Matlab.NET混合编程技巧之——直接调用Matlab内置函数(附源码)

原文:【原创】Matlab.NET混合编程技巧之——直接调用Matlab内置函数(附源码)

在我的上一篇文章【原创】Matlab.NET混编技巧之——找出Matlab内置函数中，已经大概的介绍了matlab内置函数在混合编程中的优点，并通过程序找出了matlab中的大部分内置函数，当然更多人关心是如何像我所说得那样，不用直接编译，就直接在C#中调用这些内置函数。本文就带你揭开这些谜团。

声明，这篇文章是需要一点点混合编程基础的，基本概念和过程要懂一点，如果能简单成功混编一个简单的计算或者绘图例子，可以更容易理解。

1.传统的Matlab.NET混合编程步骤

传统的Matlab.NET混合编程有2种方式：

1)Matlab编写好M函数，利用deploytool编译m函数生成dll，在C#项目中引用并调用；

2)基于接口的编写方式，也是利用deploytool工具，过程繁琐一点，对编程人员素质要求高一点，但不需要进行繁琐的数据类型转换。我的博客有一篇文章专门介绍了这个混合编程方式，也有例子，大家有兴趣的可以看看：http://www.cnblogs.com/asxinyu/archive/2013/05/16/3082299.html

不管上面用哪种方式，Matlab和C#混编的基本步骤，大概都是下面的过程：

1) 编写M函数，并首先在Matlab中测试是正确可以调用的。注意命名规范，注释规范；

2) 使用命令打开 deploytool工具，设置项目名称，选择类型：.NET Assembly，然后新建一个类，并添加编写好的M函数

3) 编译，生成dll,并在C#项目中添加引用（还需要引用对应版本的MWArray），利用对象浏览器查看生成dll的方法结构，并根据Matlab和C#的类型转换规则，进行数据转换即可， 如果是接口的编程，这个过程相对要简单。

2.深入解析传统混编所生成的代码

2.1 第一步：编写M函数，并测试可以使用

为了好我们今天的目的相匹配，特意封装一个简单的内置函数，plot，来画一个简单的图形，如下所示M函数

 function PlotTest(n)
 %编写一个简单的函数，对plot进行简单封装一下
 plot(:n,:n);
 %测试正确，才可以进行下一步工作

注意，混编必须是m函数function的形式才能被调用。上述函数简单测试一下，没有问题（复杂的函数一定要多测试，否则后续调试非常困难）。继续下一步。

2.2 第二步：在Matlab中使用deploytool建立混编项目

在Matlab工作区输入命令：deploytool,然后得到下面界面，输入混编项目的名称，选择存储位置，关键的是类型那里一定要选择".NET Assembly"。如下图所示：

选择“OK”之后，下一步matlab界面右侧会出现项目解决方案，需要添加类名称和M文件。这个类名称，就是编译完成之后C#项目中的类对象名称，然后添加我们刚才上一步编写的“PlotTest.m”,然后编译即可，如下图所示：

到此为止，一个常规 简单的Matlab.NET混编已经完成了60%了。编译完成之后，打开“Package”选项卡，即可看到生成的dll文件，然后点击右键，打开文件夹即可，如下图所示：

2.3 查看混编生成的代码

　　这个过程很关键，其实包含很多信息，只不过95%以上的人都没有注意到其实混编生成的dll是有源文件的，通过查看源文件就应该知道混编的原理，只不过这是matlab自动生成 而已。那看看生成的源码吧。

　　打开Matlab混编项目的目录，可以看到有2个文件夹，"distrib”，“src”2个文件夹。"distrib"文件夹就是上面图中生成的dll，注意有2个dll,1个是“项目名称.dll”,一个是“项目名称Native.dll”，这2个dll的差别可以通过"distrib"文件夹源码来观察。“distrib”就是源代码的文件夹。如下图所示，src文件夹的文件示意图：

我们2.2中新建的类名是TestDemo,所以生成的的源码名称也是TestDemo,看看这2个cs文件中的代码，同时类的方法也可以在VS中通过对象浏览器来查看dll有哪些方法以及方法的参数类型。直接贴这2个cs文件的代码，顺便解释和对比下：

