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);
}
}
时间： 2024-08-29 23:36:26