/// <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>
/// 获取线段L与圆C的交点集合
/// </summary>
/// <param name="L">线段L</param>
/// <param name="C">圆C</param>
/// <returns>返回交点集合.</returns>
public static PointD[] Intersection(LineI L, CircleI C)
{
List <PointD> result = new List <PointD>();
Int32? has = HasIntersection(L, C);
if (has == 0 || has == null)
{
return(result.ToArray());
}
//Points P (x,y) on a line defined by two points P1 (x1,y1,z1) and P2 (x2,y2,z2) is described by
//P = P1 + u (P2 - P1)
//or in each coordinate
//x = x1 + u (x2 - x1)
//y = y1 + u (y2 - y1)
//z = z1 + u (z2 - z1)
//A sphere centered at P3 (x3,y3,z3) with radius r is described by
//(x - x3)2 + (y - y3)2 + (z - z3)2 = r2
//Substituting the equation of the line into the sphere gives a quadratic equation of the form
//a u2 + b u + c = 0
//where:
//a = (x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2
//b = 2[ (x2 - x1) (x1 - x3) + (y2 - y1) (y1 - y3) + (z2 - z1) (z1 - z3) ]
//c = x32 + y32 + z32 + x12 + y12 + z12 - 2[x3 x1 + y3 y1 + z3 z1] - r2
//The solutions to this quadratic are described by
PointD PD = PointAlgorithm.Substract(L.Starting, L.End);
Double a = PD.X * PD.X + PD.Y * PD.Y;
Double b = 2 * ((L.End.X - L.Starting.X) * (L.Starting.X - C.Center.X) + (L.End.Y - L.Starting.Y) * (L.Starting.Y - C.Center.Y));
Double c = C.Center.X * C.Center.X + C.Center.Y * C.Center.Y + L.Starting.X * L.Starting.X + L.Starting.Y * L.Starting.Y - 2 * (C.Center.X * L.Starting.X + C.Center.Y * L.Starting.Y) - C.Radius * C.Radius;
Double u1 = ((-1) * b + System.Math.Sqrt(b * b - 4 * a * c)) / (2 * a);
Double u2 = ((-1) * b - System.Math.Sqrt(b * b - 4 * a * c)) / (2 * a);
//交点
PointD P1 = new PointD(L.Starting.X + u1 * (L.End.X - L.Starting.X), L.Starting.Y + u1 * (L.End.Y - L.Starting.Y));
PointD P2 = new PointD(L.Starting.X + u2 * (L.End.X - L.Starting.X), L.Starting.Y + u2 * (L.End.Y - L.Starting.Y));
if (LineAlgorithm.OnLine(L, P1) == true)
{
result.Add(P1);
}
if (LineAlgorithm.OnLine(L, P2) == true && P1.Equals(P2) == false)
{
result.Add(P2);
}
return(result.ToArray());
}
/// <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(CircleI C, LineI 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>
/// 判断圆C是否在多边形PG内
/// </summary>
/// <param name="PG">PG多边形</param>
/// <param name="C">圆C</param>
/// <returns>如果圆C在区域内返回True,否则返回False.</returns>
public static Boolean InPolygon(PolygonI PG, CircleI C)
{
//如果圆心不在多边形内则返回不在多边形内
if (false == InPolygon(PG, C.Center))
{
return(false);
}
Double D = PointAlgorithm.ClosestDistance(C.Center, PG);
if (D > C.Radius || DoubleAlgorithm.Equals(D, C.Radius))
{
return(true);
}
return(false);
}
/// <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>
/// 圆形是否在矩形内
/// </summary>
/// <param name="R">矩形R</param>
/// <param name="C">圆形C</param>
/// <returns> 返回True表示圆形C在区域内，返回False则不在区域内.</returns>
public static Boolean InRectangle(RectangleI R, CircleI C)
{
//很容易证明，圆在矩形中的充要条件是：圆心在矩形中且圆的半径小于等于圆心到矩形四边的距离的最小值。
if (InRectangle(R, C.Center) == false)
{
return(false);
}
Int32 MinXDistance = System.Math.Min((C.X - R.Left), (R.Right - C.X));
Int32 MinYDistance = System.Math.Min((C.Y - R.Top), (R.Bottom - C.Y));
if (C.Radius <= MinXDistance && C.Radius <= MinYDistance)
{
return(true);
}
return(false);
}
/// <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>
/// 计算圆形的偏移
/// </summary>
/// <param name="C">圆形C</param>
/// <param name="velocity">偏移速度。</param>
/// <returns>返回偏移后的圆形。</returns>
public static CircleI Offset(CircleI C, PointI velocity)
{
return(new CircleI(C.Center + velocity, C.Radius));
}
/// <summary>
/// 计算圆形面积
/// </summary>
/// <param name="C">圆形C</param>
/// <returns>返回面积。</returns>
public static Double Area(CircleI C)
{
//formula PI*R*R
return(System.Math.PI * C.Radius * C.Radius);
}
/// <summary>
/// 判断点P是否在圆边界上
/// </summary>
/// <param name="C">圆C</param>
/// <param name="P">点P</param>
/// <returns>如果在圆边界上返回True，否则返回False。</returns>
public static Boolean OnCircle(CircleI C, PointI P)
{
return(DoubleAlgorithm.Equals(Distance(C, P), 0));
}
/// <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);
}