TestDemo.cs文件源码：

 /*
 * MATLAB Compiler: 4.17 (R2012a)
 * Date: Mon Sep 09 16:19:01 2013
 * Arguments: "-B" "macro_default" "-W" "dotnet:PlotTest,TestDemo,0.0,private" "-T"
 * "link:lib" "-d" "D:\Work\DevelopMent_SVN\Matlab\MatlabBlog\PlotTest\src" "-w"
 * "enable:specified_file_mismatch" "-w" "enable:repeated_file" "-w"
 * "enable:switch_ignored" "-w" "enable:missing_lib_sentinel" "-w" "enable:demo_license"
 * "-v" "class{TestDemo:D:\Work\DevelopMent_SVN\Matlab\MatlabBlog\PlotTest.m}"
 */
 using System;
 using System.Reflection;
 using System.IO;
 using MathWorks.MATLAB.NET.Arrays;
 using MathWorks.MATLAB.NET.Utility;

 #if SHARED
 [assembly: System.Reflection.AssemblyKeyFile(@"")]
 #endif

 namespace PlotTest
 {

   /// <summary>
   /// The TestDemo class provides a CLS compliant, MWArray interface to the M-functions
   /// contained in the files:
   /// <newpara></newpara>
   /// D:\Work\DevelopMent_SVN\Matlab\MatlabBlog\PlotTest.m
   /// <newpara></newpara>
   /// deployprint.m
   /// <newpara></newpara>
   /// printdlg.m
   /// </summary>
   /// <remarks>
   /// @Version 0.0
   /// </remarks>
   public class TestDemo : IDisposable
   {
     #region Constructors

     /// <summary internal= "true">
     /// The static constructor instantiates and initializes the MATLAB Compiler Runtime
     /// instance.
     /// </summary>
     static TestDemo()
     {
       if (MWMCR.MCRAppInitialized)
       {
         Assembly assembly= Assembly.GetExecutingAssembly();

         string ctfFilePath= assembly.Location;

         int lastDelimiter= ctfFilePath.LastIndexOf(@"\");

         ctfFilePath= ctfFilePath.Remove(lastDelimiter, (ctfFilePath.Length - lastDelimiter));

         string ctfFileName = "PlotTest.ctf";

         Stream embeddedCtfStream = null;

         String[] resourceStrings = assembly.GetManifestResourceNames();

         foreach (String name in resourceStrings)
         {
           if (name.Contains(ctfFileName))
           {
             embeddedCtfStream = assembly.GetManifestResourceStream(name);
             break;
           }
         }
         mcr= new MWMCR("",
                        ctfFilePath, embeddedCtfStream, true);
       }
       else
       {
         throw new ApplicationException("MWArray assembly could not be initialized");
       }
     }

     /// <summary>
     /// Constructs a new instance of the TestDemo class.
     /// </summary>
     public TestDemo()
     {
     }

     #endregion Constructors

     #region Finalize

     /// <summary internal= "true">
     /// Class destructor called by the CLR garbage collector.
     /// </summary>
     ~TestDemo()
     {
       Dispose(false);
     }

     /// <summary>
     /// Frees the native resources associated with this object
     /// </summary>
     public void Dispose()
     {
       Dispose(true);

       GC.SuppressFinalize(this);
     }

     /// <summary internal= "true">
     /// Internal dispose function
     /// </summary>
     protected virtual void Dispose(bool disposing)
     {
       if (!disposed)
       {
         disposed= true;

         if (disposing)
         {
           // Free managed resources;
         }

         // Free native resources
       }
     }

     #endregion Finalize

     #region Methods

     /// <summary>
     /// Provides a void output, 0-input MWArrayinterface to the PlotTest M-function.
     /// </summary>
     /// <remarks>
     /// M-Documentation:
     /// 编写一个简单的函数，对plot进行简单封装一下
     /// </remarks>
     ///
     public void PlotTest()
     {
       mcr.EvaluateFunction(, "PlotTest", new MWArray[]{});
     }

     /// <summary>
     /// Provides a void output, 1-input MWArrayinterface to the PlotTest M-function.
     /// </summary>
     /// <remarks>
     /// M-Documentation:
     /// 编写一个简单的函数，对plot进行简单封装一下
     /// </remarks>
     /// <param name="n">Input argument #1</param>
     ///
     public void PlotTest(MWArray n)
     {
       mcr.EvaluateFunction(, "PlotTest", n);
     }

