92 lines
2.5 KiB
C++
92 lines
2.5 KiB
C++
#include<cstdio>
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#include<cstdlib>
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#include<cstring>
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#include<cmath>
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#include<algorithm>
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const double eps=1e-12;
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const double pi=acos(-1.0);
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using namespace std;
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typedef long long ll;
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inline double sqr(double x)
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{
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return x*x;
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}
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struct point
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{
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double x, y, r;
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point(){}
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point(double _x, double _y, double _r){x=_x;y=_y;r=_r;}
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void read(){scanf("%lf%lf%lf", &x, &y, &r);}
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point operator -(const point &tp)const
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{
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return point(x-tp.x, y-tp.y, r-tp.r);
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}
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point operator +(const point &tp)const
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{
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return point(x+tp.x, y+tp.y, r+tp.r);
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}
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point operator *(const double &k)const
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{
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return point(x*k, y*k, r*k);
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}
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}table, ball;
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double dx, dy, tot;
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int cross(point op, point sp, point ep)
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{
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double ans=(sp.y-op.y)*(ep.x-op.x)-(ep.y-op.y)*(sp.x-op.x);
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if(ans>eps)return 1;
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return -1;
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}
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double angle(point a, point b)
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{
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double area=a.x*b.x+a.y*b.y;
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double ablen=sqrt((a.x*a.x+a.y*a.y)*(b.x*b.x+b.y*b.y));
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return acos(area/ablen);
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}
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int main()
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{
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int ca;
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scanf("%d", &ca);
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while(ca-->0)
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{
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table.read();
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ball.read();
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scanf("%lf%lf%lf", &dx, &dy, &tot);
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ball.x-=table.x;
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ball.y-=table.y;
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table.r-=ball.r;
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double a=sqr(dx)+sqr(dy);
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double b=2.0*(ball.x*dx*1.0+ball.y*dy*1.0);
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double c=sqr(ball.x)+sqr(ball.y)-sqr(table.r);
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double sti=(sqrt(sqr(b)-4.0*a*c)-b)/(2.0*a);
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if(sti-tot>eps)
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{
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printf("%.1lf %.1lf\n", (ball.x+tot*dx+table.x), (ball.y+tot*dy+table.y));
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continue;
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}
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point zero=point(0, 0, 0);
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point first=point(sti*dx+ball.x, sti*dy+ball.y, 0);
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int dir=cross(zero, first, ball);
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double ref=angle(ball-first, zero-first);
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double dis=cos(ref)*table.r*2;
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double v=sqrt(dx*dx+dy*dy);
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tot-=sti;
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double len=tot*v;
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double dti=len/dis;
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ll lti=(ll)(dti+eps);
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double perti=dis/v;
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double left=tot-perti*lti;
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double pang=(pi-2*ref)*lti;
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double stang=atan2(first.y, first.x);
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stang=stang+pang*dir;
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point now=point(cos(stang)*table.r, sin(stang)*table.r, 0);
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double vang=stang+(pi-2*ref)*dir;
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point next=point(cos(vang)*table.r, sin(vang)*table.r, 0);
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double rate=left/perti;
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point vec=next-now;
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now=now+(vec*rate);
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printf("%.1lf %.1lf\n", now.x+table.x, now.y+table.y);
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}
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return 0;
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}
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