1 /// <summary>
 2 /// 判断两个平行于x轴的圆的交点
 3 /// </summary>
 4 /// <param name="centerA">第一个圆的中点</param>
 5 /// <param name="rA">半径</param>
 6 /// <param name="centerB">第二个圆的中点</param>
 7 /// <param name="rB">半径</param>
 8 /// <param name="ptInter1">交点1(若不存在返回65536)</param>
 9 /// <param name="ptInter2">交点1(若不存在返回65536)</param>
10 public static void CircleInterCircleOnXAxis(PointF centerA, double rA, PointF centerB, double rB, ref PointF ptInter1, ref PointF ptInter2)
11 {
12     ptInter1.X = ptInter2.X = 65536.0f;
13     ptInter1.Y = ptInter2.Y = 65536.0f;
14     PointF centerLeft;
15     double R, r, d;
16     if (centerA.X < centerB.X)
17     {
18         centerLeft = centerA;
19         R = rA;
20         r = rB;
21         d = centerB.X - centerA.X;
22     }
23     else
24     {
25         centerLeft = centerB;
26         R = rB;
27         r = rA;
28         d = centerA.X - centerB.X;
29     }
30     double R2 = R * R;
31     double x = (d*d - r*r + R2)/(2*d);
32     double y = Math.Sqrt(R2 - x * x);
33     ptInter1.X = centerLeft.X + (int)x;
34     ptInter1.Y = centerLeft.Y + (int)y;
35     ptInter2.X = centerLeft.X + (int)x;
36     ptInter2.Y = centerLeft.Y - (int)y;
37 }

 1 /// <summary>
 2 /// 以中心点逆时针旋转Angle角度
 3 /// </summary>
 4 /// <param name="center">中心点</param>
 5 /// <param name="p1">待旋转的点</param>
 6 /// <param name="angle">旋转角度（弧度）</param>
 7 public static PointF PointRotate(PointF center, PointF p1, double angle)
 8 {
 9     double x1 = (p1.X - center.X) * Math.Cos(angle) + (p1.Y - center.Y) * Math.Sin(angle) + center.X;
10     double y1 = -(p1.X - center.X) * Math.Sin(angle) + (p1.Y - center.Y) * Math.Cos(angle) + center.Y;
11     return new PointF((float)x1, (float)y1);
12 }

 1 /// <summary>
 2 /// 计算两个向量的夹角
 3 /// </summary>
 4 /// <param name="Va"></param>
 5 /// <param name="Vb"></param>
 6 /// <returns></returns>
 7 public static double GetAngleOfVectors(PointF Va, PointF Vb)
 8 {
 9     double da = Math.Sqrt(Va.X*Va.X + Va.Y*Va.Y);
10     double db = Math.Sqrt(Vb.X*Vb.X + Vb.Y*Vb.Y);
11     double theta = Math.Acos((Va.X*Vb.X + Va.Y*Vb.Y)/(da*db));
12     return theta;
13 }

/// <summary>
///     求任意两个圆的交点
/// </summary>
/// <param name="centerA">第一个圆的中点</param>
/// <param name="rA">半径</param>
/// <param name="centerB">第二个圆的中点</param>
/// <param name="rB">半径</param>
/// <param name="ptInter1">交点1(若不存在返回65536)</param>
/// <param name="ptInter2">交点1(若不存在返回65536)</param>
public static void CircleInterCircle(PointF centerA, double rA, PointF centerB, double rB, ref PointF ptInter1,ref PointF ptInter2)
{var v = new PointF(centerB.X - centerA.X, centerB.Y - centerA.Y);double angle = GetAngleWithXAxis(v);PointF bb = PointRotate(centerA, centerB, angle);PointF p1 = Point.Empty, p2 = Point.Empty;CircleInterCircleOnXAxis(centerA, rA, bb, rB, ref p1, ref p2);if (!Equal(p1.X, 65536.0f)){p1 = PointRotate(centerA, p1, -angle);}if (!Equal(p2.X, 65536.0f)){p2 = PointRotate(centerA, p2, -angle);}ptInter1 = p1;ptInter2 = p2;
}