poj 3335 /poj 3130/ poj 1474 半平面交 判断核是否存在 / poj1279 半平面交 求核的面积

/***************
poj 3335  点序顺时针
***************/
#include <iostream>
#include <cmath>
#include <algorithm>
using namespace std;
const double eps = 1e-8;
const double maxn = 0x7f7f7f7f;
int dcmp(double x){
    if(fabs(x)<eps)
        return 0;
    else
        return x<0?-1:1;
}
struct point {
    double x,y;
    point (double x=0,double y =0):x(x),y(y){}
};
point p[150];
typedef point Vector;

struct polygon{
    point p[150];
    int Size;
};

struct line{
    point fir,sec;
    line(point a = point(),point b = point()){
        fir = a;
        sec = b;
    }
};

Vector operator -(point a,point b){
    return Vector(a.x-b.x,a.y-b.y);
}

Vector operator *(Vector a,double p){
    return Vector (a.x*p,a.y*p);
}
Vector operator + (Vector a,Vector b){
    return Vector (a.x+b.x,a.y+b.y);
}

double cross(Vector a,Vector b){
    return a.x*b.y-a.y*b.x;
}

double dot(Vector a,Vector b){
    return a.x*b.x+a.y*b.y;
}

point getLineIntersection(point p,Vector v,point q,Vector w){
    Vector u = p-q;
    double t = cross(w,u)/cross(v,w);
    return p+v*t;
}

bool onsegment(point p,point a1,point a2){
    return dcmp(cross(a1-p,a2-p))==0&&dcmp(dot(a1-p,a2-p))<0;
}

polygon cutploygon(polygon poly,line ln){
    polygon newploy;
    int m=0;
    int n = poly.Size;
    point a = ln.fir,b = ln.sec;
    for(int i=0;i<n;i++){
        point c = poly.p[i];
        point d = poly.p[(i+1)%n];
        double cc = cross(b-a,c-a);
        double dd = cross(b-a,d-a);
        if(cc>=0)
            newploy.p[m++] = c;
        if(cc*dd<0)
            newploy.p[m++] = getLineIntersection(a,b-a,c,d-c);
    }
    newploy.Size = m;
    return newploy;
}

int main()
{
    int t;
    cin>>t;
    int n;
    while(t--){
        cin>>n;
        for(int i=0;i<n;i++)
            cin>>p[i].x>>p[i].y;
        polygon poly;
        poly.Size = 4;
        poly.p[0].x = -maxn;
        poly.p[0].y = -maxn;
        poly.p[1].x = maxn;
        poly.p[1].y = -maxn;
        poly.p[2].x = maxn;
        poly.p[2].y = maxn;
        poly.p[3].x = -maxn;
        poly.p[3].y = maxn;
        bool flag = true;
        for(int i=1;i<=n;i++){
            line ln;
            ln.fir = p[i%n];
            ln.sec = p[i-1];
            poly = cutploygon(poly,ln);
            if(poly.Size==0){
                flag = false;
                break;
            }
        }
        if(!flag)
            cout<<"NO"<<endl;
        else
            cout<<"YES"<<endl;
    }
    return 0;
}

/****************************************/
poj 3130  点序逆时针
/****************************************/

#include <iostream>
#include <cmath>
#include <algorithm>
using namespace std;
const double eps = 1e-8;
const double maxn = 0x7f7f7f7f;
int dcmp(double x){
    if(fabs(x)<eps)
        return 0;
    else
        return x<0?-1:1;
}
struct point {
    double x,y;
    point (double x=0,double y =0):x(x),y(y){}
};
point p[150];
typedef point Vector;

struct polygon{
    point p[150];
    int Size;
};

struct line{
    point fir,sec;
    line(point a = point(),point b = point()){
        fir = a;
        sec = b;
    }
};

