一 精度处理
\(eps\)和\(sgn\)
const double eps=1e-8;
int sgn(double x){//判断大小
if(fabs(x)<eps)return 0;
else return x<0?-1:1;
}
二 点
1 点的初始化
向量的表示形式上与点完全相同
重载点运算符，支持向量的四种运算
struct Point{
double x,y;
Point(){}
Point(double x,double y):x(x),y(y){}
Point operator + (Point B){return Point(x+B.x,y+B.y);}
Point operator - (Point B){return Point(x-B.x,y-B.y);}
Point operator * (double k){return Point(x*k,y*k);}
Point operator / (double k){return Point(x/k,y/k);}
};
2 两点间距离
inline double getdis(Point a,Point b){
return hypot(a.x-b.x,a.y-b.y);
}
三 向量的点积，叉积
证明略
点积：
il double Dot(Point a,Point b){
return a.x*b.x+a.y*b.y;
}
叉积：
il double Cross(Point a,Point b){
return a.x*b.y-a.y*b.x;
}
四 线，线段
1 线段的初始化
①.直接用两个点表示线/线段
struct Line{Point p1,p2;};
②.其他nb的写法，咕~
2 两直线位置关系
il int Line_relation(Line v1,Line v2){
if(sgn(Cross(v1.p2-v1.p1,v2.p2-v2.p1))==0){
return 0;
}
return 1;
}//0：共线 /平行 1：相交
3 两线段是否相交
il bool Cross_segment(Point a,Point b,Point c,Point d){
double c1=Cross(b-a,c-a),c2=Cross(b-a,d-a);
double d1=Cross(d-c,a-c),d2=Cross(d-c,b-c);
return sgn(c1)*sgn(c2)<=0 && sgn(d1)*sgn(d2)<=0;
}
4 求两线段的交点
il Point Cross_point(Point a,Point b,Point c,Point d){
double s1=Cross(b-a,c-a);
double s2=Cross(b-a,d-a);
return Point(c.x*s2-d.x*s1,c.y*s2-d.y*s1)/(s2-s1);
}
5 已知横坐标求纵坐标
il double get_y(Line v,double x){
double k=(v.p1.y-v.p2.y)/(v.p1.x-v.p2.x);
double b=v.p1.y-k*v.p1.x;
return k*x+b;
}
6 已知纵坐标求横坐标
il double get_x(Line v,double y){
double k=(v.p1.y-v.p2.y)/(v.p1.x-v.p2.x);
double b=v.p1.y-k*v.p1.x;
return (y-b)/k;
}