c# winform 中實現計算任意多邊形面積，包括 凹多邊形，線段有交叉的多邊形等。具體形式如下：

目標：計算紅色區域的面積
實現的方法：
1、首先能夠在滑鼠點選事件、滑鼠移動事件、和paint事件中實現多邊形的繪製。
2、利用GraphicsPath記錄多邊形頂點座標；System.Drawing.Region 記錄多邊形區域
3、 使用Region 變數中IsVisible方法判斷新的點是否在多邊形區域內。

主要程式碼如下（懶，沒寫註釋，但是都不難理解的）

using System;
using System.Collections.Generic;
using System.ComponentModel;
using
 
 System.Data;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows.Forms;
using System.Drawing.Drawing2D;

namespace functiontest
{
    public partial class Form1 : Form
    {
        public Form1()
        {
            InitializeComponent();
        }

        private
 
 void button1_Click(object sender, EventArgs e)
        {
        }

        private void Form1_Paint(object sender, PaintEventArgs e)
        {
            System.Drawing.Pen pen = new Pen(Color.Red);
            if(isDrawing==1)
            {
                if(drawpaths.Count>=1)
                {
                    foreach
 
 (List<PointF> drawpath in drawpaths)
                    {
                        if (drawpath.Count >= 2)
                        {
                            e.Graphics.DrawLines(pen, drawpath.ToArray());
                            if (continues.Equals(PointF.Empty) == false)
                            {
                                e.Graphics.DrawLine(pen, start, continues);
                            }
                        }
                        else
                        {
                            if(continues.Equals(PointF.Empty)==false)
                            {
                                e.Graphics.DrawLine(pen, start, continues);
                            }
                        }
                    } 
                }
                if (drawpathtemp.Count >= 2)
                {
                    e.Graphics.DrawLines(pen, drawpathtemp.ToArray());
                    if (continues.Equals(PointF.Empty) == false)
                    {
                        e.Graphics.DrawLine(pen, start, continues);
                    }
                }
                else
                {
                    if (continues.Equals(PointF.Empty) == false)
                    {
                        e.Graphics.DrawLine(pen, start, continues);
                    }
                }      
            }
            else if(isDrawing==0)
            {
                foreach (List<PointF> drawpath in drawpaths)
                {
                    if (drawpath.Count >= 2)
                    {
                        e.Graphics.DrawLines(pen, drawpath.ToArray());
                    }
                }
            }

        }
        Region r = new System.Drawing.Region();
        PointF start = PointF.Empty;
        PointF continues = PointF.Empty;
        PointF end = PointF.Empty;
        int isDrawing = 0;
        List<List<PointF>> drawpaths = new List<List<PointF>>();
        List<PointF> drawpathtemp = new List<PointF>();
        private void Form1_MouseClick(object sender, MouseEventArgs e)
        {
            if (e.Button == MouseButtons.Left)
            {
                if (isDrawing==0)
                {
                    start = e.Location;
                    isDrawing = 1;
                    drawpathtemp.Add(start);
                }
                else if(isDrawing==1)
                {
                    start = e.Location;
                    drawpathtemp.Add(start);
                }
                else if(isDrawing==2)
                {

                }
                this.Refresh();
            }
            if (e.Button == MouseButtons.Right)
            {
                if (r.IsVisible(e.Location))
                {
                    MessageBox.Show("在選中區域內");
                }
                else
                {
                    MessageBox.Show("不在選中區域內");
                }
            }            
        }

        private void Form1_MouseMove(object sender, MouseEventArgs e)
        {
            if(isDrawing==1)
            {
                continues = e.Location;
                this.Refresh();
            }

        }

        private void Form1_KeyDown(object sender, KeyEventArgs e)
        {
            switch(e.KeyCode)
            {
                case Keys.Escape:
                    drawpathtemp.Add(drawpathtemp.ElementAt(0));
                    List<PointF> temp = new List<PointF>();
                    if(drawpathtemp.Count>2)
                    {
                        temp = drawpathtemp.GetRange(0, drawpathtemp.Count);
                        drawpaths.Add(temp);
                    }
                    drawpathtemp.Clear();
                    start = PointF.Empty;
                    end = PointF.Empty;
                    continues = PointF.Empty;
                    isDrawing = 0;
                    GraphicsPath gp = new GraphicsPath();
                    gp.Reset();
                    foreach (List<PointF> item in drawpaths)
                    {
                        gp.AddPolygon(item.ToArray());
                        r.MakeEmpty();
                        r.Union(gp);
                    }
                    this.Refresh();
                    break;
                default:
                    break;
            }
        }
    }
}

操作說明：
1、新建專案，拷貝程式碼，編譯成功後執行。
2、滑鼠左鍵單擊視窗開始畫多邊形，按esc鍵結束，同時最後一個點座標與第一個點座標連線。形成封閉的多邊形。
3、可以畫多個多邊形，可以自己嘗試。
4、判斷點是否在區域內：滑鼠右鍵，即會彈出框所點選的座標是否在多邊形內。

程式碼僅供參考，因為是自己寫的demo測試程式，還沒移植到我自己的工程中，所以有點亂。