判断两条线段是否相交

判断两条线段是否相交，可以采用向量积的方式来判断，如下图所示：

 

 

现定义一个函数初步判断两线段是否相交，如下代码：

        /// <summary>

        /// 初步根据外围框大致判断两条线段是否相交

        /// </summary>

        /// <param name="line01Coords">线段1的坐标，长度为6</param>

        /// <param name="line02Coords">线段2的坐标，长度为6</param>

        /// <returns>返回类型为bool，如果为true表示两条线段可能相交，如果为false表示两条线段不相交</returns>

        private bool JudgeAboutCrossStatus(double[] line01Coords, double[] line02Coords)

        {

            bool returnResult = true;

            //先判断在XY方向的最值

            double maxX1, minX1, maxY1, minY1;

            maxX1 = minX1 = line01Coords[0];

            maxY1 = minY1 = line01Coords[1];

            if (line01Coords[0] < line01Coords[3])

                maxX1 = line01Coords[3];

            else

                minX1 = line01Coords[3];

            if (line01Coords[1] < line01Coords[4])

                maxY1 = line01Coords[4];

            else

                minY1 = line01Coords[4];

            double maxX2, minX2, maxY2, minY2;

            maxX2 = minX2 = line02Coords[0];

            maxY2 = minY2 = line02Coords[1];

            if (line02Coords[0] < line02Coords[3])

                maxX2 = line02Coords[3];

            else

                minX2 = line02Coords[3];

            if (line02Coords[1] < line02Coords[4])

                maxY2 = line02Coords[4];

            else

                minY2 = line02Coords[4];

            //比较最值大小

            if ((minX1 > maxX2) || (maxX1 < minX2) || (minY1 > maxY2) || (maxY1 < minY2))

            {

                returnResult = false;

            }

            return returnResult;

        }

函数JudgeAboutCrossStatus()如果返回值为true则表示两条线段可能相交，则需要采用向量积的方式来判断是否相交，如果为false则表示两条线段不相交。现在定义一个函数Judge2LinesRelation ()用于判断两条线段是否相交，其代码如下：

        /// <summary>

        /// 判断两条线段是否相交

        /// </summary>

        /// <param name="line01Coords">线段1的坐标，长度为6</param>

        /// <param name="line02Coords">线段2的坐标，长度为6</param>

        /// <returns>返回类型为bool，如果为true表示两条线段相交，如果为false表示两条线段不相交</returns>

        private bool Judge2LinesRelation(double[] line01Coords, double[] line02Coords)

        {

            bool returnResult = true;

            returnResult = JudgeAboutCrossStatus(line01Coords, line02Coords);

            if (returnResult)//初步判断两条线段可能相交

            {

                double BAx, BAy, BCx, BCy, BDx, BDy, BABCk, BABDk;

                BAx = line01Coords[0] - line01Coords[3];

                BAy = line01Coords[1] - line01Coords[4];

                BCx = line02Coords[0] - line01Coords[3];

                BCy = line02Coords[1] - line01Coords[4];

                BABCk = BAx * BCy - BAy * BCx;

                BDx = line02Coords[3] - line01Coords[3];

                BDy = line02Coords[4] - line01Coords[4];

                BABDk = BAx * BDy - BAy * BDx;

                if (((BABCk > 0) && (BABDk > 0)) || ((BABCk < 0) && (BABDk < 0)))

                {

                    returnResult = false;

                }

                else if (((BABCk > 0) && (BABDk < 0)) || ((BABCk < 0) && (BABDk > 0)))

                {

                    double BCBDk;

                    BCBDk = BCx * BDy - BCy * BDx;

                    if (((BABDk > 0) && (BCBDk > 0)) || ((BABDk < 0) && (BCBDk < 0)))

                    {

                        returnResult = true;

                    }

                    else

                    {

                        returnResult = false;

                    }                   

                }

                else if ((BABCk == 0)||(BABDk==0))//点C或D在直线AB上

                {

                    double[] templine02Coords = new double[3];

                    if (BABCk == 0)//点C在直线AB上

                    {

                        templine02Coords[0] = line02Coords[0];

                        templine02Coords[1] = line02Coords[1];

                        templine02Coords[2] = line02Coords[2];

                    }

                    else//点D在直线AB上

                    {

                        templine02Coords[0] = line02Coords[3];

                        templine02Coords[1] = line02Coords[4];

                        templine02Coords[2] = line02Coords[5];

                    }

                    if (line01Coords[0] == line01Coords[3])//是否垂直，是则比较Y值

                    {

                        double maxY, minY;

                        maxY = minY = line01Coords[1];

                        if (line01Coords[1] < line01Coords[4])

                            maxY = line01Coords[4];

                        else

                            minY = line01Coords[4];

                        if ((templine02Coords[1] >= minY) && (templine02Coords[1] <= maxY))//在线段上

                            returnResult = true;

                        else

                            returnResult = false;

                    }

                    else //比较X值

                    {

                        double maxX, minX;

                        maxX = minX = line01Coords[0];

                        if (line01Coords[0] < line01Coords[3])

                            maxX = line01Coords[3];

                        else

                            minX = line01Coords[3];

                        if ((templine02Coords[0] >= minX) && (templine02Coords[0] <= maxX))//在线段上

                            returnResult = true;

                        else

                            returnResult = false;

                    }

                }

            }

            return returnResult;

        }