class 点面关系
{
static void Main(string[] args)
{
//Vector2D point1 = new Vector2D(39.909209536859834, 116.3225715637207);//in
Vector2D point1 = new Vector2D(39.901045, 116.415596);//out
Vector2D cPoint = new Vector2D(39.909209536859834, 116.3225715637207); 
Console.WriteLine("点是否在圆内:" + 点是否在圆内(cPoint, 8000, point1));
Console.WriteLine("点是否在圆内:" + 点是否在圆内(cPoint, new Vector2D(39.901045, 116.415596), point1));

//Vector2D point2 = new Vector2D(39.924745, 116.379204);//in
Vector2D point2 = new Vector2D(39.928695, 116.546059);//out
Vector2D pointA = new Vector2D(39.913423004886866, 116.36890411376953);
Vector2D pointB = new Vector2D(39.93450133090293, 116.38727188110351); 
Console.WriteLine("点是否在矩形内:" + 点是否在矩形内(pointA, pointB, point2));

Vector2D point3 = new Vector2D(39.957649, 116.376801);//in
//Vector2D point3 = new Vector2D(39.919216, 116.2817);//out
List<Vector2D> polygon = new List<Vector2D>();
polygon.Add(new Vector2D(39.909209536859834, 116.3225715637207));
polygon.Add(new Vector2D(39.95920953685983, 116.3725715637207));
polygon.Add(new Vector2D(39.95920953685983, 116.42257156372072));
polygon.Add(new Vector2D(39.909209536859834, 116.4725715637207));
polygon.Add(new Vector2D(39.85920953685984, 116.42257156372072));
polygon.Add(new Vector2D(39.85920953685984, 116.3725715637207)); 
Console.WriteLine("点是否在多边形内:" + 点是否在多边形内(point3, polygon));

Console.ReadLine();
}

/// <summary>
/// 点是否在圆内(在边上也认为在圆内)
/// </summary>
/// <param name="cPoint">圆心坐标</param>
/// <param name="cRadius">圆半径</param>
/// <param name="point">当前点</param>
/// <returns></returns>
public static bool 点是否在圆内(Vector2D cPoint, double cRadius, Vector2D point)
{
var d1 = Distance(cPoint.Lat, cPoint.Lon, point.Lat, point.Lon);
double distance = Math.Sqrt(Math.Pow(Math.Abs(point.X - cPoint.X), 2) + Math.Pow(Math.Abs(point.Y - cPoint.Y), 2));
return distance <= cRadius;
}

private static double Distance(double lon1, double lat1, double lon2, double lat2)
{
double R = 6378137; //地球半径
lat1 = lat1 * Math.PI / 180.0;
lat2 = lat2 * Math.PI / 180.0; 
double sa2 = Math.Sin((lat1 - lat2) / 2.0);
double sb2 = Math.Sin(((lon1 - lon2) * Math.PI / 180.0) / 2.0);
return 2 * R * Math.Asin(Math.Sqrt(sa2 * sa2 + Math.Cos(lat1) * Math.Cos(lat2) * sb2 * sb2));
}

/// <summary>
/// 点是否在圆内(在边上也认为在圆内)
/// </summary>
/// <param name="cPoint">圆心坐标</param>
/// <param name="onPoint">圆边上坐标</param>
/// <param name="point">当前点</param>
/// <returns></returns>
public static bool 点是否在圆内(Vector2D cPoint, Vector2D onPoint, Vector2D point)
{
double cRadius = Distance(cPoint.Lat, cPoint.Lon, onPoint.Lat, onPoint.Lon);
double distance = Distance(cPoint.Lat, cPoint.Lon, point.Lat, point.Lon);
return distance <= cRadius;
}

/// <summary>
/// 点是否在多边形内(在边上也认为在多边形内)
/// </summary>
/// <param name="point">当前点</param>
/// <param name="polygon">多边形点</param>
/// <returns></returns>
public static bool 点是否在多边形内(Vector2D point, List<Vector2D> polygon)
{
var res = SMath.CalcPointPolygonRelation(point, polygon);
return res != PointPolygonRelation.OutOfPolygon;
}

