已知线段起点和终点坐标,求点到线段垂足,并判断垂直是否在线段上,用c++写出来
时间: 2024-02-21 09:02:11 浏览: 21
以下是一个求点到线段垂足,并判断垂足是否在线段上的C++代码实现:
```c++
#include <iostream>
#include <cmath>
using namespace std;
struct Point {
double x, y;
};
struct Line {
Point start, end;
};
Point getPerpendicularFoot(Line line, Point point) {
double dx = line.end.x - line.start.x;
double dy = line.end.y - line.start.y;
double u = ((point.x - line.start.x) * dx + (point.y - line.start.y) * dy) / (dx * dx + dy * dy);
Point foot;
foot.x = line.start.x + u * dx;
foot.y = line.start.y + u * dy;
return foot;
}
bool isFootOnLineSegment(Line line, Point foot) {
double min_x = min(line.start.x, line.end.x);
double max_x = max(line.start.x, line.end.x);
double min_y = min(line.start.y, line.end.y);
double max_y = max(line.start.y, line.end.y);
return foot.x >= min_x && foot.x <= max_x && foot.y >= min_y && foot.y <= max_y;
}
int main() {
Line line;
Point point;
cout << "Enter the start point of the line: ";
cin >> line.start.x >> line.start.y;
cout << "Enter the end point of the line: ";
cin >> line.end.x >> line.end.y;
cout << "Enter the point: ";
cin >> point.x >> point.y;
Point foot = getPerpendicularFoot(line, point);
cout << "The perpendicular foot is (" << foot.x << ", " << foot.y << ")" << endl;
if (isFootOnLineSegment(line, foot)) {
cout << "The foot is on the line segment" << endl;
} else {
cout << "The foot is not on the line segment" << endl;
}
return 0;
}
```
这个程序首先定义了一个 `Point` 结构体和一个 `Line` 结构体用来表示点和线段。然后定义了两个函数, `getPerpendicularFoot` 函数用来求点到线段的垂足, `isFootOnLineSegment` 函数用来判断垂足是否在线段上。
在 `getPerpendicularFoot` 函数中,首先计算线段的方向向量,然后计算垂足到线段起点的距离与线段长度之比,从而得到垂足的坐标。在 `isFootOnLineSegment` 函数中,首先计算线段的最小和最大坐标,然后判断垂足是否在线段内部。
最后,在 `main` 函数中,程序读入线段的起点和终点坐标以及点的坐标,然后调用 `getPerpendicularFoot` 函数求出垂足,并调用 `isFootOnLineSegment` 函数判断垂足是否在线段上。