学步园

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][n] = r[i];
			fishnet[i][0] = l[i];
			fishnet[0][i] = b[i];
			fishnet[n][i] = t[i];
		}

		MaxArea = -199;
		
		
		fishnet[0][0].x = 0;
		fishnet[0][0].y = 0;
		fishnet[0][n].x = 1;
		fishnet[0][n].y = 0;
		fishnet[n][0].x = 0;
		fishnet[n][0].y = 1;
		fishnet[n][n].x = 1;
		fishnet[n][n].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;
}