多边形几何

public Point Center
        {
            get
            {
                Point ptCenter = new Point();
                int i, j;
                double ai, atmp = 0, xtmp = 0, ytmp = 0;
                if (m_LogicPoints.Count == 1)
                    return m_LogicPoints[0];
                if ((m_LogicPoints.Count == 2) || (m_LogicPoints.Count == 3 && m_LogicPoints[0] == m_LogicPoints[2]))
                    return new Point() { X = (m_LogicPoints[1].X + m_LogicPoints[0].X) / 2, Y = (m_LogicPoints[1].Y + m_LogicPoints[0].Y) / 2 };

                int n = m_LogicPoints.Count;
                for (i = n - 1, j = 0; j < n; i = j, j++)
                {
                    ai = m_LogicPoints[i].X * m_LogicPoints[j].Y - m_LogicPoints[j].X * m_LogicPoints[i].Y;
                    atmp += ai;
                    xtmp += (m_LogicPoints[j].X + m_LogicPoints[i].X) * ai;
                    ytmp += (m_LogicPoints[j].Y + m_LogicPoints[i].Y) * ai;
                }

                if (atmp != 0)
                {
                    ptCenter.X = Convert.ToInt32(xtmp / (3 * atmp));
                    ptCenter.Y = Convert.ToInt32(ytmp / (3 * atmp));
                }
                return ptCenter;
            }
        }

public bool isColide(Line line)//判断是否相交,直线p1p2与线段p3p4
        {
            //判处端点
            if (this.V0 == line.V0 || this.V0 == line.V1 || this.V1 == line.V0 || this.V1 == line.V1)
                return false;

            double deviation = 0.1;//允许误差
            //排斥试验，判断p1p2在q1q2为对角线的矩形区之外
            if (Math.Max(line.V0.X, line.V1.X) < Math.Min(this.V0.X, this.V1.X)- deviation)
            {//P1P2中最大的X比Q1Q2中的最小X还要小，说明P1P2在Q1Q2的最左点的左侧，不可能相交。
                return false;
            }

            if (Math.Min(line.V0.X, line.V1.X) > Math.Max(this.V0.X, this.V1.X)+ deviation)
            {//P1P2中最小的X比Q1Q2中的最大X还要大，说明P1P2在Q1Q2的最右点的右侧，不可能相交。
                return false;
            }

            if (Math.Max(line.V0.Y, line.V1.Y) < Math.Min(this.V0.Y, this.V1.Y)- deviation)
            {//P1P2中最大的Y比Q1Q2中的最小Y还要小，说明P1P2在Q1Q2的最低点的下方，不可能相交。
                return false;
            }

            if (Math.Min(line.V0.Y, line.V1.Y) > Math.Max(this.V0.Y, this.V1.Y)+ deviation)
            {//P1P2中最小的Y比Q1Q2中的最大Y还要大，说明P1P2在Q1Q2的最高点的上方，不可能相交。
                return false;
            }

            //跨立试验
            var crossP1P2Q1 = Cross(line.V0, line.V1, this.V0);
            var crossP1Q2P2 = Cross(line.V0, this.V1, line.V1);
            var crossQ1Q2P1 = Cross(this.V0, this.V1, line.V0);
            var crossQ1P2Q2 = Cross(this.V0, line.V1, this.V1);

            return (crossP1P2Q1 * crossP1Q2P2 >= 0 || Math.Abs(crossP1P2Q1 * crossP1Q2P2) < 0.01) && (crossQ1Q2P1 * crossQ1P2Q2 >= 0 || Math.Abs(crossQ1Q2P1 * crossQ1P2Q2) < 0.01);
        }