104 lines
2.3 KiB
C++
104 lines
2.3 KiB
C++
#include<iostream>
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#include<cmath>
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using namespace std;
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struct point{
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double x,y,z;
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point(double xx=0,double yy=0,double zz=0){
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x=xx,y=yy,z=zz;
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}
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point operator ^(double h){
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return point(x*h,y*h,z*h);
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}
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double operator ^(point h){
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return x*h.x+y*h.y+z*h.z;
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}
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point operator +(point h){
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return point(x+h.x,y+h.y,z+h.z);
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}
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point operator -(point h){
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return point(x-h.x,y-h.y,z-h.z);
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}
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point operator *(point b){
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return point(y*b.z-b.y*z, z*b.x-b.z*x, x*b.y-b.x*y);
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}
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double len2()const{
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return x*x+y*y+z*z;
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}
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double len()const{
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return sqrt(len2());
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}
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point turnlen(double l)const {
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double r=l/len();
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return point(x*r,y*r,z*r);
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}
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void input()
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{
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scanf("%lf%lf%lf",&x,&y,&z);
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}
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}p1,p2,ans;
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struct sphere{
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point c;
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double r;
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void input(){
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c.input();
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scanf("%lf",&r);
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}
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}sph[110];
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int n;
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const double eps=1e-8;
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int sgn(double x)
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{
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if(fabs(x)<eps) return 0;
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return x>0?1:-1;
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}
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bool intersection(sphere s,point p1,point p2,point &c)
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{
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double d=((p1-s.c)*(p2-s.c)).len()/(p1-p2).len();
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if(sgn(d-s.r)>=0)
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return false;
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point pp=(sgn(d)==0? s.c:s.c+((p1-s.c)*(p2-s.c)*(p1-p2)).turnlen(d) ); if(sgn((pp-p1)^(p2-p1))<=0)
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return false;
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c=pp+(p1-p2).turnlen(sqrt(s.r*s.r-d*d));
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return true;
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}
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point reflection(point p1,point rep,point c)
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{
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double d=((rep-p1)*(c-p1)).len()/(rep-c).len();
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return p1+((rep-p1)*(c-p1)*(rep-c)).turnlen(d*2.0);
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}
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void compute()
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{
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while(true){
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point c;
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int k=-1;
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for(int i=0;i<n;i++)
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{
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point tmp;
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if(intersection(sph[i],p1,p2,tmp)){
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if(k==-1 || sgn((tmp-p1).len()-(c-p1).len())<0){
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c=tmp;
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k=i;
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}
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}
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}
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if(k==-1)
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break;
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p2=reflection(p1,sph[k].c,c);
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p1=c;
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}
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ans=p1;
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}
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int main()
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{
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while(scanf("%d",&n),n)
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{
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p1=point();
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p2.input();
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for(int i=0;i<n;i++)
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sph[i].input();
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compute();
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printf("%.8lf %.8lf %.8lf\n",ans.x,ans.y,ans.z);
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}
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return 0;
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}
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