HDU 4617 Weapon 三维计算几何

题意：给你一些无限长的圆柱，知道圆柱轴心直线（根据他给的三个点确定的平面求法向量即可）与半径，判断是否有圆柱相交。如果没有，输出柱面最小距离。

一共只有30个圆柱，直接暴力一下就行。

判相交/相切：空间直线距离是否小于等于两圆柱半径和
若无相交，求最小：空间直线距离-两圆柱半径和

#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;
};

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) { }
};

struct Cylinder
{
    Point3 center;   //圆柱轴线经过的一点
    Point3 a, b;     //与中心点在同一平面的两点
    Line3 FaXian;    //轴线
    double R;        //圆柱半径
};

Cylinder CC[MAXN];

Point3 Read_Point()
{
    Point3 p;
    scanf("%lf%lf%lf", &p.x, &p.y, &p.z );
    return p;
}

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;
}

//取平面法向量
Point3 NormalVector( plane3 s )
{
    return Cross3( Subt( s.a, s.b ), Subt( s.b, s.c ) );
}
Point3 NormalVector( Point3 a, Point3 b, Point3 c )
{
    return Cross3( Subt( a, b ), Subt( b, c ) );
}

//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 = Cross3( Subt( u.a, u.b ), Subt( v.a, v.b ) );
    return fabs( Dot3( Subt(u.a, v.a), tmp ) ) / VectorLenth(tmp);
}

int N;

int main()
{
    int T;
    scanf( "%d", &T );
    while ( T-- )
    {
        scanf( "%d", &N );
        for ( int i = 0; i < N; ++i )
        {
            CC[i].center = Read_Point();
            CC[i].a = Read_Point();
            CC[i].b = Read_Point();
            CC[i].R = VectorLenth( Subt( CC[i].a, CC[i].center ) );
            CC[i].FaXian.a = CC[i].center;
            CC[i].FaXian.b = Subt( CC[i].center, NormalVector( CC[i].center, CC[i].a, CC[i].b ) );
        }

        bool ok = true;
        double MinAns = 1e200;
        for ( int i = 0; ok && i < N; ++i )
        for ( int j = i + 1; ok && j < N; ++j )
        {
            double tmp = LineToLine( CC[i].FaXian, CC[j].FaXian );
            if ( dcmp( tmp - ( CC[i].R + CC[j].R ) ) <= 0 )
            {
                ok = false;
                break;
            }
            MinAns = min( MinAns, tmp - ( CC[i].R + CC[j].R ) );
        }

        if ( ok ) printf( "%.2f
", MinAns );
        else puts("Lucky");
    }
    return 0;
}