• 【模板】凸包向内推进求不严格的半平面交——poj3384


    想不明白这题写严格的半平面交为什么会错

    /*
    凸包所有边向内推进r
    */
    
    #include<iostream>
    #include<cstring>
    #include<cstdio>
    #include<cmath>
    #include<vector>
    #include<algorithm>
    #include<queue>
    using namespace std;
    #define N 205
    
    typedef double db;
    const db eps=1e-10;
    const db pi=acos(-1.0);
    int sign(db k){
        if (k>eps) return 1; else if (k<-eps) return -1; return 0;
    }
    int cmp(db k1,db k2){return sign(k1-k2);}
    int inmid(db k1,db k2,db k3){return sign(k1-k3)*sign(k2-k3)<=0;}// k3 在 [k1,k2] 内 
    struct point{
        db x,y;
        point(){}
        point(db x,db y):x(x),y(y){}
        point operator + (const point &k1) const{return point(k1.x+x,k1.y+y);}
        point operator - (const point &k1) const{return point(x-k1.x,y-k1.y);}
        point operator * (db k1) const{return point(x*k1,y*k1);}
        point operator / (db k1) const{return point(x/k1,y/k1);}
        db abs(){return sqrt(x*x+y*y);}
        db abs2(){return x*x+y*y;}
        db dis(point k1){return ((*this)-k1).abs();}
        int getP() const{return sign(y)==1||(sign(y)==0&&sign(x)>=0);}
        point turn90(){return point(-y,x);}  
        point unit(){db w=abs(); return point(x/w,y/w);}
    };
    int inmid(point k1,point k2,point k3){return inmid(k1.x,k2.x,k3.x)&&inmid(k1.y,k2.y,k3.y);}
    db cross(point k1,point k2){return k1.x*k2.y-k1.y*k2.x;}
    db dot(point k1,point k2){return k1.x*k2.x+k1.y*k2.y;}
    int comp(point k1,point k2){
        if(k1.getP()==k2.getP())return sign(cross(k1,k2))>0;
        return k1.getP()<k2.getP();
    }
    
    struct line{
        point p[2];
        line(point k1,point k2){p[0]=k1; p[1]=k2;}
        point& operator [] (int k){return p[k];}
        int include(point k){return sign(cross(p[1]-p[0],k-p[0]))>=0;}//k在l左端 
        point dir(){return p[1]-p[0];}
        line push(db eps){//向左边平移eps 
            point delta = (p[1]-p[0]).turn90().unit()*eps;
            return line(p[0]+delta,p[1]+delta); 
        }
    };
    
    //输入的点是顺时针:ans<0,逆时针:ans>0 
    bool judge(vector<point> v){
        double ans=0;
        for(int i=1;i<v.size()-1;i++)
            ans+=cross(v[i]-v[0],v[i+1]-v[0]);
        return ans>0;
    }
    point getLL(point k1,point k2,point k3,point k4){
        db w1=cross(k1-k3,k4-k3),w2=cross(k4-k3,k2-k3); return (k1*w2+k2*w1)/(w1+w2);
    }
    point getLL(line k1,line k2){return getLL(k1[0],k1[1],k2[0],k2[1]);}
    int parallel(line k1,line k2){return sign(cross(k1.dir(),k2.dir()))==0;}
    int sameDir(line k1,line k2){return parallel(k1,k2)&&sign(dot(k1.dir(),k2.dir()))==1;}
    int checkpos(line k1,line k2,line k3){return k3.include(getLL(k1,k2));}//k1,k2交点在 k3 左端 
    int operator<(line k1,line k2){//按极角排序,角度相同的从左到右排 
        if(sameDir(k1,k2))return k2.include(k1[0]);
        return comp(k1.dir(),k2.dir());
    } 
    vector<line> getHL(vector<line> L){ // 求半平面交 , 半平面是逆时针方向 , 输出按照逆时针
        sort(L.begin(),L.end()); deque<line> q;
        for (int i=0;i<(int)L.size();i++){
            if (i&&sameDir(L[i],L[i-1])) continue;
            while (q.size()>1&&!checkpos(q[q.size()-2],q[q.size()-1],L[i])) q.pop_back();
            while (q.size()>1&&!checkpos(q[1],q[0],L[i])) q.pop_front();
            q.push_back(L[i]);
        }
        while (q.size()>2&&!checkpos(q[q.size()-2],q[q.size()-1],q[0])) q.pop_back();
        while (q.size()>2&&!checkpos(q[1],q[0],q[q.size()-1])) q.pop_front();
        vector<line>ans; for (int i=0;i<q.size();i++) ans.push_back(q[i]);
        return ans;
    }
    
    vector<point>v;
    vector<line>L;
    int n;
    db r;
    
    
    int main(){
        cin>>n>>r;
            v.clear();L.clear();
            for(int i=1;i<=n;i++){
                point t;cin>>t.x>>t.y;
                v.push_back(t);
            }
            reverse(v.begin(),v.end());
            for(int i=0;i<v.size();i++)
                L.push_back(line(v[i],v[(i+1)%v.size()]));
            for(int i=0;i<v.size();i++)
                L[i]=L[i].push(r);
            vector<line> res = getHL(L);
            v.clear();
            for(int i=0;i<res.size();i++)
                v.push_back(getLL(res[i],res[(i+1)%res.size()]));
            
            int id1=0,id2=0;
            for(int i=0;i<v.size();i++)
                for(int j=i;j<v.size();j++){
                    if(v[i].dis(v[j])>v[id1].dis(v[id2]))
                        id1=i,id2=j;
                }
            if(v[id1].x>v[id2].x)swap(id1,id2);
            printf("%.4f %.4f %.4f %.4f
    ",v[id1].x,v[id1].y,v[id2].x,v[id2].y);        
        
    }
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  • 原文地址:https://www.cnblogs.com/zsben991126/p/12377178.html
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