POJ 1269 Intersecting Lines-优快云博客

本文探讨了使用叉积和解析几何方法来判断和求解两条直线是否共线、平行及求交点的数学问题。通过提供具体的代码实现，详细解释了如何通过编程解决问题。

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POJ_1269

可以先用叉积判断两条直线是否共线或者平行，如果有交点再用解析几何的办法就交点即可。

#include<stdio.h>
#include<string.h>
#define zero 1e-8
double x1, y1, x2, y2, x3, y3, x4, y4;
double det(double x1, double y1, double x2, double y2)
{
return x1 * y2 - x2 * y1;
}
double fabs(double x)
{
return x < 0 ? -x : x;
}
int dcmp(double x)
{
if(fabs(x) < zero)
return 0;
if(x < 0)
return -1;
return 1;
}
void solve()
{
double x, y, k1, k2;
if(dcmp(det(x2 - x1, y2 - y1, x4 - x3, y4 - y3)) == 0)
    {
if(dcmp(det(x2 - x1, y2 - y1, x3 - x1, y3 - y1)) == 0)
            printf("LINE\n");
else
            printf("NONE\n");
    }
else
    {
if(dcmp(x2 - x1) == 0)
        {
            x = x1;
            k2 = (y4 - y3) / (x4 - x3);
            y = k2 * (x - x3) + y3;
        }
else if(dcmp(x4 - x3) == 0)
        {
            x = x3;
            k1 = (y2 - y1) / (x2 - x1);
            y = k1 * (x - x1) + y1;
        }
else
        {
            k1 = (y2 - y1) / (x2 - x1);
            k2 = (y4 - y3) / (x4 - x3);
            x = (k1 * x1 - k2 * x3 - y1 + y3) / (k1 - k2);
            y = k1 * (x - x1) + y1;
        }
        printf("POINT %.2lf %.2lf\n", x, y);
    }
}
int main()
{
int t;
    scanf("%d", &t);
    printf("INTERSECTING LINES OUTPUT\n");
while(t --)
    {
        scanf("%lf%lf%lf%lf%lf%lf%lf%lf", &x1, &y1, &x2, &y2, &x3, &y3, &x4, &y4);
        solve();
    }
    printf("END OF OUTPUT\n");
return 0;
}