POJ 1408 Fishnet 两线段交点坐标

设线段v1v2，u1u2。

t = (v2-v1)*(u1-v1)/(v2-v1)*(u2-u1);  即两个平行四边形的面积之比。

交点坐标为p = {u1.x + (u2.x-u1.x)*t , u1.y + (u2.y-u.y)*t};

前提是两线段相交。

#include <cstdio>
#include <cmath>
#include <algorithm>

using namespace std;

struct P
{
double x,y;
}t[35],b[35],l[35],r[35],fishnet[35][35];

double CrossProduct(P a1,P a2,P b1,P b2)
{
P v1 = {a1.x - a2.x,a1.y - a2.y};
P v2 = {b1.x - b2.x,b1.y - b2.y};
return (v1.x*v2.y - v1.y*v2.x);
}

P CalLineCrossPosition(P a1,P a2,P b1,P b2)
{

double t;
t = fabs(CrossProduct(a1,b1,a1,a2))/fabs(CrossProduct(a1,a2,b1,b2));
P p = {b1.x + (b2.x-b1.x)*t,b1.y + (b2.y-b1.y)*t};
return p;
}

int main()
{
int n,i,j;
double MaxArea,TempArea;
while(scanf("%d",&n) && n)
{
for(i = 1;i <= n ; ++i)
{
b[i].y = 0;
scanf("%lf",&b[i].x);
}
for(i = 1;i <= n ; ++i)
{
t[i].y = 1;
scanf("%lf",&t[i].x);
}
for(i = 1;i <= n ; ++i)
{
l[i].x = 0;
scanf("%lf",&l[i].y);
}
for(i = 1;i <= n ; ++i)
{
r[i].x = 1;
scanf("%lf",&r[i].y);
}

++n;

for(i = 1;i < n; ++i)
{
for(j = 1;j < n; ++j)
{
fishnet[i][j] = CalLineCrossPosition(l[i],r[i],t[j],b[j]);
}
}

for(i = 1;i < n; ++i)
{
fishnet[i]
= r[i];
fishnet[i][0] = l[i];
fishnet[0][i] = b[i];
fishnet
[i] = t[i];
}

MaxArea = -199;

fishnet[0][0].x = 0;
fishnet[0][0].y = 0;
fishnet[0]
.x = 1;
fishnet[0]
.y = 0;
fishnet
[0].x = 0;
fishnet
[0].y = 1;
fishnet

.x = 1;
fishnet

.y = 1;

for(i = 0;i < n; ++i)
{
for(j = 0;j < n; ++j)
{
TempArea = (fabs(CrossProduct(fishnet[i][j],fishnet[i+1][j],fishnet[i][j],fishnet[i][j+1]))+fabs(CrossProduct(fishnet[i+1][j+1],fishnet[i+1][j],fishnet[i+1][j+1],fishnet[i][j+1])))/2;
if(MaxArea < TempArea)
MaxArea = TempArea;
}
}
printf("%.6f\n",MaxArea);
}
return 0;
}