Description
Problem D
Morley’s Theorem
Input: Standard Input
Output: Standard Output
Morley’s theorem states that that the lines trisecting the angles of an arbitrary plane triangle meet at the vertices of an equilateral triangle. For example in the figure below the tri-sectors of angles A, B and C has intersected and created an equilateral triangle DEF.
Of course the theorem has various generalizations, in particular if all of the tri-sectors are intersected one obtains four other equilateral triangles. But in the original theorem only tri-sectors nearest to BC are allowed to intersect to get point D, tri-sectors nearest to CA are allowed to intersect point E and tri-sectors nearest to AB are intersected to get point F. Trisector like BD and CE are not allowed to intersect. So ultimately we get only one equilateral triangle DEF. Now your task is to find the Cartesian coordinates of D, E and F given the coordinates of A, B, and C.
Input
First line of the input file contains an integer N (0<N<5001) which denotes the number of test cases to follow. Each of the next lines contain six integers 
. This six
integers actually indicates that the Cartesian coordinates of point A, B and C are 
respectively. You can assume that the area of triangle ABC is not equal to zero, 
and
the points A, B and C are in counter clockwise order.
Output
For each line of input you should produce one line of output. This line contains six floating point numbers 
separated by a single space. These six floating-point
actually means that the Cartesian coordinates of D, E and F are 
respectively. Errors less than 
will
be accepted.
Sample Input Output for Sample Input
2 1 1 2 2 1 2 0 0 100 0 50 50 |
1.316987 1.816987 1.183013 1.683013 1.366025 1.633975 56.698730 25.000000 43.301270 25.000000 50.000000 13.397460 |
Problemsetters: Shahriar Manzoor
Special Thanks: Joachim Wulff
--------------
/** head-file **/
#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <string>
#include <vector>
#include <queue>
#include <stack>
#include <list>
#include <set>
#include <map>
#include <algorithm>
/** define-for **/
#define REP(i, n) for (int i=0;i<int(n);++i)
#define FOR(i, a, b) for (int i=int(a);i<int(b);++i)
#define DWN(i, b, a) for (int i=int(b-1);i>=int(a);--i)
#define REP_1(i, n) for (int i=1;i<=int(n);++i)
#define FOR_1(i, a, b) for (int i=int(a);i<=int(b);++i)
#define DWN_1(i, b, a) for (int i=int(b);i>=int(a);--i)
#define REP_N(i, n) for (i=0;i<int(n);++i)
#define FOR_N(i, a, b) for (i=int(a);i<int(b);++i)
#define DWN_N(i, b, a) for (i=int(b-1);i>=int(a);--i)
#define REP_1_N(i, n) for (i=1;i<=int(n);++i)
#define FOR_1_N(i, a, b) for (i=int(a);i<=int(b);++i)
#define DWN_1_N(i, b, a) for (i=int(b);i>=int(a);--i)
/** define-useful **/
#define clr(x,a) memset(x,a,sizeof(x))
#define sz(x) int(x.size())
#define see(x) cerr<<#x<<" "<<x<<endl
#define se(x) cerr<<" "<<x
#define pb push_back
#define mp make_pair
/** test **/
#define Display(A, n, m) {
REP(i, n){
REP(j, m) cout << A[i][j] << " ";
cout << endl;
}
}
#define Display_1(A, n, m) {
REP_1(i, n){
REP_1(j, m) cout << A[i][j] << " ";
cout << endl;
}
}
using namespace std;
/** typedef **/
typedef long long LL;
/** Add - On **/
const int direct4[4][2]={ {0,1},{1,0},{0,-1},{-1,0} };
const int direct8[8][2]={ {0,1},{1,0},{0,-1},{-1,0},{1,1},{1,-1},{-1,1},{-1,-1} };
const int direct3[6][3]={ {1,0,0},{0,1,0},{0,0,1},{-1,0,0},{0,-1,0},{0,0,-1} };
const int MOD = 1000000007;
const int INF = 0x3f3f3f3f;
const long long INFF = 1LL << 60;
const double EPS = 1e-9;
const double OO = 1e15;
const double PI = acos(-1.0); //M_PI;
int dcmp(double x){
if (fabs(x)<EPS) return 0;
return x>0?1:-1;
}
struct point{
double x,y;
point(){}
point(double _x,double _y):x(_x),y(_y){}
/**运算操作**/
bool operator==(point a)const{
return dcmp(a.x-x)==0&&dcmp(a.y-y)==0;
}
bool operator<(point a)const{
return dcmp(x-a.x)==0?dcmp(y-a.y)<0:dcmp(x-a.x)<0;
}
friend point operator+(point a,point b){
return point(a.x+b.x,a.y+b.y);
}//向量+向量=向量
friend point operator-(point a,point b){