/// <summary>
/// 点是否在矩形内
/// </summary>
/// <param name="pointA">对角上点A</param>
/// <param name="pointB">对角上点B</param>
/// <param name="point">当前点</param>
/// <returns></returns>
public static bool 点是否在矩形内(Vector2D pointA, Vector2D pointB, Vector2D point)
{
List<Vector2D> polygon = new List<Vector2D>();
polygon.Add(pointA);
polygon.Add(new Vector2D(pointA.X, pointB.Y));
polygon.Add(pointB); 
polygon.Add(new Vector2D(pointB.X, pointA.Y));
var res = SMath.CalcPointPolygonRelation(point, polygon);
return res != PointPolygonRelation.OutOfPolygon;
}
}

******************

public static PointPolygonRelation CalcPointPolygonRelation(double x, double y, IList polygon)
{
if(polygon.Count < 3) return PointPolygonRelation.OutOfPolygon;
IVector start = (IVector)polygon[polygon.Count - 2];
if(start == null) return PointPolygonRelation.OutOfPolygon;
IVector middle = (IVector)polygon[polygon.Count - 1];
IVector end;
PointPolygonRelation result = PointPolygonRelation.OutOfPolygon;
int num = 0;
double minX, minY, maxX, maxY;
for(int i = 0; i < polygon.Count; i++, start = middle, middle = end)
{
end = (IVector)polygon[i];
//如果点刚好在顶点上，则直接返回
if((x == start.X && y == start.Y) || (x == middle.X && y == middle.Y) || (x == end.X && y == end.Y))
{
result = PointPolygonRelation.OnPolygonVertex;
goto Return;
}
if(middle.X == end.X && middle.Y == end.Y)
{
continue;
}
minX = Math.Min(middle.X, end.X);
maxX = Math.Max(middle.X, end.X);
//如果X不落在最大X值和最小X值之间，则跳过
if(x > maxX || x < minX) continue;

minY = Math.Min(middle.Y, end.Y);
maxY = Math.Max(middle.Y, end.Y);
//如果Y大于最大Y值则跳过，因为向上做射线不可能相交
if(y > maxY) continue;
if(minX == maxX)//需要判断相交的线段为Y轴平行线
{
if(y > minY && y < maxY)
{
result = PointPolygonRelation.OnPolygonBorder;
goto Return;
}
else if(y < minY)//如果在最小的Y之下，因为目标线段为Y轴平行线，所以记为1次
{
num++;
}
}
else
{
double k = (middle.Y - end.Y) / (middle.X - end.X);
double b = middle.Y - k * middle.X;

double crossY = k * x + b;

if(crossY < y) continue;//如果交点小于y则跳过，因为我们是向上做射线

if(crossY == y)
{
result = PointPolygonRelation.OnPolygonBorder;
goto Return;
}

if(x == maxX || x == minX)
{
if((start.X > middle.X && end.X < middle.X) || (start.X < middle.X && end.X > middle.X))
num++;
}
else
{
num++;
}
}
}

if(num % 2 != 0) result = PointPolygonRelation.InPolygon;
Return:

return result;
}

/// <summary>
/// 计算点和面的关系
/// </summary>
/// <param name="point"></param>
/// <param name="polygon"></param>
/// <returns></returns>
public static PointPolygonRelation CalcPointPolygonRelation(IVector point, IList polygon)
{
return CalcPointPolygonRelation(point.X, point.Y, polygon);
}

_____________

public enum PointPolygonRelation
{
/// <summary>
/// 点在面内
/// </summary>
InPolygon,
/// <summary>
/// 点在边上
/// </summary>
OnPolygonBorder,
/// <summary>
/// 点在面外
/// </summary>
OutOfPolygon,
/// <summary>
/// 点在面的拐点上
/// </summary>
OnPolygonVertex
}