/// 

        /// 点积,点乘就是将oa向量投影到ob向量上面
        /// 
        /// 原点
        /// 
        /// 
        /// 求出来的就是oa在ob上的投影长度
        public static Vector3d DotProduct(Point3d o, Point3d a, Point3d b)
        {
            var oa_vector = o.GetVectorTo(a);
            var ob_vector = o.GetVectorTo(b);

            //单位向量,cad自带的
            Vector3d ob_UnitVector = ob_vector.GetNormal();

            //求得op长度
            var op_length = oa_vector.DotProduct(ob_UnitVector);//点乘,=(v1.X * v2.X) + (v1.Y * v2.Y) + (v1.Z * v2.Z);

            //求得op坐标(也就是呈现90度角的坐标)
            //如果O不在坐标原点,需要平移,那么最终P的最终坐标 = O的坐标 + 求出来的P的坐标 
            Vector3d v = ob_UnitVector * op_length;
             
            //从0,0再平移回去 
            return new Vector3d(v.X + o.X, v.Y + o.Y, v.Z + o.Z);
        }


        /// 

        /// 获取单位向量,仿照向量的GetNormal的数学实现,了解原理,用了Point3d代替向量
        /// 
        /// 
        /// 
        public static Point3d GetNormal(this Point3d ob_vector)
        {
            //https://www.bilibili.com/video/BV1qb411M7wL?from=search&seid=9280697047969917119

#if true
            //向量模长
            var ob_length = Point3d.Origin.DistanceTo(ob_vector);
#else
            //两点的距离
            //向量模长数学版 √(x2+y2+z2)
            var ob_length =  Sqrt(ob_vector.X * ob_vector.X +
                                  ob_vector.Y * ob_vector.Y +
                                  ob_vector.Z * ob_vector.Z); 
#endif
            //单位向量数学版 (x/ob_length,y/ob_length,z/ob_length) 
            return ob_vector / ob_length;
        }
         

        /// 

        /// 叉积,二维叉乘计算 |p1 p2| X |p1 p|
        ///   
        /// 直线点1
        /// 直线点2  
        /// 判断是否在内的点
        /// A:返回值有正负,表示绕原点四象限的位置变换,也就是有向面积;
        /// B:返回值是一个向量,X*Y表示Z或者-Z,正负是左右手坐标系
        /// https://blog.csdn.net/pdcxs007/article/details/51436483
        public static double Cross(Point2d a, Point2d b, Point2d n)
        {
            //三种计算是一样的
            //return (b.X - a.X) * (n.Y - a.Y) - (n.X - a.X) * (b.Y - a.Y);
            //return (a.X - b.X) * (a.Y - n.Y) - (a.X - n.X) * (a.Y - b.Y);
            return (a.X - n.X) * (b.Y - n.Y) - (b.X - n.X) * (a.Y - n.Y);
        }

        /// 

        /// 叉积,参数三在顺时针方向为真
        /// 
        /// 直线点1
        /// 直线点2  
        /// 判断是否在内的点
        /// 
        public static bool CrossClockwise(Point2d a, Point2d b, Point2d n)
        {
            return Cross(a, b, n) > -1e-6;
        }

        /// 

        /// 叉积,求出法向量,三维叉乘(X轴*Y轴==Z轴)
        /// 
        /// 向量a
        /// 向量b    
        /// 
        public static Vector3d CrossNormal(Vector3d a, Vector3d b)
        {
            //y1*z2-y2*z1,z1*x2-z2*x1,x1*y2-x2*y1
            return new Vector3d(a.Y * b.Z - b.Y * a.Z, a.Z * b.X - b.Z * a.X, a.X * b.Y - b.X * a.Y); 
        }