计算几何-求线段交点算法和代码（C++语言）
//跨立判断bool isLineSegmentCross(const Point &P1,const Point &P2,const Point &Q1,const Point &Q2)
{
if(
((Q1.x-P1.x)*(Q1.y-Q2.y)-(Q1.y-P1.y)*( Q1.x-Q2.x)) * ((Q1.x-P2.x)*(Q1.y-Q2.y)-(Q1.y-P2.y)*(Q1.x-Q2.x)) < 0 &&
((P1.x-Q1.x)*(P1.y-P2.y)-(P1.y-Q1.y)*(P1.x-P2.x)) * ((P1.x-Q2.x)*(P1.y-P2.y)-(P1.y-Q2.y)*( P1.x-P2.x)) < 0
)
return true;
else
return false;
}
#include<stdio.h>
#define N 10002
/**
算法适用于整形点，不适用于浮点型
**/
typedef struct Point
{
int x;
int y;
}Point;
double min(int x, int y)
{
return x<y?x:y;
}
double max(int x, int y)
{
return x>y?x:y;
}
//排斥实验
bool IsRectCross(const Point &p1,const Point &p2,const Point &q1,const Point &q2)
{
bool ret = min(p1.x,p2.x) <= max(q1.x,q2.x) &&
min(q1.x,q2.x) <= max(p1.x,p2.x) &&
min(p1.y,p2.y) <= max(q1.y,q2.y) &&
min(q1.y,q2.y) <= max(p1.y,p2.y);
return ret;
}
/**这段代码不能得到正确答案，故注释
//跨立判断
bool IsLineSegmentCross(const Point &pFirst1,const Point &pFirst2,const Point &pSecond1,const Point &pSecond2)
{
long line1,line2;
line1 = pFirst1.x * (pSecond1.y - pFirst2.y) +
pFirst2.x * (pFirst1.y - pSecond1.y) +
pSecond1.x * (pFirst2.y - pFirst1.y);
line2 = pFirst1.x * (pSecond2.y - pFirst2.y) +
pFirst2.x * (pFirst1.y - pSecond2.y) +
pSecond2.x * (pFirst2.y - pFirst1.y);
if (((line1 ^ line2) >= 0) && !(line1 == 0 && line2 == 0))
return false;
line1 = pSecond1.x * (pFirst1.y - pSecond2.y) +
pSecond2.x * (pSecond1.y - pFirst1.y) +
pFirst1.x * (pSecond2.y - pSecond1.y);
line2 = pSecond1.x * (pFirst2.y - pSecond2.y) +
pSecond2.x * (pSecond1.y - pFirst2.y) +
pFirst2.x * (pSecond2.y - pSecond1.y);
if (((line1 ^ line2) >= 0) && !(line1 == 0 && line2 == 0))
return false;
return true;
}
**/
//跨立判断
bool IsLineSegmentCross(const Point &P1,const Point &P2,const Point &Q1,const Point &Q2)
{
if(
((Q1.x-P1.x)*(Q1.y-Q2.y)-(Q1.y-P1.y)*( Q1.x-Q2.x)) * ((Q1.x-P2.x)*(Q1.y-Q2.y)-(Q1.y-P2.y)*(Q1.x-Q2.x)) < 0 ||
((P1.x-Q1.x)*(P1.y-P2.y)-(P1.y-Q1.y)*(P1.x-P2.x)) * ((P1.x-Q2.x)*(P1.y-P2.y)-(P1.y-Q2.y)*( P1.x-P2.x)) < 0
)
return true;
else
return false;
}
/**
求线段P1P2与Q1Q2的交点。
先进行快速排斥实验和跨立实验确定有交点再进行计算。
交点（x,y）使用引用返回。
没有验证过
**/
bool GetCrossPoint(const Point &p1,const Point &p2,const Point &q1,const Point &q2,long &x,long &y)
{
if(IsRectCross(p1,p2,q1,q2))
{
if (IsLineSegmentCross(p1,p2,q1,q2))
{
//求交点
long tmpLeft,tmpRight;
tmpLeft = (q2.x - q1.x) * (p1.y - p2.y) - (p2.x - p1.x) * (q1.y - q2.y);
tmpRight = (p1.y - q1.y) * (p2.x - p1.x) * (q2.x - q1.x) + q1.x * (q2.y - q1.y) * (p2.x - p1.x) - p1.x * (p2.y - p1.y) * (q2.x - q1.x);
x = (int)((double)tmpRight/(double)tmpLeft);
tmpLeft = (p1.x - p2.x) * (q2.y - q1.y) - (p2.y - p1.y) * (q1.x - q2.x);
tmpRight = p2.y * (p1.x - p2.x) * (q2.y - q1.y) + (q2.x- p2.x) * (q2.y - q1.y) * (p1.y - p2.y) - q2.y * (q1.x - q2.x) * (p2.y - p1.y);
y = (int)((double)tmpRight/(double)tmpLeft);
return true;
}
}
return false;
}
#include <stdio.h>
#include <math.h>
const int N = 100010;
int mark;
struct Point
{
double x,y;
};
struct stline
{
Point a,b;