     /// <summary>
     /// Provides the standard 0-input MWArray interface to the PlotTest M-function.
     /// </summary>
     /// <remarks>
     /// M-Documentation:
     /// 编写一个简单的函数，对plot进行简单封装一下
     /// </remarks>
     /// <param name="numArgsOut">The number of output arguments to return.</param>
     /// <returns>An Array of length "numArgsOut" containing the output
     /// arguments.</returns>
     ///
     public MWArray[] PlotTest(int numArgsOut)
     {
       return mcr.EvaluateFunction(numArgsOut, "PlotTest", new MWArray[]{});
     }

     /// <summary>
     /// Provides the standard 1-input MWArray interface to the PlotTest M-function.
     /// </summary>
     /// <remarks>
     /// M-Documentation:
     /// 编写一个简单的函数，对plot进行简单封装一下
     /// </remarks>
     /// <param name="numArgsOut">The number of output arguments to return.</param>
     /// <param name="n">Input argument #1</param>
     /// <returns>An Array of length "numArgsOut" containing the output
     /// arguments.</returns>
     ///
     public MWArray[] PlotTest(int numArgsOut, MWArray n)
     {
       return mcr.EvaluateFunction(numArgsOut, "PlotTest", n);
     }

     /// <summary>
     /// This method will cause a MATLAB figure window to behave as a modal dialog box.
     /// The method will not return until all the figure windows associated with this
     /// component have been closed.
     /// </summary>
     /// <remarks>
     /// An application should only call this method when required to keep the
     /// MATLAB figure window from disappearing.  Other techniques, such as calling
     /// Console.ReadLine() from the application should be considered where
     /// possible.</remarks>
     ///
     public void WaitForFiguresToDie()
     {
       mcr.WaitForFiguresToDie();
     }

     #endregion Methods

     #region Class Members

     private static MWMCR mcr= null;

     private bool disposed= false;

     #endregion Class Members
   }
 }

TestDemoNative.cs文件源码:

 /*
 * MATLAB Compiler: 4.17 (R2012a)
 * Date: Mon Sep 09 16:19:01 2013
 * Arguments: "-B" "macro_default" "-W" "dotnet:PlotTest,TestDemo,0.0,private" "-T"
 * "link:lib" "-d" "D:\Work\DevelopMent_SVN\Matlab\MatlabBlog\PlotTest\src" "-w"
 * "enable:specified_file_mismatch" "-w" "enable:repeated_file" "-w"
 * "enable:switch_ignored" "-w" "enable:missing_lib_sentinel" "-w" "enable:demo_license"
 * "-v" "class{TestDemo:D:\Work\DevelopMent_SVN\Matlab\MatlabBlog\PlotTest.m}"
 */
 using System;
 using System.Reflection;
 using System.IO;
 using MathWorks.MATLAB.NET.Arrays;
 using MathWorks.MATLAB.NET.Utility;

 #if SHARED
 [assembly: System.Reflection.AssemblyKeyFile(@"")]
 #endif

 namespace PlotTestNative
 {

   /// <summary>
   /// The TestDemo class provides a CLS compliant, Object (native) interface to the
   /// M-functions contained in the files:
   /// <newpara></newpara>
   /// D:\Work\DevelopMent_SVN\Matlab\MatlabBlog\PlotTest.m
   /// <newpara></newpara>
   /// deployprint.m
   /// <newpara></newpara>
   /// printdlg.m
   /// </summary>
   /// <remarks>
   /// @Version 0.0
   /// </remarks>
   public class TestDemo : IDisposable
   {
     #region Constructors

     /// <summary internal= "true">
     /// The static constructor instantiates and initializes the MATLAB Compiler Runtime
     /// instance.
     /// </summary>
     static TestDemo()
     {
       if (MWMCR.MCRAppInitialized)
       {
         Assembly assembly= Assembly.GetExecutingAssembly();

         string ctfFilePath= assembly.Location;

         int lastDelimiter= ctfFilePath.LastIndexOf(@"\");

         ctfFilePath= ctfFilePath.Remove(lastDelimiter, (ctfFilePath.Length - lastDelimiter));

         string ctfFileName = "PlotTest.ctf";

         Stream embeddedCtfStream = null;

