/// <summary>
/// 判断点P是否在圆内
/// </summary>
/// <param name="C">圆C</param>
/// <param name="P">点P</param>
/// <returns>如果在圆内返回True，否则返回False。</returns>
public static Boolean InCircle(CircleI C, PointI P)
{
//判断点是否在圆内：
//计算圆心到该点的距离，如果小于等于半径则该点在圆内。
Double D = PointAlgorithm.Distance(P, C.Center);
return((D < C.Radius) || DoubleAlgorithm.Equals(D, C.Radius));
}
/// <summary>
/// 判断折线PL是否在圆内
/// </summary>
/// <param name="C">圆C</param>
/// <param name="R">矩形R</param>
/// <returns>如果在圆内返回True，否则返回False。</returns>
public static Boolean InCircle(CircleI C, RectangleI R)
{
if (PointAlgorithm.Distance(new PointI(R.Left, R.Top), C.Center) > C.Radius)
{
return(false);
}
if (PointAlgorithm.Distance(new PointI(R.Right, R.Bottom), C.Center) > C.Radius)
{
return(false);
}
return(true);
}
/// <summary>
/// 判断线段L是否在圆内
/// </summary>
/// <param name="C">圆C</param>
/// <param name="L">线段L</param>
/// <returns>如果在圆内返回True，否则返回False。</returns>
public static Boolean InCircle(CircleD C, LineD L)
{
//判断点是否在圆内：
//计算圆心到该点的距离，如果小于等于半径则该点在圆内。
if (PointAlgorithm.Distance(L.Starting, C.Center) > C.Radius)
{
return(false);
}
if (PointAlgorithm.Distance(L.End, C.Center) > C.Radius)
{
return(false);
}
return(true);
}
/// <summary>
/// 判断折线PL是否在圆内
/// </summary>
/// <param name="C">圆C</param>
/// <param name="PL">折线PL</param>
/// <returns>如果在圆内返回True，否则返回False。</returns>
public static Boolean InCircle(CircleI C, PolylineI PL)
{
if (PL.Points == null)
{
return(false);
}
for (Int32 i = 0; i < PL.Points.Count; ++i)
{
if (PointAlgorithm.Distance(PL.Points[i], C.Center) > C.Radius)
{
return(false);
}
}
return(true);
}
/// <summary>
/// 判断多边形PG是否在圆内
/// </summary>
/// <param name="C">圆C</param>
/// <param name="PG">多边形PG</param>
/// <returns>如果在圆内返回True，否则返回False。</returns>
public static Boolean InCircle(CircleI C, PolygonI PG)
{
if (PG.Vertex == null)
{
return(false);
}
for (Int32 i = 0; i < PG.Vertex.Count; ++i)
{
if (PointAlgorithm.Distance(PG.Vertex[i], C.Center) > C.Radius)
{
return(false);
}
}
return(true);
}
/// <summary>
/// 根据点P,Q,R三点确定一个圆,注意三点不能共线
/// </summary>
/// <param name="P">点P</param>
/// <param name="Q">点Q</param>
/// <param name="R">点R</param>
/// <returns>返回圆，如果圆不存在则返回null.</returns>
public static CircleD?CreateCircle(PointI P, PointI Q, PointI R)
{
if (DoubleAlgorithm.Equals(LineAlgorithm.Position(P, Q, R), 0))
{
return(null); //三点共线无法确定圆
}
//formula
//(x-a)^2+(y-b)^2=r^2
//f1:(x1-a)^2 + (y1-b)^2 = r^2
//f2:(x2-a)^2 + (y2-b)^2 = r^2
//f3:(x3-a)^2 + (y3-b)^2 = r^2
