HDU 4793 2013 Changsha Regional Collision[简单的平面几何]

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给出一个圆形奖牌的半径和一个圆形区域的半径，还有一枚硬币的半径，然后桌面是光滑的，给出圆硬币的速度（大小和方向，vx，vy）和坐标（圆区域和圆奖牌同心且心作为源点），问硬币在圆区域滑动的时间是多少（任何一部分在圆区域都算），硬币碰到圆奖牌会反弹，能量不变（速度不变）

第一次做平面几何题

看了题解，题解的板子真好用

大概来说有三种情况，如下图

第一种是进入圆区而不碰撞，查看h和Rm+r的关系

第二种是进入圆区且碰撞，查看h和Rm+r的关系

第三种是不进入圆区，查看方向向量和圆心到初始点向量这两个向量的夹角还有h和R+r的关系，而且应该先看向量，也可以先看R+r再讨论向量

#include <iostream>#include <cstdio>#include <cstring>#include <cmath>#include <cstdlib>#include <vector>#include <algorithm>#include <string>#include <set>#define PI acos(-1.0)#define maxn 100005#define INF 0x7fffffff#define eps 1e-8using namespace std;int cmp(double x) {if(fabs(x)<eps)return 0;if(x>0)return 1;return -1;}inline int sgn(double n) {return fabs(n)<eps?0:(n<0?-1:1);}inline double sqr(double x) {return x*x;}struct point{double x,y;point() {}point(double a,double b):x(a),y(b) {}void input() {scanf("%lf%lf",&x,&y);}friend point operator + (const point &a,const point &b) {return point(a.x+b.x,a.y+b.y);}friend point operator - (const point &a,const point &b) {return point(a.x-b.x,a.y-b.y);}friend bool operator == (const point &a,const point &b) {return cmp(a.x-b.x)==0 &&cmp(a.y-b.y)==0;}friend point operator * (const point &a,const double &b) {return point(a.x*b,a.y*b);}friend point operator * (const double &a,const point &b) {return point(a*b.x,a*b.y);}friend point operator / (const point &a,const double &b) {return point(a.x/b,a.y/b);}double norm() {return sqrt(sqr(x)+sqr(y));}//到原点距离void out () const {printf("%.2f %.2f",x,y);}};double det (const point &a,const point &b) {return a.x*b.y-a.y*b.x;}//叉积double dot (const point &a,const point &b) {return a.x*b.x+a.y*b.y;}//点乘double dist (const point &a,const point &b) {return (a-b).norm();}//距离point rotate_point(const point &p,double A) {double tx=p.x,ty=p.y;return point (tx*cos(A)-ty*sin(A),tx*sin(A)+ty*cos(A));}//旋转，A是弧度struct line {point a,b;line() {}line(point x,point y):a(x),b(y) {}point dire()const {return b-a;}//向量double len() {return dire().norm();}};bool parallel(line a,line b) {return !cmp(det(a.a-a.b,b.a-b.b));}bool line_make_point (line a,line b,point &res) {if(parallel(a,b))return false;double s1=det(a.a-b.a,b.b-b.a);double s2=det(a.b-b.a,b.b-b.a);res=(s1*a.b-s2*a.a)/(s1-s2);return true;}int main(){#ifndef ONLINE_JUDGEfreopen("/home/rainto96/in.txt","r",stdin);#endifdouble Rm,R,r,x,y,vx,vy;while(~scanf("%lf%lf%lf%lf%lf%lf%lf",&Rm,&R,&r,&x,&y,&vx,&vy)){                point s=point(x,y);                point dir=point(vx,vy);                if(dot(s,dir)>=0){                        printf("0.000\n");                        continue;                }                point tmp=point(vy,-vx);                line l1=line(point(0,0),tmp);                line l2=line(s,point(s.x+vx,s.y+vy));                point ans;                line_make_point(l1,l2,ans);                double h=ans.norm();                double h1=R+r;                double h2=Rm+r;                double speed=sqrt(vx*vx+vy*vy);                if(h>=h1){                        printf("0.000\n");                        continue;                }                if(h>=h2){                        double time=sqrt(h1*h1-h*h)/speed*2;                        printf("%f\n",time);                        continue;                }else{                        double time=sqrt(h1*h1-h*h)-sqrt(h2*h2-h*h);                        time=time/speed*2;                        printf("%f\n",time);                        continue;                }}return 0;}

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