计算几何学习笔记

没怎么做题，先放个板子，以后再补。

#include<bits/stdc++.h>
namespace my_std{
    using namespace std;
    #define pii pair<int,int>
    #define fir first
    #define sec second
    #define MP make_pair
    #define rep(i,x,y) for (int i=(x);i<=(y);i++)
    #define drep(i,x,y) for (int i=(x);i>=(y);i--)
    #define go(x) for (int i=head[x];i;i=edge[i].nxt)
    #define sz 101010
    typedef long long ll;
    template<typename T>
    inline void read(T& t)
    {
        t=0;char f=0,ch=getchar();
        double d=0.1;
        while(ch>'9'||ch<'0') f|=(ch=='-'),ch=getchar();
        while(ch<='9'&&ch>='0') t=t*10+ch-48,ch=getchar();
        if(ch=='.')
        {
            ch=getchar();
            while(ch<='9'&&ch>='0') t+=d*(ch^48),d*=0.1,ch=getchar();
        }
        t=(f?-t:t);
    }
    template<typename T,typename... Args>
    inline void read(T& t,Args&... args){read(t); read(args...);}
    void file()
    {
        #ifndef ONLINE_JUDGE
        freopen("a.txt","r",stdin);
        #endif
    }
//	inline ll mul(ll a,ll b){ll d=(ll)(a*(double)b/mod+0.5);ll ret=a*b-d*mod;if (ret<0) ret+=mod;return ret;}
}
using namespace my_std;

