计算几何基础知识--求两个线段的交点

Posted 2021-12-10 biu~跃哥冲冲冲

求两个线段的交点

1、计算推导过程（参考：AcWing y总计算几何基础知识讲解）
2、简单的示例代码：

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define x first
#define y second
using namespace std;
typedef long long ll;
typedef pair<double, double> PDD;
PDD operator-(PDD a, PDD b) {
	return { a.x - b.x,a.y - b.y };
}
PDD operator+(PDD a, PDD b) {
	return { a.x + b.x,a.y + b.y };
}
double cross(PDD a, PDD b) {
	return a.x * b.y - b.x * a.y;
}
double area(PDD a, PDD b, PDD c) {
	return cross(b - a, c - a);
}
PDD get_lines_interpoint(PDD p,PDD v,PDD q,PDD w) {
	PDD u = p - q;//向量AC
	double t = cross(w, u) / cross(v, w);//三角形面积的2倍 之比
	return { p.x + v.x * t, p.y + v.y * t };//交点坐标
}
int main() {
	PDD A = { 0,0 };
	PDD B = { 2,2 };
	PDD C = { 0,2 };
	PDD D = { 2,0 };
	PDD E = get_lines_interpoint(A, B - A, C, D - C);
	cout << E.x << " " << E.y;
	return 0;
}