//f1=f2: x1^2-2ax1+y1^2-2by1= x2^2-2ax2+y2^2-2by2;
//a=(((X(1)^2-X(2)^2+Y(1)^2-Y(2)^2)*(Y(2)-Y(3)))-((X(2)^2-X(3)^2+Y(2)^2-Y(3)^2)*(Y(1)-Y(2))))/(2*(X(1)-X(2))*(Y(2)-Y(3))-2*(X(2)-X(3))*(Y(1)-Y(2)))
//b=(((X(1)^2-X(2)^2+Y(1)^2-Y(2)^2)*(X(2)-X(3)))-((X(2)^2-X(3)^2+Y(2)^2-Y(3)^2)*(X(1)-X(2))))/(2*(Y(1)-Y(2))*(X(2)-X(3))-2*(Y(2)-Y(3))*(X(1)-X(2)))
Double a = (Double)(((P.X * P.X - Q.X * Q.X + P.Y * P.Y - Q.Y * Q.Y) * (Q.Y - R.Y)) - ((Q.X * Q.X - R.X * R.X + Q.Y * Q.Y - R.Y * R.Y) * (P.Y - Q.Y))) / (Double)(2 * (P.X - Q.X) * (Q.Y - R.Y) - 2 * (Q.X - R.X) * (P.Y - Q.Y));
Double b = (Double)(((P.X * P.X - Q.X * Q.X + P.Y * P.Y - Q.Y * Q.Y) * (Q.X - R.X)) - ((Q.X * Q.X - R.X * R.X + Q.Y * Q.Y - R.Y * R.Y) * (P.X - Q.X))) / (Double)(2 * (P.Y - Q.Y) * (Q.X - R.X) - 2 * (Q.Y - R.Y) * (P.X - Q.X));
Double r = PointAlgorithm.Distance(P, new PointD(a, b));
return(new CircleD(a, b, r));
}
/// <summary>
/// 判断线段L与圆C的交点个数
/// </summary>
/// <param name="L">线段L</param>
/// <param name="C">圆形C</param>
/// <returns>相交返回交点数目,否则返回0</returns>
public static Int32?HasIntersection(LineI L, CircleI C)
{
Int32 count = 0;
//如果和圆C有交点首先是L到圆心的距离小于或等于C的半径
if (DoubleAlgorithm.Equals(PointAlgorithm.ClosestDistance(C.Center, L), C.Radius))
{
return(1);
}
else if (PointAlgorithm.ClosestDistance(C.Center, L) > C.Radius)
{
return(0);
}
if (PointAlgorithm.Distance(C.Center, L.Starting) >= C.Radius)
{
++count;
}
if (PointAlgorithm.Distance(C.Center, L.End) >= C.Radius)
{
++count;
}
return(count);
}
/// <summary>
/// 计算线L到圆C的距离
/// </summary>
/// <param name="C">圆C</param>
/// <param name="L">线L</param>
/// <returns>返回线到圆周的距离。</returns>
/// <remarks>
/// 返回值小于0 表示线在圆内或与圆周相交。
/// 返回值等于0 表示线在圆周上与圆周相切。
/// 返回值大于0 表示线在圆外与圆周没有交点。
/// </remarks>
public static Double Distance(CircleI C, LineI L)
{
return(PointAlgorithm.Distance(C.Center, L) - C.Radius);
}
/// <summary>
/// 计算点到圆的距离
/// </summary>
/// <param name="C">圆C</param>
/// <param name="P">点P</param>
/// <returns>返回点到圆周的距离。</returns>
/// <remarks>
/// 返回值小于0 表示点在圆内。
/// 返回值等于0 表示点在圆周上。
/// 返回值大于0 表示点在圆外。
/// </remarks>
public static Double Distance(CircleI C, PointI P)
{
return(PointAlgorithm.Distance(C.Center, P) - C.Radius);
}
/// <summary>
/// 判断圆C2是否在圆C1内
/// </summary>
/// <param name="C1">圆C1</param>
/// <param name="C2">圆C2</param>
/// <returns>如果在圆内返回True，否则返回False。</returns>
public static Boolean InCircle(CircleI C1, CircleI C2)
{
//formula
//C2的中心点到C1中心点的距离 加上C2的半径小于C1的半径
return(((PointAlgorithm.Distance(C1.Center, C2.Center) + C2.Radius) > C1.Radius) ? false : true);
}
