莫利定理：UVa 11178 Morley's Theorey

莫利定理（Morley‘s theorem），也称为莫雷角三分线定理。将三角形的三个内角三等分，靠近某边的两条三分角线相交得到一个交点，则这样的三个交点可以构成一个正三角形。这个三角形常被称作莫利正三角形。

参考《算法竞赛入门经典——训练指南》第四章 计算几何

参考代码+部分注释

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <map>
#include <vector>
#include <queue>
#include <cstring>
#include <cmath>
#include <climits>
#define eps 1e-10
using namespace std;
typedef long long ll;
const int INF=INT_MAX;
const int maxn = 110;
int dcmp(double x){//三态函数，克服浮点数精度陷阱，判断x==0?x<0?x>0?
  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){}//构造函数，方便代码编写
};
typedef Point Vector;//Vector是 Point的别名

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);}
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;}
//rad是弧度不是角度
Vector Rotate(Vector A,double rad){return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));}
//调用前请确保两条直线P+tv,Q+tw有唯一交点。当且仅当Cross（v,w）非0
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;
}

Point getD(Point A,Point B,Point C){
  Vector v1=C-B;
  double a1=Angle(A-B,v1);
  v1=Rotate(v1,a1/3);//正数表示逆时针旋转

  Vector v2=B-C;
  double a2=Angle(A-C,v2);
  v2=Rotate(v2,-a2/3);//负数表示顺时针旋转

  return GetLineIntersection(B,v1,C,v2);
}
int main()
{
  // freopen("input.txt","r",stdin);
   Point A,B,C,D,E,F;
   int T;cin>>T;
   while(T--){
    cin>>A.x>>A.y>>B.x>>B.y>>C.x>>C.y;
    D=getD(A,B,C);
    E=getD(B,C,A);//注意方向对应
    F=getD(C,A,B);
    printf("%f %f %f %f %f %f\n",D.x,D.y,E.x,E.y,F.x,F.y);
   }
   return 0;
}

莫利定理：UVa 11178 Morley's Theorey