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12.cpp
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#define _USE_MATH_DEFINES
#include <iostream>
#include <math.h>
using namespace std;
struct point
{
double x, y;
};
inline double sqr(double num)
{
return num*num;
}
inline double dist(double&xa, double& ya, double&xb, double& yb)
{
return sqrt(sqr(xa-xb)+sqr(ya-yb));
}
inline double dist(point& a, point& b)
{
return sqrt(sqr(a.x-b.x)+sqr(a.y-b.y));
}
//++++++++++++++++++++++++ FUNCTIONS +++++++++++++++++++++++++++
bool itsc(point& a, point& b, point& c, point& d) //Does the tile intersect the painting?
{
bool ans=false;
if(max(a.x, b.x)>=min(c.x, d.x)&&
max(c.x, d.x)>=min(a.x, b.x)&&
max(a.y, b.y)>=min(c.y, d.y)&&
max(c.y, d.y)>=min(a.y, b.y)
)
{
if((c.x-a.x)*(b.y-a.y)-(b.x-a.x)*(c.y-a.y)*(d.x-c.x)*(d.y-c.y)-(b.x-a.x)*(d.y-a.y)<=0)
if((a.x-c.x)*(d.y-c.y)-(d.x-c.x)*(a.y-c.y)*(b.x-c.x)*(d.y-c.y)-(d.x-c.x)*(b.y-c.y)<=0)
ans=true;
}
return ans;
}
void point_itsc(point& a, point& b, point& c, point& d, double& x, double& y, int& k) //Find the point of intersection (Kramer method)
{
double a1, b1, c1, a2, b2, c2, D, Dx, Dy;
k=1;
a1=b.y-a.y;
b1=a.x-b.x;
c1=a.x*b.y-a.y*b.x;
a2=d.y-c.y;
b2=c.x-d.x;
c2=c.x*d.y-d.y*c.x;
D=a1*b2-a2*b1;
Dx=c1*b2-c2*b1;
Dy=a1*c2-a2*c1;
x=Dx/D;
y=Dy/D;
}
int which_case(point& a, point& b, point& c, point& d) //I HATE THIS @!#$% FUNCTION!
{
if ((a.x>=b.x) && (a.y>=b.y) && (b.x>=c.x) && (b.y>=c.y) && (c.x>=d.x) && (c.y>=d.y) ||
(a.x>=b.x) && (a.y<=b.y) && (b.x>=c.x) && (b.y<=c.y) && (c.x>=d.x) && (c.y<=d.y)) return 1;
if ((a.x<=b.x) && (a.y<=b.y) && (b.x<=d.x) && (b.y<=d.y) && (d.x<=c.x) && (d.y<=c.y) ||
(a.x>=b.x) && (a.y<=b.y) && (b.x>=d.x) && (b.y<=d.y) && (d.x>=c.x) && (d.y<=c.y) ||
(a.x>=b.x) && (a.y>=b.y) && (b.x>=d.x) && (b.y>=d.y) && (d.x>=c.x) && (d.y>=c.y) ||
(a.x>=b.x) && (a.y<=b.y) && (b.x>=d.x) && (b.y<=d.y) && (d.x>=c.x) && (d.y<=c.y)) return 2;
if ((b.x<=a.x) && (b.y<=a.y) && (a.x<=c.x) && (a.y<=c.y) && (c.x<=d.x) && (c.y<=d.y) ||
(b.x>=a.x) && (b.y<=a.y) && (a.x>=c.x) && (a.y<=c.y) && (c.x>=d.x) && (c.y<=d.y) ||
(b.x>=a.x) && (b.y>=a.y) && (a.x>=c.x) && (a.y>=c.y) && (c.x>=d.x) && (c.y>=d.y) ||
(b.x>=a.x) && (b.y<=a.y) && (a.x>=c.x) && (a.y<=c.y) && (c.x>=d.x) && (c.y<=d.y)) return 3;
if ((b.x<=a.x) && (b.y<=a.y) && (a.x<=d.x) && (a.y<=d.y) && (d.x<=c.x) && (d.y<=c.y) ||
(b.x>=a.x) && (b.y<=a.y) && (a.x>=d.x) && (a.y<=d.y) && (d.x>=c.x) && (d.y<=c.y) ||
(b.x>=a.x) && (b.y>=a.y) && (a.x>=d.x) && (a.y>=d.y) && (d.x>=c.x) && (d.y>=c.y) ||
