用c#编写一个求取包络线面积的程序

以下是一个用 C# 编写的求取包络线面积的程序示例：

using System;
using System.Collections.Generic;
using System.Linq;

namespace EnvelopeArea
{
    class Program
    {
        static void Main(string[] args)
        {
            // 输入多边形点坐标
            List<Point> points = new List<Point>();
            Console.WriteLine("请输入多边形点坐标，输入 end 结束输入：");
            string input = Console.ReadLine();
            while (input != "end")
            {
                string[] values = input.Split(',');
                double x = double.Parse(values[0]);
                double y = double.Parse(values[1]);
                Point point = new Point(x, y);
                points.Add(point);
                input = Console.ReadLine();
            }

            // 计算包络线面积
            double area = CalculateEnvelopeArea(points);
            Console.WriteLine("包络线面积为：" + area);
            Console.ReadKey();
        }

        // 定义点类
        class Point
        {
            public double X { get; set; }
            public double Y { get; set; }

            public Point(double x, double y)
            {
                X = x;
                Y = y;
            }
        }

        // 计算两点之间的距离
        static double Distance(Point p1, Point p2)
        {
            double dx = p2.X - p1.X;
            double dy = p2.Y - p1.Y;
            return Math.Sqrt(dx * dx + dy * dy);
        }

        // 计算三角形面积
        static double TriangleArea(Point p1, Point p2, Point p3)
        {
            double a = Distance(p1, p2);
            double b = Distance(p2, p3);
            double c = Distance(p3, p1);
            double p = (a + b + c) / 2;
            return Math.Sqrt(p * (p - a) * (p - b) * (p - c));
        }

        // 计算包络线面积
        static double CalculateEnvelopeArea(List<Point> points)
        {
            // 找到最左边和最右边的点
            Point leftMost = points.OrderBy(p => p.X).First();
            Point rightMost = points.OrderBy(p => p.X).Last();

            // 分别计算左边和右边的包络线
            List<Point> leftEnvelope = new List<Point>();
            List<Point> rightEnvelope = new List<Point>();
            Point current = leftMost;
            while (current != rightMost)
            {
                leftEnvelope.Add(current);
                current = points.Where(p => p.X < current.X && !leftEnvelope.Contains(p))
                                .OrderByDescending(p => Distance(current, p))
                                .First();
            }
            leftEnvelope.Add(rightMost);
            current = rightMost;
            while (current != leftMost)
            {
                rightEnvelope.Add(current);
                current = points.Where(p => p.X > current.X && !rightEnvelope.Contains(p))
                                .OrderByDescending(p => Distance(current, p))
                                .First();
            }
            rightEnvelope.Add(leftMost);

            // 合并左右包络线
            List<Point> envelope = leftEnvelope.Concat(rightEnvelope.Skip(1)).ToList();

            // 计算包络线面积
            double area = 0;
            for (int i = 1; i < envelope.Count - 1; i++)
            {
                area += TriangleArea(envelope[0], envelope[i], envelope[i + 1]);
            }

            return area;
        }
    }
}

在程序中，首先输入多边形各个点的坐标，输入 "end" 结束输入。然后通过 CalculateEnvelopeArea 方法计算多边形的包络线面积。CalculateEnvelopeArea 方法首先找到最左边和最右边的点，然后分别计算左边和右边的包络线，最后合并左右包络线并计算包络线面积。其中，Distance 方法用于计算两点之间的距离，TriangleArea 方法用于计算三角形面积。