POJ1269_Intersecting Lines(幾何/叉積判斷直線位置關係)

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解題報告

題目傳送門

題意：

判斷直線的位置關係（平行，重合，相交）

思路：

兩直線可以用叉積來判斷位置關係。

AB直線和CD直線

平行的話端點C和端點D會在直線AB的同一側。

重合的話在直線AB上。

剩下就是相交。

求兩直線交點可以用面積比和邊長比來求。

看下面的圖就知道了，推導就比較容易了

#include <iostream>#include <cstring>#include <cstdio>#define eps 1e-6#define zero(x) (((x)>0?(x):-(x))>eps)using namespace std;struct Point{    double x,y;};struct L{    Point l,r;};double xmulti(Point a,Point b,Point p){    return (b.x-a.x)*(p.y-a.y)-(p.x-a.x)*(b.y-a.y);}int main(){    int n,i,j;    scanf("%d",&n);    cout<<"INTERSECTING LINES OUTPUT"<<endl;    L l1,l2;    Point p;    for(i=0; i<n; i++)    {        scanf("%lf%lf%lf%lf%lf%lf%lf%lf",&l1.l.x,&l1.l.y,&l1.r.x,&l1.r.y,&l2.l.x,&l2.l.y,&l2.r.x,&l2.r.y);        double a,b,c,d;        a=xmulti(l1.l,l1.r,l2.l);//c        b=xmulti(l1.l,l1.r,l2.r);//d        c=xmulti(l2.l,l2.r,l1.l);        d=xmulti(l2.l,l2.r,l1.r);        if(a==0&&b==0)            cout<<"LINE"<<endl;        else if(a*b>0&&c*d>0)        {            cout<<"NONE"<<endl;        }        else        {            p.x=(b*l2.l.x-a*l2.r.x)/(b-a);            p.y=(b*l2.l.y-a*l2.r.y)/(b-a);            printf("POINT %.2lf %.2lf\n",p.x,p.y);        }    }    cout<<"END OF OUTPUT"<<endl;}

Intersecting Lines

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 10764		Accepted: 4803

Description

We all know that a pair of distinct points on a plane defines a line and that a pair of lines on a plane will intersect in one of three ways: 1) no intersection because they are parallel, 2) intersect in a line because they are on top of one another (i.e. they are the same line), 3) intersect in a point. In this problem you will use your algebraic knowledge to create a program that determines how and where two lines intersect. 
Your program will repeatedly read in four points that define two lines in the x-y plane and determine how and where the lines intersect. All numbers required by this problem will be reasonable, say between -1000 and 1000. 

Input

The first line contains an integer N between 1 and 10 describing how many pairs of lines are represented. The next N lines will each contain eight integers. These integers represent the coordinates of four points on the plane in the order x1y1x2y2x3y3x4y4. Thus each of these input lines represents two lines on the plane: the line through (x1,y1) and (x2,y2) and the line through (x3,y3) and (x4,y4). The point (x1,y1) is always distinct from (x2,y2). Likewise with (x3,y3) and (x4,y4).

Output

There should be N+2 lines of output. The first line of output should read INTERSECTING LINES OUTPUT. There will then be one line of output for each pair of planar lines represented by a line of input, describing how the lines intersect: none, line, or point. If the intersection is a point then your program should output the x and y coordinates of the point, correct to two decimal places. The final line of output should read "END OF OUTPUT".

Sample Input

50 0 4 4 0 4 4 05 0 7 6 1 0 2 35 0 7 6 3 -6 4 -32 0 2 27 1 5 18 50 3 4 0 1 2 2 5

Sample Output

INTERSECTING LINES OUTPUTPOINT 2.00 2.00NONELINEPOINT 2.00 5.00POINT 1.07 2.20END OF OUTPUT

Source

Mid-Atlantic 1996