C#求两圆相交点，转载自百度知道 作者lrh3321

using System;

 

namespace ConsoleZ

{

    struct Point

    {

        public double X;

        public double Y;

        public override string ToString()

        {

            return string.Format("({0},{1})",X,Y);

        }

    }

 

    struct Circle

    {

        public Point Center;

        public double X { get { return Center.X; }set { Center.X = value; } }

        public double Y { get { return Center.Y; } set { Center.X = value; } }

        public double Radius;

    };

    class Program

    {

        const double ZERO = 1e-9;//误差，小于这个就当作0

        static bool double_equals(double a, double b)

        {

            return Math.Abs(a - b) < ZERO;

        }

 

        static double distance_sqr(Point a, Point b)

        {

            return (a.X - b.X) * (a.X - b.X) + (a.Y - b.Y) * (a.Y - b.Y);

        }

 

        static double distance(Point a, Point b)

        {

            return Math.Sqrt(distance_sqr(a, b));

        }

 

       static int insect(Circle[] circles, Point[] points)

        {

            double d, a, b, c, p, q, r;

            double[] cos_value = new double[2], sin_value = new double[2];

            if (double_equals(circles[0].Center.X, circles[1].Center.X)

                && double_equals(circles[0].Center.Y, circles[1].Center.Y)

                && double_equals(circles[0].Radius, circles[1].Radius))

            {

                return -1;

            }

 

            d = distance(circles[0].Center, circles[1].Center);

            if (d > circles[0].Radius + circles[1].Radius

                || d < Math.Abs(circles[0].Radius - circles[1].Radius))

            {

                return 0;

            }

 

            a = 2.0 * circles[0].Radius * (circles[0].Center.X - circles[1].Center.X);

            b = 2.0 * circles[0].Radius * (circles[0].Center.Y - circles[1].Center.Y);

            c = circles[1].Radius * circles[1].Radius - circles[0].Radius * circles[0].Radius

                - distance_sqr(circles[0].Center, circles[1].Center);

            p = a * a + b * b;

            q = -2.0 * a * c;

            if (double_equals(d, circles[0].Radius + circles[1].Radius)

                || double_equals(d, Math.Abs(circles[0].Radius - circles[1].Radius)))

            {

                cos_value[0] = -q / p / 2.0;

                sin_value[0] = Math.Sqrt(1 - cos_value[0] * cos_value[0]);

 

                points[0].X = circles[0].Radius * cos_value[0] + circles[0].Center.X;

                points[0].Y = circles[0].Radius * sin_value[0] + circles[0].Center.Y;

 

                if (!double_equals(distance_sqr(points[0], circles[1].Center),

                                   circles[1].Radius * circles[1].Radius))

                {

                    points[0].Y = circles[0].Center.Y - circles[0].Radius * sin_value[0];

                }

                return 1;

            }

 

            r = c * c - b * b;

            cos_value[0] = (Math.Sqrt(q * q - 4.0 * p * r) - q) / p / 2.0;

            cos_value[1] = (-Math.Sqrt(q * q - 4.0 * p * r) - q) / p / 2.0;

            sin_value[0] = Math.Sqrt(1 - cos_value[0] * cos_value[0]);

            sin_value[1] = Math.Sqrt(1 - cos_value[1] * cos_value[1]);

 

            points[0].X = circles[0].Radius * cos_value[0] + circles[0].Center.X;

            points[1].X = circles[0].Radius * cos_value[1] + circles[0].Center.X;

            points[0].Y = circles[0].Radius * sin_value[0] + circles[0].Center.Y;

            points[1].Y = circles[0].Radius * sin_value[1] + circles[0].Center.Y;

 

            if (!double_equals(distance_sqr(points[0], circles[1].Center),

                               circles[1].Radius * circles[1].Radius))

            {

                points[0].Y = circles[0].Center.Y - circles[0].Radius * sin_value[0];

            }

            if (!double_equals(distance_sqr(points[1], circles[1].Center),

                               circles[1].Radius * circles[1].Radius))

            {

                points[1].Y = circles[0].Center.Y - circles[0].Radius * sin_value[1];

            }

            if (double_equals(points[0].Y, points[1].Y)

                && double_equals(points[0].X, points[1].X))

            {

                if (points[0].Y > 0)

                {

                    points[1].Y = -points[1].Y;

                }

                else

                {

                    points[0].Y = -points[0].Y;

                }

            }

            return 2;

        }

        static void Main(string[] args)

        {

            Circle[] circles = new Circle[2];

            Point[] points = new Point[2];

            Console.Write("请输入两圆x，y，半径(以逗号分开)：");

            char[] sep = new char[] {' ',',','，' };

            string[] tempstr;

            while (true)

            {

                tempstr=Console.ReadLine().Split(sep,StringSplitOptions.RemoveEmptyEntries);

                if (tempstr.Length!=6)

                {

                    Console.Write("输入有误\n按任意键退出...");

                    Console.ReadKey();

                    Environment.Exit(0);

                }

                circles[0].X = double.Parse(tempstr[0]);

                circles[0].Y= double.Parse(tempstr[1]);

                circles[0].Radius=double.Parse(tempstr[2]);

                circles[1].X = double.Parse(tempstr[3]);

                circles[1].Y = double.Parse(tempstr[4]);

                circles[1].Radius = double.Parse(tempstr[5]);                

                switch (insect(circles, points))

                {

                    case -1:

                        Console.Write("两圆相同\n");

                        break;

                    case 0:

                        Console.Write("不相交\n");

                        break;

                    case 1:

                        Console.WriteLine(points[0]);

                        break;

                    case 2:

                        Console.WriteLine(string.Join(" ", points));

                        break;

                }

            }

        }

    }

 

}