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][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;}