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计算扇形与圆的交点

效果图:

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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

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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);    }}
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计算扇形与圆的交点