
Task

Implement a solution to the Problem of Apollonius   (description on Wikipedia)   which is the problem of finding the circle that is tangent to three specified circles   (colored black in the diagram below to the right).

There is an   algebraic solution   which is pretty straightforward.



The solutions to the example in the code are shown in the diagram   (below and to the right).

The red circle is "internally tangent" to all three black circles,   and the green circle is "externally tangent" to all three black circles.




 
using System;
 
namespace ApolloniusProblemCalc
{
    class Program
    {
        static float rs = 0;
        static float xs = 0;
        static float ys = 0;
 
        public static void Main(string[] args)
        {
            float gx1;
            float gy1;
            float gr1;
            float gx2;
            float gy2;
            float gr2;
            float gx3;
            float gy3;
            float gr3;
 
            //----------Enter values for the given circles here----------
            gx1 = 0;
            gy1 = 0;
            gr1 = 1;
            gx2 = 4;
            gy2 = 0;
            gr2 = 1;
            gx3 = 2;
            gy3 = 4;
            gr3 = 2;
            //-----------------------------------------------------------
 
            for (int i = 1; i <= 8; i++)
            {
                SolveTheApollonius(i, gx1, gy1, gr1, gx2, gy2, gr2, gx3, gy3, gr3);
 
 
                if (i == 1)
                {
                    Console.WriteLine("X of point of the " + i + "st solution: " + xs.ToString());
                    Console.WriteLine("Y of point of the " + i + "st solution: " + ys.ToString());
                    Console.WriteLine(i + "st Solution circle's radius: " + rs.ToString());
                }
                else if (i == 2)
                {
                    Console.WriteLine("X of point of the " + i + "ed solution: " + xs.ToString());
                    Console.WriteLine("Y of point of the " + i + "ed solution: " + ys.ToString());
                    Console.WriteLine(i + "ed Solution circle's radius: " + rs.ToString());
                }
                else if(i == 3)
                {
                    Console.WriteLine("X of point of the " + i + "rd solution: " + xs.ToString());
                    Console.WriteLine("Y of point of the " + i + "rd solution: " + ys.ToString());
                    Console.WriteLine(i + "rd Solution circle's radius: " + rs.ToString());
                }
                else
                {
                    Console.WriteLine("X of point of the " + i + "th solution: " + xs.ToString());
                    Console.WriteLine("Y of point of the " + i + "th solution: " + ys.ToString());
                    Console.WriteLine(i + "th Solution circle's radius: " + rs.ToString());
                }
 
                Console.WriteLine();
            }
 
 
            Console.ReadKey(true);
        }
 
        private static void SolveTheApollonius(int calcCounter, float x1, float y1, float r1, float x2, float y2, float r2, float x3, float y3, float r3)
        {
            float s1 = 1;
            float s2 = 1;
            float s3 = 1;
 
            if (calcCounter == 2)
            {
                s1 = -1;
                s2 = -1;
                s3 = -1;
            }
            else if (calcCounter == 3)
            {
                s1 = 1;
                s2 = -1;
                s3 = -1;
            }
            else if (calcCounter == 4)
            {
                s1 = -1;
                s2 = 1;
                s3 = -1;
            }
            else if (calcCounter == 5)
            {
                s1 = -1;
                s2 = -1;
                s3 = 1;
            }
            else if (calcCounter == 6)
            {
                s1 = 1;
                s2 = 1;
                s3 = -1;
            }
            else if (calcCounter == 7)
            {
                s1 = -1;
                s2 = 1;
                s3 = 1;
            }
            else if (calcCounter == 8)
            {
                s1 = 1;
                s2 = -1;
                s3 = 1;
            }
 
            //This calculation to solve for the solution circles is cited from the Java version 
            float v11 = 2 * x2 - 2 * x1;
            float v12 = 2 * y2 - 2 * y1;
            float v13 = x1 * x1 - x2 * x2 + y1 * y1 - y2 * y2 - r1 * r1 + r2 * r2;
            float v14 = 2 * s2 * r2 - 2 * s1 * r1;
 
            float v21 = 2 * x3 - 2 * x2;
            float v22 = 2 * y3 - 2 * y2;
            float v23 = x2 * x2 - x3 * x3 + y2 * y2 - y3 * y3 - r2 * r2 + r3 * r3;
            float v24 = 2 * s3 * r3 - 2 * s2 * r2;
 
            float w12 = v12 / v11;
            float w13 = v13 / v11;
            float w14 = v14 / v11;
 
            float w22 = v22 / v21 - w12;
            float w23 = v23 / v21 - w13;
            float w24 = v24 / v21 - w14;
 
            float P = -w23 / w22;
            float Q = w24 / w22;
            float M = -w12 * P - w13;
            float N = w14 - w12 * Q;
 
            float a = N * N + Q * Q - 1;
            float b = 2 * M * N - 2 * N * x1 + 2 * P * Q - 2 * Q * y1 + 2 * s1 * r1;
            float c = x1 * x1 + M * M - 2 * M * x1 + P * P + y1 * y1 - 2 * P * y1 - r1 * r1;
 
            float D = b * b - 4 * a * c;
 
            rs = (-b - float.Parse(Math.Sqrt(D).ToString())) / (2 * float.Parse(a.ToString()));
            xs = M + N * rs;
            ys = P + Q * rs;
        }
    }
}
 