UVA 11178 Morley's Theorem

     给一个三角形，由各点引出两条三等分线，在三角形中相交于三点，求三个交点的坐标..

     求出角度以后，旋转两条边，求交点。重复三次...

    

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <string>
typedef double type;
using namespace std;
const double pi=acos(-1.0);
struct Point
{
    type x,y;
    Point(){}
    Point(type a,type b)
    {
        x=a;
        y=b;
    }
    void read()
    {
        scanf("%lf%lf",&x,&y);
    }
    void print()
    {
        printf("%.6lf %.6lf",x,y);
    }
};
typedef Point Vector;
Vector operator + (Vector A,Vector B)
{
    return Vector(A.x+B.x,A.y+B.y);
}
Vector operator - (Point A,Point B)
{
    return Vector(A.x-B.x,A.y-B.y);
}
Vector operator * (Vector A,type p)
{
    return Vector(A.x*p,A.y*p);
}
Vector operator / (Vector A,type 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;
}
//atan2(x,y) :向量(x,y)的极角，即从x轴正半轴旋转到该向量方向所需要的角度。
type Dot(Vector A,Vector B)
{
    return A.x*B.x+A.y*B.y;
}
type Cross(Vector A,Vector B)
{
    return A.x*B.y-A.y*B.x;
}
type Length(Vector A)
{
    return sqrt(Dot(A,A));
}
type Angle(Vector A,Vector B)
{
    return acos(Dot(A,B)/Length(A)/Length(B));
}

type 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)//单位法线,左转90度，长度归一
{
    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)//P在AB上的投影
{
    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)//多边形面积
{
    double area=0;
    for (int i=1; i<n-1; i++)
    area+=Cross(p[i]-p[0],p[i+1]-p[0]);
    return area/2.0;
}
double PolygonArea(Point* p,int n)//有向面积
{
    double area=0;
    for (int i=1; i<n-1; i++)
    area+=Cross(p[i]-p[0],p[i+1]-p[0]);
    return area/2.0;
}

int n,m,k;
Point p[10],q[10];
Point find(Point a,Point b,Point c)
{
    Vector l1=b-a,l2=a-b;
    Vector l3=c-a,l4=c-b;
    double rad1=Angle(l1,l3)/3.0,rad2=Angle(l2,l4)/3.0;
    Vector la=Rotate(l1,rad1);
    Vector lb=Rotate(l2,2.0*pi-rad2);
    Point res=GetLineIntersection(a,la,b,lb);
    return res;

}
int tt;
int main()
{
//    freopen("in.txt","r",stdin);
    scanf("%d",&tt);
    while(tt--)
    {
        for (int i=0; i<3; i++)
        p[i].read();
        q[0]=find(p[1],p[2],p[0]);
        q[1]=find(p[2],p[0],p[1]);
        q[2]=find(p[0],p[1],p[2]);
        q[0].print();
        for (int i=1; i<3; i++)
        {
            printf(" ");
            q[i].print();
        }
        puts("");
    }
    return 0;
}