Vector operator -(point a,point b){
    return Vector(a.x-b.x,a.y-b.y);
}

Vector operator *(Vector a,double p){
    return Vector (a.x*p,a.y*p);
}
Vector operator + (Vector a,Vector b){
    return Vector (a.x+b.x,a.y+b.y);
}

double cross(Vector a,Vector b){
    return a.x*b.y-a.y*b.x;
}

double dot(Vector a,Vector b){
    return a.x*b.x+a.y*b.y;
}

point getLineIntersection(point p,Vector v,point q,Vector w){
    Vector u = p-q;
    double t = cross(w,u)/cross(v,w);
    return p+v*t;
}

bool onsegment(point p,point a1,point a2){
    return dcmp(cross(a1-p,a2-p))==0&&dcmp(dot(a1-p,a2-p))<0;
}

polygon cutploygon(polygon poly,line ln){
    polygon newploy;
    int m=0;
    int n = poly.Size;
    point a = ln.fir,b = ln.sec;
    for(int i=0;i<n;i++){
        point c = poly.p[i];
        point d = poly.p[(i+1)%n];
        double cc = cross(b-a,c-a);
        double dd = cross(b-a,d-a);
        if(cc>=0)
            newploy.p[m++] = c;
        if(cc*dd<0)
            newploy.p[m++] = getLineIntersection(a,b-a,c,d-c);
    }
    newploy.Size = m;
    return newploy;
}

int main()
{
    int n;
    while(cin>>n&&n){
        for(int i=0;i<n;i++)
            cin>>p[i].x>>p[i].y;
        polygon poly;
        poly.Size = 4;
        poly.p[0].x = -maxn;
        poly.p[0].y = -maxn;
        poly.p[1].x = maxn;
        poly.p[1].y = -maxn;
        poly.p[2].x = maxn;
        poly.p[2].y = maxn;
        poly.p[3].x = -maxn;
        poly.p[3].y = maxn;
        bool flag = true;
        for(int i=0;i<n;i++){
            line ln;
            ln.fir = p[i%n];
            ln.sec = p[(i+1)%n];
            poly = cutploygon(poly,ln);
            if(poly.Size==0){
                flag = false;
                break;
            }
        }
        if(!flag)
            cout<<"0"<<endl;
        else
            cout<<"1"<<endl;
    }
    return 0;
}


/*************************************/
poj  1474  点序顺时针
/*************************************/
#include <iostream>
#include <cmath>
#include <algorithm>
using namespace std;
const double eps = 1e-8;
const double maxn = 0x7f7f7f7f;
int dcmp(double x){
    if(fabs(x)<eps)
        return 0;
    else
        return x<0?-1:1;
}
struct point {
    double x,y;
    point (double x=0,double y =0):x(x),y(y){}
};
point p[150];
typedef point Vector;

struct polygon{
    point p[150];
    int Size;
};

struct line{
    point fir,sec;
    line(point a = point(),point b = point()){
        fir = a;
        sec = b;
    }
};

Vector operator -(point a,point b){
    return Vector(a.x-b.x,a.y-b.y);
}

Vector operator *(Vector a,double p){
    return Vector (a.x*p,a.y*p);
}
Vector operator + (Vector a,Vector b){
    return Vector (a.x+b.x,a.y+b.y);
}

double cross(Vector a,Vector b){
    return a.x*b.y-a.y*b.x;
}

double dot(Vector a,Vector b){
    return a.x*b.x+a.y*b.y;
}

point getLineIntersection(point p,Vector v,point q,Vector w){
    Vector u = p-q;
    double t = cross(w,u)/cross(v,w);
    return p+v*t;
}

bool onsegment(point p,point a1,point a2){
    return dcmp(cross(a1-p,a2-p))==0&&dcmp(dot(a1-p,a2-p))<0;
}

polygon cutploygon(polygon poly,line ln){
    polygon newploy;
    int m=0;
    int n = poly.Size;
    point a = ln.fir,b = ln.sec;
    for(int i=0;i<n;i++){
        point c = poly.p[i];
        point d = poly.p[(i+1)%n];
        double cc = cross(b-a,c-a);
        double dd = cross(b-a,d-a);
        if(cc>=0)
            newploy.p[m++] = c;
        if(cc*dd<0)
            newploy.p[m++] = getLineIntersection(a,b-a,c,d-c);
    }
    newploy.Size = m;
    return newploy;
}

