POJ 1269 Intersecting Lines

题目链接：http://poj.org/problem?id=1269

Intersecting Lines

Time Limit: 1000MS
Memory Limit: 10000KTotal Submissions: 14693
Accepted: 6488

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

思路：判断两条直线是否相交的一个模板题。没什么技巧可言，直接上代码吧！

附上AC代码：

#include <cstdio>#include <cmath>using namespace std;const double eps = 1e-10;struct point{double x, y;point(double x=0, double y=0): x(x), y(y) {}} a, b, c, d;typedef point Vector;Vector operator + (Vector a, Vector b) { return Vector(a.x+b.x, a.y+b.y); }Vector operator - (point a, point b) { return Vector(a.x-b.x, a.y-b.y); }Vector operator * (Vector a, double p) { return Vector(a.x*p, a.y*p); }int dcmp(double x){if (fabs(x) < eps)return 0;return x<0 ? -1 : 1;}double dot(Vector a, Vector b){return a.x*b.x+a.y*b.y;}double length(Vector a){return sqrt(dot(a, a));}double cross(Vector a, Vector b){return a.x*b.y-a.y*b.x;}point get_line_intersection(point p, Vector v, point q, Vector w){Vector u = p-q;double t = cross(w, u)/cross(v, w);return p+v*t;}double distance_to_line(point p, point a, point b){Vector v1=b-a, v2=p-a;return fabs(cross(v1, v2))/length(v1);// 如果不取绝对值,得到的是有向距离}int main(){puts("INTERSECTING LINES OUTPUT");int T;scanf("%d", &T);while (T--){scanf("%lf%lf%lf%lf", &a.x, &a.y, &b.x, &b.y);scanf("%lf%lf%lf%lf", &c.x, &c.y, &d.x, &d.y);Vector v1=b-a, v2=d-c;if (cross(v1, v2)){point t = get_line_intersection(a, v1, c, v2);printf("POINT %.2f %.2f\n", t.x, t.y);}else if (dcmp(distance_to_line(c, a, b)))puts("NONE");elseputs("LINE");}puts("END OF OUTPUT");return 0;}