HDU 4741 Save Labman No.004 (异面直线距离&直线与平面的交点)

来源：互联网发布：微信加好友软件编辑：程序博客网时间：2024/05/16 18:11

http://acm.hdu.edu.cn/showproblem.php?pid=4741

模板题。

理论知识见代码注释。

~~这题背景居然是命运石之门。。~~

/*218ms,276KB*/#include<cstdio>#include<cmath>const double eps = 1e-9;struct P3{double x, y, z;P3(double x = 0.0, double y = 0.0, double z = 0.0): x(x), y(y), z(z) {}void read(){scanf("%lf%lf%lf", &x, &y, &z);}void output(){printf("%f %f %f", x, y, z);}P3 operator + (P3 p){return P3(x + p.x, y + p.y, z + p.z);}P3 operator - (P3 p){return P3(x - p.x, y - p.y, z - p.z);}double dot(P3 p){return x * p.x + y * p.y + z * p.z;}P3 det(P3 p){return P3(y * p.z - z * p.y, z * p.x - x * p.z, x * p.y - y * p.x);}double length() ///向量的模{return sqrt(x * x + y * y + z * z);}};struct L3{P3 a, b;L3() {}L3(P3 a, P3 b): a(a), b(b) {}void read(){a.read(), b.read();}};struct plane{P3 a, b, c;plane() {}plane(P3 a, P3 b, P3 c): a(a), b(b), c(c) {}P3 normal_vector() ///法向量(ab x ac){return (b - a).det(c - a);}};///空间两点距离inline double TwoPointsDistance(P3 &p1, P3 &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));}///空间直线距离，等价于UaVa在公垂线上的投影///参见 http://219.218.160.73:8000/jxjh/kc/fla/jhlw/gn/7.pdf 图1inline double LineToLine(L3 u, L3 v, P3 &cross){cross = (u.b - u.a).det(v.b - v.a);return fabs((u.a - v.a).dot(cross)) / cross.length(); ///UaVa在公垂线上的投影}///空间线面交点///解法参见 http://blog.csdn.net/abcjennifer/article/details/6688080inline P3 Intersection(L3 l, plane s){P3 ret = s.normal_vector();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; ///将t带入直线参数方程return ret;}/************以上模板*************/void solve(L3 l1, L3 l2){P3 s; ///两直线公垂线的方向向量printf("%f\n", LineToLine(l1, l2, s));Intersection(l1, plane(l2.a, l2.b, l2.a + s)).output();///构造直线与公垂线所构成的平面putchar(32);Intersection(l2, plane(l1.a, l1.b, l1.a + s)).output();putchar(10);}int main(){int T;L3 l1, l2;scanf("%d", &T);while (T--){l1.read(), l2.read();solve(l1, l2);}return 0;}

附题：UVa 10794 The Deadly Olympic Returns!!!

2 0