(b.x>=a.x) && (b.y<=a.y) && (a.x>=d.x) && (a.y<=d.y) && (d.x>=c.x) && (d.y<=c.y)) return 4;
if ((a.x<=d.x) && (a.y<=d.y) && (d.x<=b.x) && (d.y<=b.y) && (b.x<=c.x) && (b.y<=c.y) ||
(a.x>=d.x) && (a.y<=d.y) && (d.x>=b.x) && (d.y<=b.y) && (b.x>=c.x) && (b.y<=c.y) ||
(a.x>=d.x) && (a.y>=d.y) && (d.x>=b.x) && (d.y>=b.y) && (b.x>=c.x) && (b.y>=c.y) ||
(a.x>=d.x) && (a.y<=d.y) && (d.x>=b.x) && (d.y<=b.y) && (b.x>=c.x) && (b.y<=c.y)) return 5;
if ((a.x<=d.x) && (a.y<=d.y) && (d.x<=c.x) && (d.y<=c.y) && (c.x<=b.x) && (c.y<=b.y) ||
(a.x>=d.x) && (a.y<=d.y) && (d.x>=c.x) && (d.y<=c.y) && (c.x>=b.x) && (c.y<=b.y) ||
(a.x>=d.x) && (a.y>=d.y) && (d.x>=c.x) && (d.y>=c.y) && (c.x>=b.x) && (c.y>=b.y) ||
(a.x>=d.x) && (a.y<=d.y) && (d.x>=c.x) && (d.y<=c.y) && (c.x>=b.x) && (c.y<=b.y)) return 6;
if ((a.x<=c.x) && (a.y<=c.y) && (c.x<=b.x) && (c.y<=b.y) && (b.x<=d.x) && (b.y<=d.y) ||
(a.x>=c.x) && (a.y<=c.y) && (c.x>=b.x) && (c.y<=b.y) && (b.x>=d.x) && (b.y<=d.y) ||
(a.x>=c.x) && (a.y>=c.y) && (c.x>=b.x) && (c.y>=b.y) && (b.x>=d.x) && (b.y>=d.y) ||
(a.x>=c.x) && (a.y<=c.y) && (c.x>=b.x) && (c.y<=b.y) && (b.x>=d.x) && (b.y<=d.y)) return 7;
if ((a.x<=c.x) && (a.y<=c.y) && (c.x<=d.x) && (c.y<=d.y) && (d.x<=b.x) && (d.y<=b.y) ||
(a.x>=c.x) && (a.y<=c.y) && (c.x>=d.x) && (c.y<=d.y) && (d.x>=b.x) && (d.y<=b.y) ||
(a.x>=c.x) && (a.y>=c.y) && (c.x>=d.x) && (c.y>=d.y) && (d.x>=b.x) && (d.y>=b.y) ||
(a.x>=c.x) && (a.y<=c.y) && (c.x>=d.x) && (c.y<=d.y) && (d.x>=b.x) && (d.y<=b.y)) return 8;
if ((b.x<=c.x) && (b.y<=c.y) && (c.x<=a.x) && (c.y<=a.y) && (a.x<=d.x) && (a.y<=d.y) ||
(b.x>=c.x) && (b.y<=c.y) && (c.x>=a.x) && (c.y<=a.y) && (a.x>=d.x) && (a.y<=d.y) ||
(b.x>=c.x) && (b.y>=c.y) && (c.x>=a.x) && (c.y>=a.y) && (a.x>=d.x) && (a.y>=d.y) ||
(b.x>=c.x) && (b.y<=c.y) && (c.x>=a.x) && (c.y<=a.y) && (a.x>=d.x) && (a.y<=d.y)) return 9;
if ((b.x<=d.x) && (b.y<=d.y) && (d.x<=a.x) && (d.y<=a.y) && (a.x<=c.x) && (a.y<=c.y) ||
(b.x>=d.x) && (b.y<=d.y) && (d.x>=a.x) && (d.y<=a.y) && (a.x>=c.x) && (a.y<=c.y) ||
(b.x>=d.x) && (b.y>=d.y) && (d.x>=a.x) && (d.y>=a.y) && (a.x>=c.x) && (a.y>=c.y) ||
(b.x>=d.x) && (b.y<=d.y) && (d.x>=a.x) && (d.y<=a.y) && (a.x>=c.x) && (a.y<=c.y)) return 10;
if ((c.x<=a.x) && (c.y<=a.y) && (a.x<=b.x) && (a.y<=b.y) && (b.x<=d.x) && (b.y<=d.y) ||
(c.x>=a.x) && (c.y<=a.y) && (a.x>=b.x) && (a.y<=b.y) && (b.x>=d.x) && (b.y<=d.y) ||
(c.x>=a.x) && (c.y>=a.y) && (a.x>=b.x) && (a.y>=b.y) && (b.x>=d.x) && (b.y>=d.y) ||
