex];
            HaxLine.ItemsSource = Hax3DLists[angleIndex, deepIndex];
            //旋转球体图像
            //width / 2, height / 2  使绕图像中心旋转
            RotateTransform rt = new RotateTransform(angle, width / 2, height / 2);
            SphereImage.RenderTransform = rt;
        }

        private void DeepSlider_ValueChanged(object sender, RoutedPropertyChangedEventArgs<double> e)
        {
            if (DeepText == null)
            {
                return;
            }
            int iDeep = (int)e.NewValue;
            int deep = 10 + 2 * iDeep;
            deepIndex = iDeep;
            DeepText.Text = "球体埋深\n" + deep+"m";
            ZaLine.ItemsSource = Za3DLists[angleIndex, deepIndex];
            HaxLine.ItemsSource = Hax3DLists[angleIndex, deepIndex];
        }

        //角度*深度
        public List<DataPoint>[,] Za3DLists
        {
            get;
            private set;
        }

        //角度*深度
        public List<DataPoint>[,] Hax3DLists
        {
            get;
            private set;
        }

        public int angleIndex
        {
            get;
            private set;
        }

        public int deepIndex
        {
            get;
            private set;
        }
    }
}

另外，我还在程序中用了一个球体磁场图像，让它随着角度Slider的改变而旋转相应的角度，其实现也很简单，再次不再赘述。

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