线段是否相交

给定两条线段，判断是否相交

#include<iostream>  #include<algorithm>//use sort#include<cmath>//use fabsusing namespace std;struct Point//点坐标{double x;double y;};struct Line//线段属性{double k;double b;Point p1;Point p2;};void IsIntersect(Line &line1, Line &line2);int main(){Line l1, l2;cin >> l1.p1.x >> l1.p1.y;cin >> l1.p2.x >> l1.p2.y;cin >> l2.p1.x >> l2.p1.y;cin >> l2.p2.x >> l2.p2.y;IsIntersect(l1, l2);return 0;}void GetLine(Line &line)//求出线段的k和b{//不考虑两点横坐标相等line.k = (line.p1.y - line.p2.y) / (line.p1.x - line.p2.x);line.b = line.p1.y - line.k*line.p1.x;}bool JudgeIsIntersect(Line &line,double &pointY)//判断斜率存在的线段的两个纵坐标与直线交点的纵坐标，如果相交，那么交点的纵坐标是在line2两点纵坐标的中间{if (line.p1.y >= line.p2.y){if (pointY <= line.p1.y&&pointY >= line.p2.y)return true;elsereturn false;}if (line.p1.y < line.p2.y){if (pointY <= line.p2.y&&pointY >= line.p1.y)return true;elsereturn false;}}void IsIntersect(Line &line1, Line &line2){//两个变量判断斜率是否存在double line1X = line1.p1.x - line1.p2.x;double line2X = line2.p1.x - line2.p2.x;/*分四种情况1.line1，line2斜率都不存在2.line1斜率不存在，line2存在3.line1存在，line2的斜率不存在4.line1，line2的斜率都存在*///1.//line1，line2斜率都不存在if (line1X == 0 && line2X == 0){if (line1.p1.x == line2.p1.x)//共线：分为两个，相交（重合）与不相交{//如何判断是重合呢还是没有相交呢？//两条线段，四个点，一条直线上，取两条线段横坐标之和即fabs(line1.p1.x - line1.p2.x) + fabs(line2.p1.x - line2.p2.x)//这四个横坐标，有最大也有最小，那么最大到最小的距离double length = a[4] - a[0]//通过比较这两个数值即可判断double a[4] = { line1.p1.y,line1.p2.y,line2.p1.y,line2.p2.y };sort(a, a + 4);double length = a[3] - a[0];double lengthSum = fabs(line1.p1.y - line1.p2.y) + fabs(line2.p1.y - line2.p2.y);if (length > lengthSum)cout << "不相交\n";elsecout << "相交\n";}elsecout << "不想交\n";}//2.//line1斜率不存在，line2存在else if (line1X == 0 && line2X != 0){GetLine(line2);double intersectionY = line2.k*line1.p1.x + line2.b;//直线交点的纵坐标，如果相交，那么交点的纵坐标是在line2两点纵坐标的中间if (JudgeIsIntersect(line2, intersectionY))cout << "相交\n";elsecout << "不相交\n";}//3.//line1存在，line2的斜率不存在else if (line1X != 0 && line2X == 0){GetLine(line1);double intersectionY = line1.k*line2.p1.x + line1.b;if (JudgeIsIntersect(line1, intersectionY))cout << "相交\n";elsecout << "不相交\n";}//4.//line1，line2的斜率都存在else{GetLine(line1);GetLine(line2);if (line1.k == line2.k)//斜率相同{if (line1.b == line2.b)//共线：分为两个，相交（重合）与不相交{double a[4] = { line1.p1.x,line1.p2.x,line2.p1.x,line2.p2.x };sort(a, a + 4);double length = a[3] - a[0];double lengthSum = fabs(line1.p1.x - line1.p2.x) + fabs(line2.p1.x - line2.p2.x);if (length > lengthSum)cout << "不相交\n";elsecout << "相交\n";}elsecout << "不相交\n";}else//斜率不同{double intersectionX = (line2.b - line1.b) / (line1.k - line2.k);double line1XLength = fabs(line1.p1.x - line1.p2.x);double line1Length = fabs(line1.p1.x - intersectionX) + fabs(line1.p2.x - intersectionX);double line2XLength = fabs(line2.p1.x - line2.p2.x);double line2Length = fabs(line2.p1.x - intersectionX) + fabs(line2.p2.x - intersectionX);if ((line1XLength == line1Length) && (line2XLength == line2Length))cout << "相交\n";elsecout << "不相交\n";}}}