计算扇形与圆的交点

效果图：

算法：

基本思路是检测圆和圆的交点，检测扇形边和圆的交点，其中圆和圆的交点还要判断点是否在扇形的角度内部。判断方法参考：

http://stackoverflow.com/questions/13652518/efficiently-find-points-inside-a-circle-sector

交点判断方法可以看之前的博客

internal class MathEx
{
    /// <summary>
    ///     浮点类型的精度要求
    /// </summary>
    public const float EPS = 0.00001f;

    /// <summary>
    ///     线段与圆的交点
    /// </summary>
    /// <param name="ptStart">线段起点</param>
    /// <param name="ptEnd">线段终点</param>
    /// <param name="ptCenter">圆心坐标</param>
    /// <param name="Radius">圆半径</param>
    /// <param name="ptInter1">交点1(若不存在返回65536)</param>
    /// <param name="ptInter2">交点2(若不存在返回65536)</param>
    public static bool LineInterCircle(PointF ptStart, PointF ptEnd, PointF ptCenter, double Radius,
                                        ref PointF ptInter1, ref PointF ptInter2)
    {
        double Radius2 = Radius*Radius;
        ptInter1.X = ptInter2.X = 65536.0f;
        ptInter1.Y = ptInter2.Y = 65536.0f;
        var fDis =
            (float)
            Math.Sqrt((ptEnd.X - ptStart.X)*(ptEnd.X - ptStart.X) + (ptEnd.Y - ptStart.Y)*(ptEnd.Y - ptStart.Y));
        var d = new PointF();
        d.X = (ptEnd.X - ptStart.X)/fDis;
        d.Y = (ptEnd.Y - ptStart.Y)/fDis;
        var E = new PointF();
        E.X = ptCenter.X - ptStart.X;
        E.Y = ptCenter.Y - ptStart.Y;
        float a = E.X*d.X + E.Y*d.Y;
        float a2 = a*a;
        float e2 = E.X*E.X + E.Y*E.Y;
        if ((Radius2 - e2 + a2) < 0)
        {
            return false;
        }
        else
        {
            var f = (float) Math.Sqrt(Radius2 - e2 + a2);
            float t = a - f;
            if (((t - 0.0) > -EPS) && (t - fDis) < EPS)
            {
                ptInter1.X = ptStart.X + t*d.X;
                ptInter1.Y = ptStart.Y + t*d.Y;
            }
            t = a + f;
            if (((t - 0.0) > -EPS) && (t - fDis) < EPS)
            {
                ptInter2.X = ptStart.X + t*d.X;
                ptInter2.Y = ptStart.Y + t*d.Y;
            }
            return true;
        }
    }

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

    /// <summary>
    ///     判断两个平行于x轴的圆的交点
    /// </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 CircleInterCircleOnXAxis(PointF centerA, double rA, PointF centerB, double rB,
                                                ref PointF ptInter1, ref PointF ptInter2)
    {
        ptInter1.X = ptInter2.X = 65536.0f;
        ptInter1.Y = ptInter2.Y = 65536.0f;
        PointF centerLeft;
        double R, r, d;
        if (centerA.X < centerB.X)
        {
            centerLeft = centerA;
            R = rA;
            r = rB;
            d = centerB.X - centerA.X;
        }
        else
        {
            centerLeft = centerB;
            R = rB;
            r = rA;
            d = centerA.X - centerB.X;
        }
        double R2 = R*R;
        double x = (d*d - r*r + R2)/(2*d);
        double y = Math.Sqrt(R2 - x*x);
        ptInter1.X = centerLeft.X + (int) x;
        ptInter1.Y = centerLeft.Y + (int) y;
        ptInter2.X = centerLeft.X + (int) x;
        ptInter2.Y = centerLeft.Y - (int) y;
    }

    /// <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;
    }

    /// <summary>
    ///     计算两个向量的夹角
    /// </summary>
    /// <param name="Va"></param>
    /// <param name="Vb"></param>
    /// <returns></returns>
    public static float GetAngleOfVectors(PointF Va, PointF Vb)
    {
        var da = (float) Math.Sqrt(Va.X*Va.X + Va.Y*Va.Y);
        var db = (float) Math.Sqrt(Vb.X*Vb.X + Vb.Y*Vb.Y);
        var theta = (float) Math.Acos((Va.X*Vb.X + Va.Y*Vb.Y)/(da*db));
        return theta;
    }