(c.x>=a.x) && (c.y<=a.y) && (a.x>=b.x) && (a.y<=b.y) && (b.x>=d.x) && (b.y<=d.y)) return 11;
if ((c.x<=b.x) && (c.y<=b.y) && (b.x<=a.x) && (b.y<=a.y) && (a.x<=d.x) && (a.y<=d.y) ||
(c.x>=b.x) && (c.y<=b.y) && (b.x>=a.x) && (b.y<=a.y) && (a.x>=d.x) && (a.y<=d.y) ||
(c.x>=b.x) && (c.y>=b.y) && (b.x>=a.x) && (b.y>=a.y) && (a.x>=d.x) && (a.y>=d.y) ||
(c.x>=b.x) && (c.y<=b.y) && (b.x>=a.x) && (b.y<=a.y) && (a.x>=d.x) && (a.y<=d.y)) return 12;
}
double line(point& a, point& b, point& c, point& d, double& H)
{
double a1, a2, a3, b2, b3, c3;
int tmp;
a1=dist(a, b);
a2=dist(a, c);
a3=dist(a, d);
b2=dist(b, c);
b3=dist(b, d);
c3=dist(c, d);
tmp=which_case(a, b, c, d);
if(tmp==5) {
if(sqrt(sqr(a1)-sqr(a3))<=H)
return a1*atan(sqrt(sqr(a1)-sqr(a3))/a3);
else
return a1*atan(H/sqrt(sqr(a1)-sqr(H)));
}
if(tmp==6) {
if(sqrt(sqr(a1)-sqr(a3))<=H)
return a1*(atan(sqrt(sqr(a1)-sqr(a3))/a3)-atan(sqrt(sqr(a1)-sqr(a2))/a2));
else
if(sqrt(sqr(a1)-sqr(a2))<H&&a2!=0)
return a1*(atan(H/sqrt(sqr(a1)-sqr(H)))-atan(sqrt(sqr(a1)-sqr(a2))/a2));
}
if(tmp==7) {
if(sqrt(sqr(a1)-sqr(a2))<=H)
return a1*atan(sqrt(sqr(a1)-sqr(a2))/a2);
else
return a1*atan(H/sqrt(sqr(a1)-sqr(H)));
}
if(tmp==8) {
if(sqrt(sqr(a1)-sqr(a2))<=H)
return a1*(atan(sqrt(sqr(a1)-sqr(a2))/a2)-atan(sqrt(sqr(a1)-sqr(a3))/a3));
else
if(sqrt(sqr(a1)-sqr(a2))<H&&a3!=0)
return a1*(atan(H/sqrt(sqr(a1)-sqr(H)))-atan(sqrt(sqr(a1)-sqr(a3))/a3));
}
if(tmp==9) {
if(a1<=H)
return a1*(M_PI/2-atan(sqrt(sqr(a1)-sqr(a2))/a2));
else
if(sqrt(sqr(a1)-sqr(a2))<H)
return a1*(atan(H/sqrt(sqr(a1)-sqr(H)))-atan(sqrt(sqr(a1)-sqr(a2))/a2));
}
if(tmp==10) {
if(a1<=H)
return a1*(M_PI/2-atan(sqrt(sqr(a1)-sqr(a3))/a3));
else
if(sqrt(sqr(a1)-sqr(a3))<H)
return a1*(atan(H/sqrt(sqr(a1)-sqr(H)))-atan(sqrt(sqr(a1)-sqr(a3))/a3));
}
if(tmp==11||tmp==12) {
if(a1<=H)
return a1*M_PI/2;
else
return a1*atan(H/sqrt(sqr(a1)-sqr(H)));
}
return 0;
}
//++++++++++++++++++++++++ MAIN ++++++++++++++++++++++++++++++++
int main()
{
point A, B, C, D;
double H, res;
cin >> A.x >> A.y;
cin >> B.x >> B.y;
cin >> C.x >> C.y;
cin >> D.x >> D.y;
cin >> H;
double a, b, c, x, y, s, s1;
int k;
a=B.y-A.y;
b=A.x-B.x;
c=A.x*B.y-A.y*B.x;
if((a*C.x+b*C.y==c)&&(a*D.x+b*D.y==c))
res=line(A, B, C, D, H);
else
{
if(itsc(A, B, C, D)) {
point_itsc(A, B, C, D, x, y, k);
if(k>0) {
s=dist(A.x, A.y, x, y);
s1=dist(A.x, A.y, B.x, B.y);
if(s1>s)
res=sqrt(sqr(s1)-sqr(s));
if(res>H)
res=H;
if((x==C.x&&y==C.y||(x==D.x&&y==D.y)))
res=0;
if(!s)
res=0;
}
else
res=0;
}
printf("%.3lf", res);
}
return 0;
}