[RGEOS]空间拓扑关系

-1.判断两个线段是否平行

inline bool parallel_seg_seg(Segment_2 S1, Segment_2 S2)
{
    Vector_2 u(S1);
    Vector_2 v(S2);
    Vector_2 w = S1.source() - S2.source();
    float D = perp(u, v);
    if (abs(D)<SMALL_NUM)
    {
        return true;
    }
    return false;
}

0.线段的拐向：已知向量P0P1，向量P1P2

（1）判断点P2在直线P0P1的左边还是在右边，还是在直线上

// 判断点P2在直线P0P1的左边还是在右边，还是在直线上
//isLeft(): tests if a point is Left|On|Right of an infinite line.
//    Input:  three points P0, P1, and P2
//    Return: >0 for P2 left of the line through P0 and P1
//            =0 for P2 on the line
//            <0 for P2 right of the line
inline int isLeft( Point P0, Point P1, Point P2 )
{
    return ( (P1.x - P0.x) * (P2.y - P0.y)
            - (P2.x - P0.x) * (P1.y - P0.y) );
}

1.点在线段上

（1）点是否在共线的线段上

/// <summary>
        /// 点是否在共线的线段上
        /// 1 = P is inside S;
        /// 0 = P is not inside S
        /// </returns> 
        /// </summary>
        /// <param name="P">a point P</param>
        /// <param name="S">a collinear segment S</param>
        /// <returns></returns>
        public static int InSegment(RPoint P, RSegment S)
        {
            if (S.P0.X != S.P1.X)
            {    // S is not vertical
                if (S.P0.X <= P.X && P.X <= S.P1.X)
                    return 1;
                if (S.P0.X >= P.X && P.X >= S.P1.X)
                    return 1;
            }
            else
            {    // S is vertical, so test y coordinate
                if (S.P0.Y <= P.Y && P.Y <= S.P1.Y)
                    return 1;
                if (S.P0.Y >= P.Y && P.Y >= S.P1.Y)
                    return 1;
            }
            return 0;
        }

（2）点是否包含在任意线段内

        /// <summary>
        /// 点是否在线段上
      /// </summary>
        /// <param name="P">任意的点</param>
        /// <param name="S">任意线段</param>
        /// <returns>1=P点在线段S上;0=P点不在线段S上</returns>
        public static int Inside2D_Point_Segment(RPoint P, RSegment S)
        {
    Vector3d u = S.P1 - S.P0;
                Vector3d v = P - S.P0;
                double D = RMath.perp(u, v);
    //判断u和v是否平行
             if (Math.Abs(D) < RMath.SMALL_NUM)
               {
        if (InSegment(P, S) == 1) 
       {
       return 1;
       }
               }
               return 0;
        }

2.点在矩形内

// 点在矩形内
// 1 = P is inside E;
// 0 = P is not inside E
public static int Inside2D_Point_Envelope(RPoint P, REnvelope E)
        {
    if(P.X>E.LowerLeft.X && P.X>E.TopRight.X && P.Y>E.LowerLeft.Y && P.Y<E.TopRight.Y)
    {
                    return 1;
    }
    else
    {
        return 0;
    }
        }

3.点在圆内

　　点到圆心的距离小于半径

4.点在2D多边形内

　　转角方法

　　射线方法

5.2D线段在矩形内

6.2D多边形与多边形是否相交

 　　一种笨方法：首先判断包围盒是否相交，再判断一个多边形的点在另外一个多边形内。