poj 1263 Reflections (Simple Geometry)

1263 -- Reflections

　　简单计算几何。题目给出射线以及若干个不相交的圆，求出射线会在哪些圆上反弹，依次写出反弹球的编号。

代码如下：

 #include <cstdio>
 #include <cstring>
 #include <iostream>
 #include <algorithm>
 #include <cmath>
 #include <vector>

 using namespace std;

 const double EPS = 1e-;
 template<class T> T sqr(T x) { return x * x;}
 inline int sgn(double x) { return (x > EPS) - (x < -EPS);}
 struct Point {
     double x, y;
     Point() {}
     Point(double x, double y) : x(x), y(y) {}
     bool operator < (Point a) const { return sgn(x - a.x) <  || sgn(x - a.x) ==  && y < a.y;}
     bool operator == (Point a) const { return sgn(x - a.x) ==  && sgn(y - a.y) == ;}
     Point operator + (Point a) { return Point(x + a.x, y + a.y);}
     Point operator - (Point a) { return Point(x - a.x, y - a.y);}
     Point operator * (double p) { return Point(x * p, y * p);}
     Point operator / (double p) { return Point(x / p, y / p);}
 } ;
 typedef Point Vec;

 inline double cross(Vec a, Vec b) { return a.x * b.y - a.y * b.x;}
 inline double cross(Point o, Point a, Point b) { return cross(a - o, b - o);}
 inline double dot(Vec a, Vec b) { return a.x * b.x + a.y * b.y;}
 inline double dot(Point o, Point a, Point b) { return dot(a - o, b - o);}
 inline double veclen(Vec x) { return sqrt(dot(x, x));}
 inline Vec normal(Vec x) { return Vec(-x.y, x.x) / veclen(x);}

 struct Line {
     Point s, t;
     Line() {}
     Line(Point s, Point t) : s(s), t(t) {}
     Vec vec() { return t - s;}
     Point pt(double x) { return s + vec() * x;}
     Line move(double x) {
         Vec nor = normal(vec());
         return Line(s + nor * x, t + nor * x);
     }
 } ;

 inline Point llint(Point P, Vec v, Point Q, Vec w) { return P + v * (cross(w, P - Q) / cross(v, w));}
 inline Point llint(Line a, Line b) { return llint(a.s, a.vec(), b.s, b.vec());}

 struct Circle {
     Point c;
     double r;
     Circle() {}
     Circle(Point c, double r) : c(c), r(r) {}
 } ;

 void lcint(Line L, Circle C, vector<Point> &sol) {
     Point ip = llint(L, Line(C.c, C.c + normal(L.vec())));
     double dis = veclen(ip - C.c);
     if (sgn(dis - C.r) >= ) return ;
     Vec u = L.vec() / veclen(L.vec());
     double d = sqrt(sqr(C.r) - sqr(dis));
     sol.push_back(ip + u * d);
     sol.push_back(ip - u * d);
 }

 Point reflect(Point x, Line L) {
     Vec nor = normal(L.vec());
     Point ip = llint(L, Line(x, x + nor));
     return ip + ip - x;
 }

 vector<Circle> rec;
 Point src;
 Vec dir;

 const double FINF = 1e100;
 inline bool onCircle(Point p, Circle c) { return sgn(veclen(p - c.c) - c.r) == ;}

 void work() {
     int cnt = , sz = rec.size();
     vector<Point> tmp;
     Point ip;
     while (true) {
         tmp.clear();
         double d = FINF;
         for (int i = ; i < sz; i++) lcint(Line(src, src + dir), rec[i], tmp);
         for (int i = , sz = tmp.size(); i < sz; i++) {
             double t = (tmp[i].x - src.x) / dir.x;
             if (t > EPS) d = min(d, t);
         }
         if (sgn(d - FINF) >= ) break;
         cnt++;
         if (cnt > ) break;
         ip = src + dir * d;
         int mk = -;
         for (int i = ; i < sz; i++) if (onCircle(ip, rec[i])) { mk = i; break;}
         if (mk == -) { puts("shit!!"); while () ;}
         printf("%d ", mk + );
         dir = reflect(src, Line(ip, rec[mk].c)) - ip;
         src = ip;
     }
     if (cnt > ) puts("...");
     else puts("inf");
 }

 int main() {
 //    freopen("in", "r", stdin);
     int cas = , n;
     double x, y, r;
     while (cin >> n && n) {
         rec.clear();
         while (n--) {
             cin >> x >> y >> r;
             rec.push_back(Circle(Point(x, y), r));
         }
         cin >> src.x >> src.y;
         cin >> dir.x >> dir.y;
         dir = dir / veclen(dir);
         printf("Scene %d\n", cas++);
         work();
         puts("");
     }
     return ;
 }

　　速度好慢，整整写了一个小时。对几何模板还是不算非常熟悉，虽然已经能够灵活写出部分基础函数了，但是速度还真是一个大问题。最后结果，因为手多血多个换行PE了一次，然后就AC了~

——written by Lyon