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// 二维空间点到直线的垂足

struct Point

{

　　double x,y;

}

Point GetFootOfPerpendicular(

    const Point &pt,     // 直线外一点

    const Point &begin,  // 直线开始点

    const Point &end)   // 直线结束点

{

    Point retVal;

    double dx = begin.x - end.x;

    double dy = begin.y - end.y;

    if(abs(dx) < 0.00000001 && abs(dy) < 0.00000001 )

    {

        retVal = begin;

        return retVal;

    }

    double u = (pt.x - begin.x)*(begin.x - end.x) +

        (pt.y - begin.y)*(begin.y - end.y);

    u = u/((dx*dx)+(dy*dy));

    retVal.x = begin.x + u*dx;

    retVal.y = begin.y + u*dy;

    return retVal;

}

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// 三维空间点到直线的垂足

struct Point

{

　　double x,y,z;

}

Point GetFootOfPerpendicular(

    const Point &pt,     // 直线外一点

    const Point &begin,  // 直线开始点

    const Point &end)   // 直线结束点

{

    Point retVal;

    double dx = begin.x - end.x;

    double dy = begin.y - end.y;

　　double dz = begin.z - end.z;

    if(abs(dx) < 0.00000001 && abs(dy) < 0.00000001 && abs(dz) < 0.00000001 )

    {

        retVal = begin;

        return retVal;

    }

    double u = (pt.x - begin.x)*(begin.x - end.x) +

        (pt.y - begin.y)*(begin.y - end.y) + (pt.z - begin.z)*(begin.z - end.z);

    u = u/((dx*dx)+(dy*dy)+(dz*dz));

    retVal.x = begin.x + u*dx;

    retVal.y = begin.y + u*dy;

　　retVal.y = begin.z + u*dz;

    return retVal;

}