LA 3263 好看的一笔画 欧拉几何+计算几何模板

Posted 2020-06-21 smilesundream

题意：训练指南260

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
#include <cmath>
using namespace std;

struct Point {
    double x, y;
    Point(double x = 0, double y = 0) : x(x) , y(y) { }
};

typedef Point Vector;

Vector operator + (Vector A, Vector B) { return Vector(A.x+B.x, A.y+B.y); }
Vector operator - (Vector A, Vector 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, double p) { return Vector(A.x/p, A.y/p); }

bool operator < (const Point& a, const Point& b) {
    return a.x < b.x || (a.x == b.x && a.y < b.y);
}

const double eps = 1e-10;
int dcmp(double x) {
    if(fabs(x) < eps) return 0; else return x < 0 ? -1 : 1;
}

bool operator == (const Point& a, const Point& b) {
    return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0;
}

double Dot(Vector A, Vector B) { return A.x*B.x + A.y*B.y; }
double Length(Vector A) { return sqrt(Dot(A, A)); }
double Angle(Vector A, Vector B) { return acos(Dot(A, B) / Length(A) / Length(B)); }

double Cross(Vector A, Vector B) { return A.x*B.y - A.y*B.x; }
double Area2(Point A, Point B, Point C) { return Cross(B-A, C-A); }

Vector Rotate(Vector A, double rad) {
    return Vector(A.x*cos(rad) - A.y*sin(rad), A.x*sin(rad)+A.y*cos(rad) );
}

Vector Normal(Vector A) {
    double L = Length(A);
    return Vector(-A.y/L, A.x/L);
}

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;
}

double DistanceToLine(Point P, Point A, Point B) {
    Vector v1 = B-A, v2 = P - A;
    return fabs(Cross(v1,v2) / Length(v1));
}

double DistanceToSegment(Point P, Point A, Point B) {
    if(A==B) return Length(P-A);
    Vector v1 = B - A, v2 = P - A, v3 = P - B;
    if(dcmp(Dot(v1, v2)) < 0) return Length(v2);
    else if(dcmp(Dot(v1, v3)) > 0) return Length(v3);
    else return fabs(Cross(v1, v2)) / Length(v1);
}

Point GetLineProjection(Point P, Point A, Point B) {
    Vector v = B - A;
    return A + v * ( Dot(v, P-A) / Dot(v, v) );
}

bool SegmentProperIntersection(Point a1, Point a2, Point b1, Point b2) {
    double c1 = Cross(a2 - a1, b1 - a1), c2 = Cross(a2 - a1, b2 - a1),
            c3 = Cross(b2 - b1, a1 - b1), c4 = Cross(b2 - b1, a2 - b1);
    return dcmp(c1) * dcmp(c2) < 0 && dcmp(c3) * dcmp(c4) < 0;
}

bool OnSegment(Point p, Point a1, Point a2) {
    return dcmp(Cross(a1 - p, a2 - p)) == 0 && dcmp(Dot(a1 - p, a2 - p)) < 0;
}

double ConvexPolygonArea(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;
}

const int maxn = 300 + 10;
Point P[maxn], V[maxn*maxn];

Point p[305],v[305*305];
int main()
{
    int n,cas=0;
    while(~scanf("%d",&n)&&n)
    {
        cas++;
        for(int i=1;i<=n;i++)
           {
                scanf("%lf %lf",&p[i].x,&p[i].y);
                v[i]=p[i];
           }
        n--;

        int cnt=n+1;
        for(int i=1;i<=n;i++)
          for(int j=i+1;j<=n;j++)
           if(SegmentProperIntersection(p[i],p[i+1],p[j],p[j+1]))
                v[++cnt]=GetLineIntersection(p[i],p[i+1]-p[i],p[j],p[j+1]-p[j]);


        sort(v+1,v+cnt+1);
        int vnum=unique(v+1,v+cnt+1)-(v+1);
        //for(int i=1;i<=vnum;i++)
          //  printf("v %d:%f %f\n",i,v[i].x,v[i].y);
        int e=n;
        //cout<<"ori   "<<e<<endl;
        for(int i=1;i<=vnum;i++)
            for(int j=1;j<=n;j++)
              if(OnSegment(v[i],p[j],p[j+1]))
                  e++;
       //cout<<"vnum:"<<vnum<<"  e:"<<e<<endl;
        printf("Case %d: There are %d pieces.\n",cas,e+2-vnum);
    }
    return 0;//v+f-e=2;
}