HDU 4741 Save Labman No.004 ( 三维计算几何 空间异面直线距离 )

空间异面直线的距离直接套模板。

求交点：求出两条直线的公共法向量，其中一条直线与法向量构成的平面 与 另一条直线 的交点即可。还是套模板o(╯□╰)o

1.不会有两条线平行的情况。

2.两条直线可能相交

 

#include <cstdio>

#include <cstdlib>

#include <cstring>

#include <algorithm>

#include <cmath>



using namespace std;



const double EPS = 1e-9;

const int MAXN = 40;



struct Point3  //空间点

{

    double x, y, z;

    Point3( double x=0, double y=0, double z=0 ): x(x), y(y), z(z) { }

    Point3( const Point3& a )

    {

        x = a.x;

        y = a.y;

        z = a.z;

        return;

    }

    void showP()

    {

        printf("%f %f %f \n", x, y, z);

    }

    Point3 operator+( Point3& rhs )

    {

        return Point3( x+rhs.x, y+rhs.y, z+rhs.z );

    }

};



struct Line3   //空间直线

{

    Point3 a, b;

};



struct plane3   //空间平面

{

    Point3 a, b, c;

    plane3() {}

    plane3( Point3 a, Point3 b, Point3 c ):

        a(a), b(b), c(c) { }

    void showPlane()

    {

        a.showP();

        b.showP();

        c.showP();

        return;

    }

};



double dcmp( double a )

{

    if ( fabs( a ) < EPS ) return 0;

    return a < 0 ? -1 : 1;

}



//三维叉积

Point3 Cross3( Point3 u, Point3 v )

{

    Point3 ret;

    ret.x = u.y * v.z - v.y * u.z;

    ret.y = u.z * v.x - u.x * v.z;

    ret.z = u.x * v.y - u.y * v.x;

    return ret;

}



//三维点积

double Dot3( Point3 u, Point3 v )

{

    return u.x * v.x + u.y * v.y + u.z * v.z;

}



//矢量差

Point3 Subt( Point3 u, Point3 v )

{

    Point3 ret;

    ret.x = u.x - v.x;

    ret.y = u.y - v.y;

    ret.z = u.z - v.z;

    return ret;

}



//两点距离

double TwoPointDistance( Point3 p1, Point3 p2 )

{

    return sqrt( (p1.x - p2.x)*(p1.x - p2.x) + (p1.y - p2.y)*(p1.y - p2.y) + (p1.z - p2.z)*(p1.z - p2.z) );

}



//向量的模

double VectorLenth( Point3 p )

{

    return sqrt( p.x*p.x + p.y*p.y + p.z*p.z );

}



//空间直线距离

double LineToLine( Line3 u, Line3 v, Point3& tmp )

{

    tmp = Cross3( Subt( u.a, u.b ), Subt( v.a, v.b ) );

    return fabs( Dot3( Subt(u.a, v.a), tmp ) ) / VectorLenth(tmp);

}



//取平面法向量

Point3 pvec( plane3 s )

{

    return Cross3( Subt( s.a, s.b ), Subt( s.b, s.c ) );

}



//空间平面与直线的交点

Point3 Intersection( Line3 l, plane3 s )

{

    Point3 ret = pvec(s);

    double t = ( ret.x*(s.a.x-l.a.x)+ret.y*(s.a.y-l.a.y)+ret.z*(s.a.z-l.a.z) )/( ret.x*(l.b.x-l.a.x)+ret.y*(l.b.y-l.a.y)+ret.z*(l.b.z-l.a.z) );

    ret.x = l.a.x + ( l.b.x - l.a.x ) * t;

    ret.y = l.a.y + ( l.b.y - l.a.y ) * t;

    ret.z = l.a.z + ( l.b.z - l.a.z ) * t;

    return ret;

}



/************以上模板*************/



void solved( Line3 A, Line3 B )

{

    Point3 normal;

    double dis = LineToLine( A, B, normal );

    printf( "%.6f\n", dis );

    plane3 pla;

    pla = plane3( A.a, A.b, A.a + normal );

    Point3 u = Intersection( B, pla );

    pla = plane3( B.a, B.b, B.a + normal );

    Point3 v = Intersection( A, pla );

    printf("%.6f %.6f %.6f %.6f %.6f %.6f\n", v.x, v.y, v.z, u.x, u.y, u.z );

    return;

}



int main()

{

    int T;

    scanf( "%d", &T );

    while ( T-- )

    {

        Line3 A, B;

        scanf("%lf%lf%lf", &A.a.x, &A.a.y, &A.a.z );

        scanf("%lf%lf%lf", &A.b.x, &A.b.y, &A.b.z );

        scanf("%lf%lf%lf", &B.a.x, &B.a.y, &B.a.z );

        scanf("%lf%lf%lf", &B.b.x, &B.b.y, &B.b.z );

        solved( A, B );

    }

    return 0;

}