         String[] resourceStrings = assembly.GetManifestResourceNames();

         foreach (String name in resourceStrings)
         {
           if (name.Contains(ctfFileName))
           {
             embeddedCtfStream = assembly.GetManifestResourceStream(name);
             break;
           }
         }
         mcr= new MWMCR("",
                        ctfFilePath, embeddedCtfStream, true);
       }
       else
       {
         throw new ApplicationException("MWArray assembly could not be initialized");
       }
     }

     /// <summary>
     /// Constructs a new instance of the TestDemo class.
     /// </summary>
     public TestDemo()
     {
     }

     #endregion Constructors

     #region Finalize

     /// <summary internal= "true">
     /// Class destructor called by the CLR garbage collector.
     /// </summary>
     ~TestDemo()
     {
       Dispose(false);
     }

     /// <summary>
     /// Frees the native resources associated with this object
     /// </summary>
     public void Dispose()
     {
       Dispose(true);

       GC.SuppressFinalize(this);
     }

     /// <summary internal= "true">
     /// Internal dispose function
     /// </summary>
     protected virtual void Dispose(bool disposing)
     {
       if (!disposed)
       {
         disposed= true;

         if (disposing)
         {
           // Free managed resources;
         }

         // Free native resources
       }
     }

     #endregion Finalize

     #region Methods

     /// <summary>
     /// Provides a void output, 0-input Objectinterface to the PlotTest M-function.
     /// </summary>
     /// <remarks>
     /// M-Documentation:
     /// 编写一个简单的函数，对plot进行简单封装一下
     /// </remarks>
     ///
     public void PlotTest()
     {
       mcr.EvaluateFunction(, "PlotTest", new Object[]{});
     }

     /// <summary>
     /// Provides a void output, 1-input Objectinterface to the PlotTest M-function.
     /// </summary>
     /// <remarks>
     /// M-Documentation:
     /// 编写一个简单的函数，对plot进行简单封装一下
     /// </remarks>
     /// <param name="n">Input argument #1</param>
     ///
     public void PlotTest(Object n)
     {
       mcr.EvaluateFunction(, "PlotTest", n);
     }

     /// <summary>
     /// Provides the standard 0-input Object interface to the PlotTest M-function.
     /// </summary>
     /// <remarks>
     /// M-Documentation:
     /// 编写一个简单的函数，对plot进行简单封装一下
     /// </remarks>
     /// <param name="numArgsOut">The number of output arguments to return.</param>
     /// <returns>An Array of length "numArgsOut" containing the output
     /// arguments.</returns>
     ///
     public Object[] PlotTest(int numArgsOut)
     {
       return mcr.EvaluateFunction(numArgsOut, "PlotTest", new Object[]{});
     }

     /// <summary>
     /// Provides the standard 1-input Object interface to the PlotTest M-function.
     /// </summary>
     /// <remarks>
     /// M-Documentation:
     /// 编写一个简单的函数，对plot进行简单封装一下
     /// </remarks>
     /// <param name="numArgsOut">The number of output arguments to return.</param>
     /// <param name="n">Input argument #1</param>
     /// <returns>An Array of length "numArgsOut" containing the output
     /// arguments.</returns>
     ///
     public Object[] PlotTest(int numArgsOut, Object n)
     {
       return mcr.EvaluateFunction(numArgsOut, "PlotTest", n);
     }

     /// <summary>
     /// Provides an interface for the PlotTest function in which the input and output
     /// arguments are specified as an array of Objects.
     /// </summary>
     /// <remarks>
     /// This method will allocate and return by reference the output argument
     /// array.<newpara></newpara>
     /// M-Documentation:
     /// 编写一个简单的函数，对plot进行简单封装一下
     /// </remarks>
     /// <param name="numArgsOut">The number of output arguments to return</param>
     /// <param name= "argsOut">Array of Object output arguments</param>
     /// <param name= "argsIn">Array of Object input arguments</param>
     /// <param name= "varArgsIn">Array of Object representing variable input
     /// arguments</param>
     ///
     [MATLABSignature("PlotTest", , , )]
     protected void PlotTest(int numArgsOut, ref Object[] argsOut, Object[] argsIn, params Object[] varArgsIn)
     {
         mcr.EvaluateFunctionForTypeSafeCall("PlotTest", numArgsOut, ref argsOut, argsIn, varArgsIn);
     }