} line1,line2, p;
int dblcmp(double a,double b)
{
if (fabs(a-b)<=1E-6) return 0;
if (a>b) return 1;
else return -1;
}
//***************点积判点是否在线段上***************
double dot(double x1,double y1,double x2,double y2) //点积
{
return x1*x2+y1*y2;
}
int point采用on采用line(Point a,Point b,Point c) //求a点是不是在线段bc上，>0不在，=0与端点重合，<0在。
{
return dblcmp(dot(b.x-a.x,b.y-a.y,c.x-a.x,c.y-a.y),0);
}
//**************************************************
double cross(double x1,double y1,double x2,double y2)
{
return x1*y2-x2*y1;
}
double ab采用cross采用ac(Point a,Point b,Point c) //ab与ac的叉积
{
return cross(b.x-a.x,b.y-a.y,c.x-a.x,c.y-a.y);
}
int ab采用cross采用cd (Point a,Point b,Point c,Point d) //求ab是否与cd相交，交点为p。1规范相交，0交点是一线段的端点，-1不相交。
{
double s1,s2,s3,s4;
int d1,d2,d3,d4;
Point p;
d1=dblcmp(s1=ab采用cross采用ac(a,b,c),0);
d2=dblcmp(s2=ab采用cross采用ac(a,b,d),0);
d3=dblcmp(s3=ab采用cross采用ac(c,d,a),0);
d4=dblcmp(s4=ab采用cross采用ac(c,d,b),0);
//如果规范相交则求交点
if ((d1^d2)==-2 && (d3^d4)==-2)
{
p.x=(c.x*s2-d.x*s1)/(s2-s1);
p.y=(c.y*s2-d.y*s1)/(s2-s1);
return 1;
}
//如果不规范相交
if (d1==0 && point采用on采用line(c,a,b)<=0)
{
p=c;
return 0;
}
if (d2==0 && point采用on采用line(d,a,b)<=0)
{
p=d;
return 0;
}
if (d3==0 && point采用on采用line(a,c,d)<=0)
{
p=a;
return 0;
}
if (d4==0 && point采用on采用line(b,c,d)<=0)
{
p=b;
return 0;
}
//如果不相交
return -1;
} Point getCrossPoint(Segment s1, Segment s2) {
Vector base = s2.p2 - s2.p1;
double d1 = abs(cross(base, s1.p1 - s2.p1));
double d2 = abs(cross(base, s1.p2 - s2.p1));
double t = d1 / (d1 + d2);
return s1.p1 + (s1.p2 - s1.p1) * t;
} #include<stdio.h>
#include<iostream>
#include<cmath>
using namespace std;
#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)
class Point {//Point类，点
public:
double x, y;
Point(double x = 0, double y = 0): x(x), y(y) {}
Point operator + (Point p) { return Point(x + p.x, y + p.y); }
Point operator - (Point p) { return Point(x - p.x, y - p.y); }
Point operator * (double a) { return Point(a * x, a * y); }
Point operator / (double a) { return Point(x / a, y / a); }
double abs() { return sqrt(norm()); }
double norm() { return x * x + y * y; }
bool operator < (const Point &p) const {
return x != p.x ? x < p.x : y < p.y;
}
bool operator == (const Point &p) const {
return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
}
};
typedef Point Vector;//Vector类，向量
struct Segment{//Segment 线段
Point p1, p2;
};
double dot(Vector a, Vector b) {//内积
return a.x * b.x + a.y * b.y;
}
double cross(Vector a, Vector b) {//外积
return a.x*b.y - a.y*b.x;
}
Point getCrossPoint(Segment s1, Segment s2) {
Vector base = s2.p2 - s2.p1;
double d1 = abs(cross(base, s1.p1 - s2.p1));
double d2 = abs(cross(base, s1.p2 - s2.p1));
double t = d1 / (d1 + d2);
return s1.p1 + (s1.p2 - s1.p1) * t;
}
int main(){
int q;
cin>>q;
Segment s1, s2;
Point p;
while(q--){
cin>>s1.p1.x>>s1.p1.y>>s1.p2.x>>s1.p2.y>>s2.p1.x>>s2.p1.y>>s2.p2.x>>s2.p2.y;
p = getCrossPoint(s1, s2);
printf("%.10f %.10f\n", p.x, p.y);
}
}
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