int main()
{
    int n;
    int cnt =1;
    while(cin>>n&&n){
        for(int i=0;i<n;i++)
            cin>>p[i].x>>p[i].y;
        polygon poly;
        poly.Size = 4;
        poly.p[0].x = -maxn;
        poly.p[0].y = -maxn;
        poly.p[1].x = maxn;
        poly.p[1].y = -maxn;
        poly.p[2].x = maxn;
        poly.p[2].y = maxn;
        poly.p[3].x = -maxn;
        poly.p[3].y = maxn;
        bool flag = true;
        for(int i=1;i<=n;i++){
            line ln;
            ln.fir = p[i%n];
            ln.sec = p[i-1];
            poly = cutploygon(poly,ln);
            if(poly.Size==0){
                flag = false;
                break;
            }
        }
        //cout<<poly.Size<<endl;
        cout<<"Floor #"<<cnt++<<endl;
        if(!flag)
            cout<<"Surveillance is impossible."<<endl;
        else
            cout<<"Surveillance is possible."<<endl;
        cout<<endl;
    }
    return 0;
}


/**********************************
poj 1279  点序顺时针
**********************************/
#include <iostream>
#include <cmath>
#include <algorithm>
#include <cstdio>
using namespace std;
const double eps = 1e-8;
const double maxn = 0x7f7f7f7f;
int dcmp(double x){
    if(fabs(x)<eps)
        return 0;
    else
        return x<0?-1:1;
}
struct point {
    double x,y;
    point (double x=0,double y =0):x(x),y(y){}
};
point p[2000];
typedef point Vector;

struct polygon{
    point p[2000];
    int Size;
};

struct line{
    point fir,sec;
    line(point a = point(),point b = point()){
        fir = a;
        sec = b;
    }
};

Vector operator -(point a,point b){
    return Vector(a.x-b.x,a.y-b.y);
}

Vector operator *(Vector a,double p){
    return Vector (a.x*p,a.y*p);
}
Vector operator + (Vector a,Vector b){
    return Vector (a.x+b.x,a.y+b.y);
}

double cross(Vector a,Vector b){
    return a.x*b.y-a.y*b.x;
}

double dot(Vector a,Vector b){
    return a.x*b.x+a.y*b.y;
}

point getLineIntersection(point p,Vector v,point q,Vector w){
    Vector u = p-q;
    double t = cross(w,u)/cross(v,w);
    return p+v*t;
}

bool onsegment(point p,point a1,point a2){
    return dcmp(cross(a1-p,a2-p))==0&&dcmp(dot(a1-p,a2-p))<0;
}

polygon cutploygon(polygon poly,line ln){
    polygon newploy;
    int m=0;
    int n = poly.Size;
    point a = ln.fir,b = ln.sec;
    for(int i=0;i<n;i++){
        point c = poly.p[i];
        point d = poly.p[(i+1)%n];
        double cc = cross(b-a,c-a);
        double dd = cross(b-a,d-a);
        if(cc>=0)
            newploy.p[m++] = c;
        if(cc*dd<0)
            newploy.p[m++] = getLineIntersection(a,b-a,c,d-c);
    }
    newploy.Size = m;
    return newploy;
}

double polyArea(point *p,int n){
    double area =0;
    for(int i=1;i<n-1;i++){
        area += cross(p[i]-p[0],p[i+1]-p[0]);
    }
    return area/2;
}

int main()
{
    int t;
    cin>>t;
    int n;
    while(t--){
        cin>>n;
        for(int i=0;i<n;i++)
            cin>>p[i].x>>p[i].y;
        polygon poly;
        poly.Size = 4;
        poly.p[0].x = -maxn;
        poly.p[0].y = -maxn;
        poly.p[1].x = maxn;
        poly.p[1].y = -maxn;
        poly.p[2].x = maxn;
        poly.p[2].y = maxn;
        poly.p[3].x = -maxn;
        poly.p[3].y = maxn;
        bool flag = true;
        for(int i=1;i<=n;i++){
            line ln;
            ln.fir = p[i%n];
            ln.sec = p[i-1];
            poly = cutploygon(poly,ln);
            if(poly.Size==0){
                flag = false;
                break;
            }
        }
        double res;
        if(!flag)
            res =0;
        else{
            res = polyArea(poly.p,poly.Size);
        }
        printf("%.2lf
",res);
    }
    return 0;
}