     /// <summary>
     /// This method will cause a MATLAB figure window to behave as a modal dialog box.
     /// The method will not return until all the figure windows associated with this
     /// component have been closed.
     /// </summary>
     /// <remarks>
     /// An application should only call this method when required to keep the
     /// MATLAB figure window from disappearing.  Other techniques, such as calling
     /// Console.ReadLine() from the application should be considered where
     /// possible.</remarks>
     ///
     public void WaitForFiguresToDie()
     {
       mcr.WaitForFiguresToDie();
     }

     #endregion Methods

     #region Class Members

     private static MWMCR mcr= null;

     private bool disposed= false;

     #endregion Class Members
   }
 }

对比大家就可以发现，只不过一个更加傻瓜化，参数都是Object了，其实这样反而不好，增加了类型转换的代价，如果知道，为何不给一个正确的给他呢。关于这2个dll的速度，曾经听说过是有差别的，博客园有人给过测试，我没实际测试过，还是习惯用传统的TestDemo.cs，因为参数类型都是Object，不直观，出了问题也有点头疼。

2.4 上述Matlab自动生成代码的要点

　　后面某些类或者方法的XML注释就不说了，自动生成的东西，可以对照M文件的注释来看。

1.首先看第一段的注释信息：

 /*
 * MATLAB Compiler: 4.17 (R2012a)
 * Date: Mon Sep 09 16:19:01 2013
 * Arguments: "-B" "macro_default" "-W" "dotnet:PlotTest,TestDemo,0.0,private" "-T"
 * "link:lib" "-d" "D:\Work\DevelopMent_SVN\Matlab\MatlabBlog\PlotTest\src" "-w"
 * "enable:specified_file_mismatch" "-w" "enable:repeated_file" "-w"
 * "enable:switch_ignored" "-w" "enable:missing_lib_sentinel" "-w" "enable:demo_license"
 * "-v" "class{TestDemo:D:\Work\DevelopMent_SVN\Matlab\MatlabBlog\PlotTest.m}"
 */
 using System;
 using System.Reflection;
 using System.IO;
 using MathWorks.MATLAB.NET.Arrays;
 using MathWorks.MATLAB.NET.Utility;

上面这段信息主要是说明当前Matlab编译器的版本，因为编译的版本和部署的MCR版本必须对应起来，否则是不能运行的。然后有编译日期，以及编译的参数，类名以及M函数的地址等信息，其实知道这些参数，理论上是可以自己在程序里面调用Matlab的编译器进行编译工作的，只不过比较复杂，能力有限，研究不下去。下面的引用大家应该明白，这个是MWArray.dll里面的命名空间，所以混编的项目都要引用对应版本的MWArray.dll

2.关键的静态构造函数

 static TestDemo()
     {
       if (MWMCR.MCRAppInitialized)
       {
         Assembly assembly= Assembly.GetExecutingAssembly();
         string ctfFilePath= assembly.Location;
         int lastDelimiter= ctfFilePath.LastIndexOf(@"\");
         ctfFilePath= ctfFilePath.Remove(lastDelimiter, (ctfFilePath.Length - lastDelimiter));
         string ctfFileName = "PlotTest.ctf";
         Stream embeddedCtfStream = null;
         String[] resourceStrings = assembly.GetManifestResourceNames();
         foreach (String name in resourceStrings)
         {
           if (name.Contains(ctfFileName))
           {
             embeddedCtfStream = assembly.GetManifestResourceStream(name);
             break;
           }
         }
         mcr= new MWMCR("",ctfFilePath, embeddedCtfStream, true);
       }
       else
       {
         throw new ApplicationException("MWArray assembly could not be initialized");
       }
     }

　　如果有一些C#的开发和编程经验看上面的代码问题应该不大，否则还真有点难说清楚，简单的说几个要点：

　　1）这个构造函数的作用主要是检测MCR对象是否初始化，如果没有，则寻找程序集，并拼接资源的位置，正确进行初始化

　　2) 上面的ctf其实是包含在dll程序集里面的，以资源的形式，这个文件是核心，它才真正的包括了Matlab编译之后的，MCR可以运行的中间程序。

　　3) 必须要合法正确的ctf文件和dll文件才能 正确的初始化mcr对象，合法的意思，是Matlab内部有校验机制，包括对相关版本，在以前的版本生成文件中，很明显，现在2012a里面都隐藏起来了，不过要求都一样。

