轉 已知兩點坐標和半徑求圓心坐標程序C++

 

數學思想：利用圓方程和直線方程

已知兩點坐標和半徑求圓心坐標程序  
#include <iostream>
#include <fstream>
#include <cmath>

using namespace std;

ofstream fout;

typedef struct 
{
    double x;
    double y;
}Point;

double Y_Coordinates(double x,double y,double k,double x0);//4個參數
void Circle_Center(Point p1,Point p2,double dRadius);
bool Data_Validation(Point p1,Point p2,double dRadius);
void ReadData(Point &p1,Point &p2,double &dRadius);

void main()
{
    Point p1,p2;
    double dRadius = 0.0;

    ReadData(p1,p2,dRadius);

    fout.open("Result.txt");
    Circle_Center(p1,p2,dRadius);
    fout.close();
}

void Circle_Center(Point p1,Point p2,double dRadius)
{
    double k = 0.0,k_verticle = 0.0;
    double mid_x = 0.0,mid_y = 0.0;
    double a = 1.0;
    double b = 1.0;
    double c = 1.0;
    Point center1,center2;
    k = (p2.y - p1.y) / (p2.x - p1.x);
    if(k == 0)
    {
        center1.x = (p1.x + p2.x) / 2.0;
        center2.x = (p1.x + p2.x) / 2.0;
        center1.y = p1.y + sqrt(dRadius * dRadius -(p1.x - p2.x) * (p1.x - p2.x) / 4.0);
        center2.y = p2.y - sqrt(dRadius * dRadius -(p1.x - p2.x) * (p1.x - p2.x) / 4.0);
    }
    else
    {
        k_verticle = -1.0 / k;
        mid_x = (p1.x + p2.x) / 2.0;
        mid_y = (p1.y + p2.y) / 2.0;
        a = 1.0 + k_verticle * k_verticle;
        b = -2 * mid_x - k_verticle * k_verticle * (p1.x + p2.x);
        c = mid_x * mid_x + k_verticle * k_verticle * (p1.x + p2.x) * (p1.x + p2.x) / 4.0 - 
            (dRadius * dRadius - ((mid_x - p1.x) * (mid_x - p1.x) + (mid_y - p1.y) * (mid_y - p1.y)));
        
        center1.x = (-1.0 * b + sqrt(b * b -4 * a * c)) / (2 * a);
        center2.x = (-1.0 * b - sqrt(b * b -4 * a * c)) / (2 * a);
        center1.y = Y_Coordinates(mid_x,mid_y,k_verticle,center1.x);
        center2.y = Y_Coordinates(mid_x,mid_y,k_verticle,center2.x);
    }

    fout << center1.x << "    " << center1.y << endl;
    fout << center2.x << "    " << center2.y << endl;
}

double Y_Coordinates(double x,double y,double k,double x0)
{
    return k * x0 - k * x + y;
}

bool Data_Validation(Point p1,Point p2,double dRadius)
{
    double dDistance = 0.0;
    dDistance = sqrt((p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y));
    if(dDistance == 0.0)
    {
        cout << "\n輸入了相同的點!\n";
        return false;
    }
    if((2 * dRadius) >= dDistance)
        return true;
    else
    {
        cout << "\n兩點間距離大於直徑!\n";
        return false;
    }
}

void ReadData(Point &p1,Point &p2,double &dRadius)
{
    cout << "請輸入圓周上一點的坐標：";
    cin >> p1.x >> p1.y;
    cout << "請輸入圓周上另一點的坐標：";
    cin >> p2.x >> p2.y;
    cout << "請輸入圓的半徑：";
    cin >> dRadius;

    if(! Data_Validation(p1,p2,dRadius))
    {
        cout << endl << "數據不合理!\n";
        exit(0);
    }
}