#define I inline
typedef double db;
const db eps=1e-8;
I int dcmp(db x){return fabs(x)<=eps?0:(x>0?1:-1);}
struct Vector
{
    db x,y;
    Vector(db xx=0,db yy=0){x=xx,y=yy;}
    I const Vector operator + (const Vector &a) const {return Vector(x+a.x,y+a.y);}
    I const Vector operator - (const Vector &a) const {return Vector(x-a.x,y-a.y);}
    I const Vector operator * (const db &a) const {return Vector(x*a,y*a);}
    I const Vector operator / (const db &a) const {return Vector(x/a,y/a);}
    I const bool operator < (const Vector &a) const {return dcmp(x-a.x)==0?dcmp(y-a.y)<0:dcmp(x-a.x)<0;}
    I const bool operator == (const Vector &a) const {return dcmp(x-a.x)==0&&dcmp(y-a.y)==0;}
    I const bool operator != (const Vector &a) const {return dcmp(x-a.x)!=0||dcmp(y-a.y)!=0;}
};
typedef Vector Point;
I Vector Normal(Vector a){return Vector(-a.y,a.x);} // counterclockwise
I db Dot(Vector a,Vector b){return a.x*b.x+a.y*b.y;}
I db Cross(Vector a,Vector b){return a.x*b.y-a.y*b.x;}
I db Len(Vector a){return sqrt(Dot(a,a));}
I db Len2(Vector a){return Dot(a,a);}
I db Angle(Vector a,Vector b){return acos(Dot(a,b)/Len(a)/Len(b));}
I Vector Rotate(Vector a,db rad){return Vector(cos(rad)*a.x-sin(rad)*a.y,sin(rad)*a.x+cos(rad)*a.y);}
struct Line
{
    Point a,b; // a->b
    Line(){}
    Line(Point aa,Point bb){a=aa,b=bb;}
};
I db DisL(Point p,Line l){Vector u=p-l.a,v=l.b-l.a;return fabs(Cross(u,v))/Len(v);} // dist to line
I db DisS(Point p,Point a,Point b) // dist to segment
{
    if (a==b) return Len(p-a);
    Vector v1=b-a,v2=p-a,v3=p-b;
    if (dcmp(Dot(v1,v2))<0) return Len(v2);
    if (dcmp(Dot(v1,v3))>0) return Len(v3);
    return fabs(Cross(v1,v2))/Len(v1);
}
I bool OnLeft(Point p,Line l){return dcmp(Cross(p-l.a,l.b-l.a))<=0;}
I bool OnLine(Point p,Line l){return dcmp(Cross(p-l.a,l.a-l.b))==0;}
I bool OnSeg(Point p,Point a,Point b){return dcmp(Cross(p-a,a-b))==0&&dcmp(Dot(p-a,p-b))<0&&p!=a&&p!=b;}
I Point LI(Line l1,Line l2) // line intersection
{
    Vector v=l1.a-l2.a,v1=l1.b-l1.a,v2=l2.b-l2.a;
    db t=Cross(v,v2)/Cross(v2,v1);
    return l1.a+v1*t;
}
I bool LSI(Line l,Point a,Point b) // line-seg intersection
{
    Vector v=l.b-l.a,v1=a-l.a,v2=b-l.a;
    return dcmp(Cross(v,v1))!=dcmp(Cross(v,v2));
}
I bool SSI(Point a1,Point b1,Point a2,Point b2) /*seg-seg intersection*/ {Line l1(a1,b1),l2(a2,b2);return LSI(l1,a2,b2)&&LSI(l2,a1,b1);}
I Point Circumcenter(Point a,Point b,Point c) // wai xin
{
    Point p=(a+b)/2,q=(a+c)/2;
    Vector u=Normal(b-a),v=Normal(c-a);
    if (!dcmp(Len(a-b)+Len(a-c)-Len(b-c))) return (b+c)/2;
    if (!dcmp(Len(a-b)+Len(b-c)-Len(a-c))) return (a+c)/2;
    if (!dcmp(Len(a-c)+Len(b-c)-Len(a-b))) return (a+b)/2;
    return LI(Line(p,p+u),Line(q,q+v));
}
I Point Barycenter(Point a,Point b,Point c) /*zhong xin*/ {return (a+b+c)/3;}
I bool PolarCmp(Point a,Point b){db c=Cross(a,b);return dcmp(c)==0?a.x<b.x:dcmp(c)>0;}
db PolygonArea(Point *p,int n)
{
    db ret=0;
    rep(i,2,n-1) ret+=Cross(p[i]-p[1],p[i+1]-p[1]);
    return fabs(ret/2);
}
int InPolygon(Point *poly,int n,Point p) // 1:in 0:out -1:on
{
    int ret=0;
    rep(i,1,n)
    {
        int j=i%n+1;
        if (OnSeg(p,poly[i],poly[j])||p==poly[i]||p==poly[j]) return -1;
        if (poly[i].y==poly[j].y) continue;
        int tmp=(poly[i].y>poly[j].y?i:j);
        if (p.y==poly[tmp].y&&p.x<poly[tmp].x) { ret^=1; continue; }
        tmp=(poly[i].y<poly[j].y?i:j);
        if (p.y==poly[tmp].y&&p.x<poly[tmp].x) continue;
        if (SSI(p,p+Vector(1e18,0),poly[i],poly[j])) ret^=1;
    }
    return ret;
}
bool IsConvex(Point *poly,int n)
{
    int now=0,last=0;
    rep(i,1,n)
    {
        int j=i+1,k=i+2;j>n?j-=n:0;k>n?k-=n:0;
        now=dcmp(Cross(poly[k]-poly[j],poly[j]-poly[i]));
        if (now*last<0) return 0;
        last=now;
    }
    return 1;
}
int GetConvex(Point *p,int n,Point *ret) // return the size of the convex
{
    sort(p+1,p+n+1);n=unique(p+1,p+n+1)-p-1;
    int m=0;
    rep(i,1,n)
    {
        while (m>1&&dcmp(Cross(ret[m]-ret[m-1],p[i]-ret[m-1]))<=0) --m;
        ret[++m]=p[i];
    }
    int _m=m;
    drep(i,n-1,1)
    {
        while (m>_m&&dcmp(Cross(ret[m]-ret[m-1],p[i]-ret[m-1]))<=0) --m;
        ret[++m]=p[i];
    }
    if (n>1) --m;
    return m;
}
db RotatingCalipers(Point *p,int n)
{
    db ret=0;
    if (n==1) return ret;
    if (n==2) return Len(p[1]-p[2]);
    int now=1;Point _=p[n+1];p[n+1]=p[1];
    rep(i,1,n)
    {
        while (dcmp(DisL(p[now],Line(p[i],p[i+1]))-DisL(p[now+1],Line(p[i],p[i+1])))<0) now=now%n+1;
        ret=max(ret,max(Len(p[now]-p[i]),Len(p[now]-p[i+1])));
    }
    p[n+1]=_;
    return ret;
}
db MinCircleCover(Point *p,int n,Point &O) // return the minimum radius
{
    random_shuffle(p+1,p+n+1);
    O=p[1];db r=0;
    rep(i,2,n) if (dcmp(r-Len(p[i]-O))<0)
    {
        O=p[i],r=0;
        rep(j,1,i-1) if (dcmp(r-Len(p[j]-O))<0)
        {
            O=(p[i]+p[j])/2,r=Len(O-p[j]);
            rep(k,1,j-1) if (dcmp(r-Len(p[k]-O))<0)
            {
                O=Circumcenter(p[i],p[j],p[k]);
                r=Len(O-p[k]);
            }
        }
    }
    return r;
}

int main()
{
    file();
    
    return 0;
}