　　4) 上面方法其实已经间接的告诉了我们怎么初始化mcr对象，有了mcr对象，一切都好办了，因为它才是MCR的核心。

3.PlotTest封装的方法代码

     public void PlotTest()
     {
       mcr.EvaluateFunction(, "PlotTest", new MWArray[]{});
     }
     public void PlotTest(MWArray n)
     {
       mcr.EvaluateFunction(, "PlotTest", n);
     }
     public MWArray[] PlotTest(int numArgsOut)
     {
       return mcr.EvaluateFunction(numArgsOut, "PlotTest", new MWArray[]{});
     }
     public MWArray[] PlotTest(int numArgsOut, MWArray n)
     {
       return mcr.EvaluateFunction(numArgsOut, "PlotTest", n);
     }

　　看了字段代码，再对应mcr的初始化，其实都很明朗了。通过mcr的EvaluateFunction来调用M函数。上面的代码有几个重载方法，可以实用很多不同的情况，有时候，这些方法的个数会更多，其实没多大必要，也可以自己编译一下，把没用的删掉，保留少数几个有用的即可。同时也可以看到，这里直接通过字符串来传递函数名称的，因此必须保证这个函数能被mcr搜索到。比如我们这里的"PlotTest"这个函数其实就包含了ctf文件中（注意ctf文件是可以和dll分开的，在混编项目里可以设置）。　　

3.上述代码到内置函数的调用

　　上述已经讲解了整个mcr调用的过程，其实就是通过mcr的EvaluateFunction来调用M函数，但要保证对于的函数名称在mcr搜索的范围内。那么我们是不是可以假设：内置函数都在MCR内部，应该是可以搜索到的，那么把上面的函数名称换一下，是不是也是可行的。这个假设也是我最早接触时候的想法，有了假设，当然要去验证。现在看来这个当然是肯定的，那么不妨重新演示一遍。过程不详细讲了，代码也有注释，混编要引用的MWArray.dll和命名空间也不提了，看代码：

 using System;
 using System.Collections.Generic;
 using System.Linq;
 using System.Text;
 using System.Reflection;
 using System.IO;

 using MathWorks.MATLAB.NET.Utility;
 using MathWorks.MATLAB.NET.Arrays;

 namespace BuildInFunctionDemo
 {
     class Program
     {
         static MWMCR mcr;
         static void Main(string[] args)
         {
             #region 首先使用PlotTest.dll来初始化mcr,因为这个dll是混编“合法”产生的，只有这样才能顺利启动mcr
             if (MWMCR.MCRAppInitialized)
             {
                 string path = Path.Combine(System.Environment.CurrentDirectory, "PlotTest.dll");
                 Assembly assembly = Assembly.LoadFile(path);
                 string ctfFilePath = assembly.Location;
                 int lastDelimiter = ctfFilePath.LastIndexOf(@"\");
                 ctfFilePath = ctfFilePath.Remove(lastDelimiter, (ctfFilePath.Length - lastDelimiter));
                 string ctfFileName = "PlotTest.ctf";
                 Stream embeddedCtfStream = null;
                 String[] resourceStrings = assembly.GetManifestResourceNames();

                 foreach (String name in resourceStrings)
                 {
                     if (name.Contains(ctfFileName))
                     {
                         embeddedCtfStream = assembly.GetManifestResourceStream(name);
                         break;
                     }
                 }
                 mcr = new MWMCR("",ctfFilePath, embeddedCtfStream, true);
             }
             else
             {
                 throw new ApplicationException("MWArray assembly could not be initialized");
             }
             #endregion

             #region 直接调用混编dll中的封装函数进行测试
             mcr.EvaluateFunction(, "PlotTest", );

             //注意这里要断点调试才能看到效果哦，因为mcr会把图绘制在一个Figure上面，
             //后面的会覆盖前面的，这里暂停一下，可以看前面的效果
             //下面就是直接调用matlab的plot函数的效果
             MWNumericArray x = new double[]{,,,,};
             MWNumericArray y = new double[]{,,2.8,5.3,4.7};
             mcr.EvaluateFunction(, "plot",x,y );
             #endregion

             Console.ReadKey();
         }
     }
 }

唯一要注意的就是50-52的说明，要加断点看2次绘制的效果。分别截图如下：
=

4.总结

　　抛砖引玉，这里只是一个思路，附代码下载吧。

http://www.kuaipan.cn/file/id_4279479643944070.htm