已知三点求圆⼼c语⾔，转已知两点坐标和半径求圆⼼坐标程序
C++
数学思想：利⽤圆⽅程和直线⽅程
已知两点坐标和半径求圆⼼坐标程序
#include
#include
#include
using namespace std;
ofstream fout;
typedef struct
{
double x;
double y;
}Point;
double Y_Coordinates(double x,double y,double k,double x0);//4个参数
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("");
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 == )
{
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 = - * 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 - * a * c)) / ( * a);
center2.x = (-1.0 * b - sqrt(b * b - * a * c)) / ( * 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输⼊了相同的点!\n";
return false;
}
if(( * dRadius) >= dDistance)
return true;
else
{
cout << "\n两点间距离⼤于直径!\n";
return false;
}
}
void ReadData(Point &p1,Point &p2,double &dRadius)
{
cout << "请输⼊圆周上⼀点的坐标：";
cin >> p1.x >> p1.y;
cout << "请输⼊圆周上另⼀点的坐标：";
cin >> p2.x >> p2.y;
cout << "请输⼊圆的半径：";
cin >> dRadius;
if(! Data_Validation(p1,p2,dRadius))
{
cout << endl << "数据不合理!\n";
exit();
}
}
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