    /// <summary>
    ///     计算向量与x轴正方形的夹角
    /// </summary>
    /// <param name="V"></param>
    /// <returns>（0~360）</returns>
    public static double GetAngleWithXAxis(PointF V)
    {
        double theta = GetFov(new PointF(0, 0), V)*Math.PI/180;
        return theta;
    }

    public static bool Equal(double a, double b)
    {
        return Math.Abs(a - b) < EPS;
    }

    public static List<PointF> SectorInterCircle(PointF centerS, float rS, float fov, float angle, PointF centerC,
                                                    float rC)
    {
        double angleC2 = angle/2;
        PointF Na = GetPointFovTo(new PointF(0,0), fov - angleC2, 1);
        PointF Nb = GetPointFovTo(new PointF(0, 0), fov + angleC2, 1);
        PointF a = new PointF(Na.X*rS+centerS.X,Na.Y*rS+centerS.Y);
        PointF b = new PointF(Nb.X * rS + centerS.X, Nb.Y * rS + centerS.Y);
        var list = new List<PointF>();
        PointF p1 = PointF.Empty, p2 = PointF.Empty;
        LineInterCircle(centerS, a, centerC, rC, ref p1, ref p2);
        if (!Equal(p1.X, 65536.0f))
        {
            list.Add(new PointF(p1.X, p1.Y));
        }
        if (!Equal(p2.X, 65536.0f))
        {
            list.Add(new PointF(p2.X, p2.Y));
        }

        p1 = PointF.Empty;
        p2 = PointF.Empty;
        LineInterCircle(centerS, b, centerC, rC, ref p1, ref p2);
        if (!Equal(p1.X, 65536.0f))
        {
            list.Add(new PointF(p1.X, p1.Y));
        }
        if (!Equal(p2.X, 65536.0f))
        {
            list.Add(new PointF(p2.X, p2.Y));
        }
        p1 = PointF.Empty;
        p2 = PointF.Empty;
        CircleInterCircle(centerS, rS, centerC, rC, ref p1, ref p2);
        if (!Equal(p1.X, 65536.0f) 
            && !areClockwise(Na, new PointF(p1.X - centerS.X, p1.Y - centerS.Y))
            && areClockwise(Nb, new PointF(p1.X - centerS.X, p1.Y - centerS.Y)))
        {
            list.Add(new PointF(p1.X, p1.Y));
        }
        if (!Equal(p2.X, 65536.0f) 
            && !areClockwise(Na, new PointF(p2.X - centerS.X, p2.Y - centerS.Y))
            && areClockwise(Nb, new PointF(p2.X - centerS.X, p2.Y - centerS.Y)))
        {
            list.Add(new PointF(p2.X, p2.Y));
        }
        return list;
    }

    private static bool areClockwise(PointF v1, PointF v2)
    {
        return -v1.X*v2.Y + v1.Y*v2.X > 0;
    }

    public static float Distance(PointF a, PointF b)
    {
        return (float)Math.Sqrt((a.X - b.X) * (a.X - b.X) + (a.Y - b.Y) * (a.Y - b.Y));
    }

    /// <summary>
    ///     已知点a，和方向arf（0-360），求点a，arf方向上距离为L的点坐标
    /// </summary>
    /// <param name="s"></param>
    /// <param name="arf"></param>
    /// <param name="l"></param>
    /// <returns></returns>
    public static PointF GetPointFovTo(PointF s, double arf, double l)
    {
        while (arf < 0)
            arf += 360;
        while (arf >= 360)
            arf -= 360;
        if (arf >= 0 && arf < 90)
        {
            double angle = arf*Math.PI/180;
            return new PointF((float) (s.X + l*Math.Cos(angle)), (float) (s.Y + l*Math.Sin(angle)));
        }
        else if (arf >= 90 && arf < 180)
        {
            double r = 180 - arf;
            double angle = r*Math.PI/180;
            return new PointF((float) (s.X - l*Math.Cos(angle)), (float) (s.Y + l*Math.Sin(angle)));
        }
        else if (arf >= 180 && arf < 270)
        {
            double r = 270 - arf;
            double angle = r*Math.PI/180;
            return new PointF((float) (s.X - l*Math.Sin(angle)), (float) (s.Y - l*Math.Cos(angle)));
        }
        else if (arf >= 270 && arf < 360)
        {
            double r = 360 - arf;
            double angle = r*Math.PI/180;
            return new PointF((float) (s.X + l*Math.Cos(angle)), (float) (s.Y - l*Math.Sin(angle)));
        }
        return PointF.Empty;
    }

    /// <summary>
    ///     已知两个点a，b求射线ab的方向
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <returns></returns>
    public static float GetFov(PointF a, PointF b)
    {
        if (a.X == b.X)
        {
            if (a.Y >= b.Y)
                return 270;
            else
                return 90;
        }
        else if (a.Y == b.Y)
        {
            if (a.X < b.X)
                return 0;
            else
                return 180;
        }
        else
        {
            double Xab = b.X - a.X;
            double Yab = b.Y - a.Y;
            double Rab = Math.Atan(Math.Abs(Xab)/Math.Abs(Yab));
            Rab = Rab*(180/Math.PI);
            if (Xab > 0 && Yab >= 0)
                return (float) (450 - Rab)%360;
            if (Xab < 0 && Yab >= 0)
                return (float) (450 + Rab)%360;
            if (Xab < 0 && Yab <= 0)
                return (float) (630 - Rab)%360;
            if (Xab > 0 && Yab <= 0)
                return (float) (Rab + 270)%360;
        }
        return 0;
//            var p = new PointF(b.X - a.X, b.Y - a.Y);
//            return (float)(GetAngleOfVectors(p, new PointF(1, 0))*180/Math.PI);
    }
}