计算几何线，点，多边形，位置关系较全模板

Posted 2022-04-23 qieqiemin

const double eps = 1e-6;
int sgn(double x)

    if(fabs(x) < eps)return 0;
    if(x < 0)return -1;
    else return 1;

struct Point

    double x,y;
    Point()
    Point(double _x,double _y)
    
        x = _x;y = _y;
    
    Point operator -(const Point &b)const
    
        return Point(x - b.x,y - b.y);
    
    //叉积
    double operator ^(const Point &b)const
    
        return x*b.y - y*b.x;
    
    //点积
    double operator *(const Point &b)const
    
        return x*b.x + y*b.y;
    
    //绕原点旋转角度B（弧度值），后x,y的变化
    void transXY(double B)
    
        double tx = x,ty = y;
        x = tx*cos(B) - ty*sin(B);
        y = tx*sin(B) + ty*cos(B);
    
;
struct Line

    Point s,e;
    Line()
    Line(Point _s,Point _e)
    
        s = _s;e = _e;
    
    //两直线相交求交点
    //第一个值为0表示直线重合，为1表示平行，为0表示相交,为2是相交
    //只有第一个值为2时，交点才有意义
    pair<int,Point> operator &(const Line &b)const
    
        Point res = s;
        if(sgn((s-e)^(b.s-b.e)) == 0)
        
            if(sgn((s-b.e)^(b.s-b.e)) == 0)
                return make_pair(0,res);//重合
            else return make_pair(1,res);//平行
        
        double t = ((s-b.s)^(b.s-b.e))/((s-e)^(b.s-b.e));
        res.x += (e.x-s.x)*t;
        res.y += (e.y-s.y)*t;
        return make_pair(2,res);
    
;

//判断线段相交
bool inter(Line l1,Line l2)

    return
    max(l1.s.x,l1.e.x) >= min(l2.s.x,l2.e.x) &&
    max(l2.s.x,l2.e.x) >= min(l1.s.x,l1.e.x) &&
    max(l1.s.y,l1.e.y) >= min(l2.s.y,l2.e.y) &&
    max(l2.s.y,l2.e.y) >= min(l1.s.y,l1.e.y) &&
    sgn((l2.s-l1.e)^(l1.s-l1.e))*sgn((l2.e-l1.e)^(l1.s-l1.e)) <= 0 &&
    sgn((l1.s-l2.e)^(l2.s-l2.e))*sgn((l1.e-l2.e)^(l2.s-l2.e)) <= 0;


//判断点在线段上
//判断点在线段上
bool OnSeg(Point P,Line L)

    return
    sgn((L.s-P)^(L.e-P)) == 0 &&
    sgn((P.x - L.s.x) * (P.x - L.e.x)) <= 0 &&
    sgn((P.y - L.s.y) * (P.y - L.e.y)) <= 0;

//判断点在凸多边形内
//点形成一个凸包，而且按逆时针排序（如果是顺时针把里面的<0改为>0）
//点的编号:0~n-1
//返回值：
//-1:点在凸多边形外
//0:点在凸多边形边界上
//1:点在凸多边形内
int inConvexPoly(Point a,Point p[],int n)

    for(int i = 0;i < n;i++)
    
        if(sgn((p[i]-a)^(p[(i+1)%n]-a)) < 0)return -1;
        else if(OnSeg(a,Line(p[i],p[(i+1)%n])))return 0;
    
    return 1;

//判断点在任意多边形内
//射线法，poly[]的顶点数要大于等于3,点的编号0~n-1
//返回值
//-1:点在凸多边形外
//0:点在凸多边形边界上
//1:点在凸多边形内
int inPoly(Point p,Point poly[],int n)

    int cnt;
    Line ray,side;
    cnt = 0;
    ray.s = p;
    ray.e.y = p.y;
    ray.e.x = -100000000000.0;//-INF,注意取值防止越界

    for(int i = 0;i < n;i++)
    
        side.s = poly[i];
        side.e = poly[(i+1)%n];

        if(OnSeg(p,side))return 0;

        //如果平行轴则不考虑
        if(sgn(side.s.y - side.e.y) == 0)
            continue;

        if(OnSeg(side.s,ray))
        
            if(sgn(side.s.y - side.e.y) > 0)cnt++;
        
        else if(OnSeg(side.e,ray))
        
            if(sgn(side.e.y - side.s.y) > 0)cnt++;
        
        else if(inter(ray,side))
            cnt++;
    
    if(cnt % 2 == 1)return 1;
    else return -1;