已知圆上三点坐标求圆心和半径

R半径 PCenter圆点坐标 

        public void GetCircular(PointF P1,PointF P2,PointF P3,ref float R,ref PointF PCenter)
        {
            float a = 2 * (P2.X - P1.X);
            float b = 2 * (P2.Y - P1.Y);
            float c = P2.X * P2.X + P2.Y * P2.Y - P1.X * P1.X - P1.Y * P1.Y;
            float d = 2 * (P3.X - P2.X);
            float e = 2 * (P3.Y - P2.Y);
            float f = P3.X * P3.X + P3.Y * P3.Y - P2.X * P2.X - P2.Y * P2.Y;
            float x = (b * f - e * c) / (b * d - e * a);
            float y = (d * c - a * f) / (b * d - e * a);
            float r = (float)Math.Sqrt( (double)((x - P1.X) * (x - P1.X) + (y - P1.Y) * (y - P1.Y)));
            R = r;
            PointF pc = new PointF(x,y);
            PCenter = pc;
        }



                
以下是用 C++ 实现已知上三圆心半径的代码: ```cpp #include <iostream> #include <cmath> using namespace std; struct Point { double x, y; }; // 计算两之间的距离 double distance(Point p1, Point p2) { return sqrt(pow(p1.x - p2.x, 2) + pow(p1.y - p2.y, 2)); } // 已知上三圆心半径 void circleFromPoints(Point p1, Point p2, Point p3, Point& center, double& radius) { double a = distance(p1, p2); double b = distance(p2, p3); double c = distance(p3, p1); double s = (a + b + c) / 2; double area = sqrt(s * (s - a) * (s - b) * (s - c)); double A = asin((p2.y - p1.y) / a); double B = asin((p3.y - p1.y) / c); double x = area * (cos(A) + cos(B)) / (sin(A) + sin(B)) / 2 + p1.x; double y = (p2.y - p1.y) / (p2.x - p1.x) * (x - (p1.x + p2.x) / 2) + (p1.y + p2.y) / 2; center.x = x; center.y = y; radius = distance(center, p1); } int main() { Point p1 = { 0, 0 }; Point p2 = { 1, 1 }; Point p3 = { 2, 0 }; Point center; double radius; circleFromPoints(p1, p2, p3, center, radius); cout << "Center: (" << center.x << ", " << center.y << ")" << endl; cout << "Radius: " << radius << endl; return 0; } ``` 在本例中,我们定义了一个 `Point` 结构体来表示坐标,并定义了一个 `distance` 函数来计算两之间的距离。`circleFromPoints` 函数接收三个作为参数,并计算出圆心半径,结果保存在 `center` `radius` 变量中。主函数中调用 `circleFromPoints` 函数,并输出圆心半径的值。
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