return point(a.x-b.x,a.y-b.y);
}//点-点=向量
friend point operator*(point a,double p){
return point(a.x*p,a.y*p);
}//向量*数=向量
friend point operator/(point a,double p){
return point(a.x/p,a.y/p);
}//向量/数=向量
/**基本信息计算**/
double len(){
return hypot(x,y);
}
double len2(){
return x*x+y*y;
}
double distance(point p){
return hypot(x-p.x,y-p.y);
}
/**向量变换**/
point rotate(double rad){
return point(x*cos(rad)-y*sin(rad),x*sin(rad)+y*cos(rad));
}//绕起点逆时针旋转rad
point rotate(point p,double angle)//绕点p逆时针旋转angle角度
{
point v=(*this)-p;
double c=cos(angle),s=sin(angle);
return point(p.x+v.x*c-v.y*s,p.y+v.x*s+v.y*c);
}
point rotleft(){
return point(-y,x);
}//逆时针转90度
point rotright(){
return point(y,-x);
}//顺时针转90度
point normal(){
double L=len();
return point(-y/L,x/L);
}//单位法线即左转90度长度归一
point trunc(double r){
double l=len();
if (!dcmp(l)) return *this;
r/=l;
return point(x*r,y*r);
}//长度变为r
/**读入与输出**/
void input(){
scanf("%lf%lf",&x,&y);
}
void output(){
printf("%0.2f %0.2f
",x,y);
}
};
typedef point vect;
double dot(point a,point b){
return a.x*b.x+a.y*b.y;
}
double cross(point a,point b){
return a.x*b.y-a.y*b.x;
}
double area3p(point a,point b,point c){
return cross(b-a,c-a)/2;
}//三角形abc的面积
double angle(vect a,vect b){
return acos(dot(a,b)/a.len()/b.len());
}
point GetLineIntersection(point P,vect v,point Q,vect w){
vect u=P-Q;
double t=cross(w,u)/cross(v,w);
return P+v*t;
}//直线交点
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;
}//多边形面积
struct line{
point a,b;
line(){}
line(point _a,point _b){a=_a;b=_b;}
line(point p,double angle){
a=p;
if (dcmp(angle-PI/2)==0) b=a+point(0,1);
else b=a+point(1,tan(angle));
}//倾斜角angle
line (double _a,double _b,double _c){
if (dcmp(_a)==0){
a=point(0,-_c/_b);
b=point(1,-_c/_b);
}else if (dcmp(_b)==0){
a=point(-_c/_a,0);
b=point(-_c/_a,1);
}else{
a=point(0,-_c/_b);
b=point(1,(-_c-_a)/_b);
}
}//ax+by+c=0
void adjust(){
if (b<a) swap(a,b);
}//两点校准
/**运算操作**/
bool operator==(line v){
return (a==v.a)&&(b==v.b);
}
/**基本信息计算**/
double length(){
return a.distance(b);
}
double angle(){
double k=atan2(b.y-a.y,b.x-a.x);
if (dcmp(k)<0) k+=PI;
if (dcmp(k-PI)==0) k-=PI;
return k;
}
/**线段相关**/
int relation(point p){
int c=dcmp(cross(p-a,b-a));
if (c<0) return 1;//点在逆时针
if (c>0) return 2;//点在顺时针
return 3;//平行
}
bool pointonseg(point p){
return dcmp(cross(p-a,b-a))==0&&dcmp(cross(p-a,p-b))<=0;
}//点p在线段上？
bool parallel(line v){
return dcmp(cross(b-a,v.b-v.a))==0;
}//与线段v平行？
int segcrossseg(line v){
int d1=dcmp(cross(b-a,v.a-a));
int d2=dcmp(cross(b-a,v.b-a));
int d3=dcmp(cross(v.b-v.a,a-v.a));
int d4=dcmp(cross(v.b-v.a,b-v.a));
if ((d1^d2)==-2&&(d3^d4)==-2)return 2;
return ((d1==0&&dcmp(dot(v.a-a,v.a-b)<=0))||
(d2==0&&dcmp(dot(v.b-a,v.b-b)<=0))||
(d3==0&&dcmp(dot(a-v.a,a-v.b)<=0))||
(d4==0&&dcmp(dot(b-v.a,b-v.b)<=0)));
}//线段相交 0-不相交 1-非规范相交 2-规范相交
/**直线相关**/
int linecrosseg(line v){//直线v
int d1=dcmp(cross(b-a,v.a-a));
int d2=dcmp(cross(b-a,v.b-a));
if ((d1^d2)==-2) return 2;
return (d1==0||d2==0);
}//0-平行 1-重合 2-相交
int linecrossline(line v){
if ((*this).parallel(v)) return v.relation(a)==3;
return 2;
}//0-平行 1-重合 2-相交
point crosspoint(line v){
double a1=cross(v.b-v.a,a-v.a);
double a2=cross(v.b-v.a,b-v.a);
return point((a.x*a2-b.x*a1)/(a2-a1),(a.y*a2-b.y*a1)/(a2-a1));
}//交点
double dispointtoline(point p){
return fabs(cross(p-a,b-a))/length();
}//点到线的距离
double dispointtoseg(point p){
if (dcmp(cross(p-b,a-b))<0||dcmp(cross(p-a,b-a))<0) return min(p.distance(a),p.distance(b));
return dispointtoline(p);
}
/**输入输出**/
void input(){
a.input();
b.input();
}
void output(){
a.output();
b.output();
}
};
point getD(point A,point B,point C){
vect v1=C-B;
double a1=angle((A-B),v1);
v1=v1.rotate(a1/3);
vect v2=B-C;
double a2=angle((A-C),v2);
v2=v2.rotate(-a2/3);
return GetLineIntersection(B,v1,C,v2);
}
int main()
{
int T;
scanf("%d",&T);
while(T--)
{
point A,B,C,D,E,F;
A.input();
B.input();
C.input();
D=getD(A,B,C);
E=getD(B,C,A);
F=getD(C,A,B);
printf("%0.6f %0.6f %0.6f %0.6f %0.6f %0.6f
",D.x,D.y,E.x,E.y,F.x,F.y);
}
return 0;
}