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-;
 const int MAXN = ;

 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 ;
     return a <  ? - : ;
 }

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

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