多边形判断模板

#include <stdlib.h>#include <math.h>#define MAXN 1000#define offset 10000#define eps 1e-8#define zero(x) (((x)>0?(x):-(x))<eps)#define _sign(x) ((x)>eps?1:((x)<-eps?2:0))struct point{double x,y;};struct line{point a,b;};double xmult(point p1,point p2,point p0){    return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);}//判定凸多边形,顶点按顺时针或逆时针给出,允许相邻边共线int is_convex(int n,point* p){    int i,s[3]={1,1,1};    for (i=0;i<n&&s[1]|s[2];i++)        s[_sign(xmult(p[(i+1)%n],p[(i+2)%n],p[i]))]=0;    return s[1]|s[2];}//判定凸多边形,顶点按顺时针或逆时针给出,不允许相邻边共线int is_convex_v2(int n,point* p){    int i,s[3]={1,1,1};    for (i=0;i<n&&s[0]&&s[1]|s[2];i++)        s[_sign(xmult(p[(i+1)%n],p[(i+2)%n],p[i]))]=0;    return s[0]&&s[1]|s[2];}//判点在凸多边形内或多边形边上,顶点按顺时针或逆时针给出int inside_convex(point q,int n,point* p){    int i,s[3]={1,1,1};    for (i=0;i<n&&s[1]|s[2];i++)        s[_sign(xmult(p[(i+1)%n],q,p[i]))]=0;    return s[1]|s[2];}//判点在凸多边形内,顶点按顺时针或逆时针给出,在多边形边上返回0int inside_convex_v2(point q,int n,point* p){    int i,s[3]={1,1,1};    for (i=0;i<n&&s[0]&&s[1]|s[2];i++)        s[_sign(xmult(p[(i+1)%n],q,p[i]))]=0;    return s[0]&&s[1]|s[2];}//判点在任意多边形内,顶点按顺时针或逆时针给出//on_edge表示点在多边形边上时的返回值,offset为多边形坐标上限int inside_polygon(point q,int n,point* p,int on_edge=1){    point q2;    int i=0,count;    while (i<n)        for (count=i=0,q2.x=rand()+offset,q2.y=rand()+offset;i<n;i++)            if (zero(xmult(q,p[i],p[(i+1)%n]))&&(p[i].x-q.x)*(p[(i+1)%n].x-q.x)<eps&&(p[i].y-q.y)*(p[(i+1)%n].y-q.y)<eps)                return on_edge;            else if (zero(xmult(q,q2,p[i])))                break;            else if (xmult(q,p[i],q2)*xmult(q,p[(i+1)%n],q2)<-eps&&xmult(p[i],q,p[(i+1)%n])*xmult(p[i],q2,p[(i+1)%n])<-eps)                count++;    return count&1;}inline int opposite_side(point p1,point p2,point l1,point l2){    return xmult(l1,p1,l2)*xmult(l1,p2,l2)<-eps;}inline int dot_online_in(point p,point l1,point l2){    return zero(xmult(p,l1,l2))&&(l1.x-p.x)*(l2.x-p.x)<eps&&(l1.y-p.y)*(l2.y-p.y)<eps;}//判线段在任意多边形内,顶点按顺时针或逆时针给出,与边界相交返回1int inside_polygon(point l1,point l2,int n,point* p){    point t[MAXN],tt;    int i,j,k=0;    if (!inside_polygon(l1,n,p)||!inside_polygon(l2,n,p))        return 0;    for (i=0;i<n;i++)        if (opposite_side(l1,l2,p[i],p[(i+1)%n])&&opposite_side(p[i],p[(i+1)%n],l1,l2))            return 0;        else if (dot_online_in(l1,p[i],p[(i+1)%n]))            t[k++]=l1;        else if (dot_online_in(l2,p[i],p[(i+1)%n]))            t[k++]=l2;        else if (dot_online_in(p[i],l1,l2))            t[k++]=p[i];    for (i=0;i<k;i++)        for (j=i+1;j<k;j++){            tt.x=(t[i].x+t[j].x)/2;            tt.y=(t[i].y+t[j].y)/2;            if (!inside_polygon(tt,n,p))                return 0;                   }    return 1;}point intersection(line u,line v){    point ret=u.a;    double t=((u.a.x-v.a.x)*(v.a.y-v.b.y)-(u.a.y-v.a.y)*(v.a.x-v.b.x))            /((u.a.x-u.b.x)*(v.a.y-v.b.y)-(u.a.y-u.b.y)*(v.a.x-v.b.x));    ret.x+=(u.b.x-u.a.x)*t;    ret.y+=(u.b.y-u.a.y)*t;    return ret;}point barycenter(point a,point b,point c){    line u,v;    u.a.x=(a.x+b.x)/2;    u.a.y=(a.y+b.y)/2;    u.b=c;    v.a.x=(a.x+c.x)/2;    v.a.y=(a.y+c.y)/2;    v.b=b;    return intersection(u,v);}//多边形重心point barycenter(int n,point* p){    point ret,t;    double t1=0,t2;    int i;    ret.x=ret.y=0;    for (i=1;i<n-1;i++)        if (fabs(t2=xmult(p[0],p[i],p[i+1]))>eps){            t=barycenter(p[0],p[i],p[i+1]);            ret.x+=t.x*t2;            ret.y+=t.y*t2;            t1+=t2;        }    if (fabs(t1)>eps)        ret.x/=t1,ret.y/=t1;    return ret;}