Uva 11178 Morley's Theorem 向量旋转+求直线交点

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=9

题意：

Morlery定理是这样的：作三角形ABC每个内角的三等分线。相交成三角形DEF。则DEF为等边三角形，你的任务是给你A,B,C点坐标求D,E,F的坐标

思路:

根据对称性，我们只要求出一个点其他点一样：我们知道三点的左边即可求出每个夹角，假设求Ｄ，我们只要将向量BC

旋转rad/3的到直线BD，然后旋转向量CB然后得到CD，然后就是求两直线的交点了。

#include <iostream>

#include <cstdio>

#include <cmath>

#include <vector>

#include <cstring>

#include <algorithm>

#include <string>

#include <set>

#include <functional>

#include <numeric>

#include <sstream>

#include <stack>

#include <map>

#include <queue>



#define CL(arr, val) memset(arr, val, sizeof(arr))



#define lc l,m,rt<<1

#define rc m + 1,r,rt<<1|1

#define pi acos(-1.0)

#define L(x)    (x) << 1

#define R(x)    (x) << 1 | 1

#define MID(l, r)   (l + r) >> 1

#define Min(x, y)   (x) < (y) ? (x) : (y)

#define Max(x, y)   (x) < (y) ? (y) : (x)

#define E(x)        (1 << (x))

#define iabs(x)     (x) < 0 ? -(x) : (x)

#define OUT(x)  printf("%I64d\n", x)

#define lowbit(x)   (x)&(-x)

#define Read()  freopen("din.txt", "r", stdin)

#define Write() freopen("d.out", "w", stdout)

#define ll unsigned long long

#define keyTree (chd[chd[root][1]][0])



#define M 100007

#define N 300017



using namespace std;



const double eps = 1e-8;

const int inf = 0x7f7f7f7f;

const int mod = 1000000007;



struct Point

{

    double x,y;

    Point(double tx = 0,double ty = 0) : x(tx),y(ty){}

};

typedef Point Vtor;

//向量的加减乘除

Vtor operator + (Vtor A,Vtor B) { return Vtor(A.x + B.x,A.y + B.y); }

Vtor operator - (Point A,Point B) { return Vtor(A.x - B.x,A.y - B.y); }

Vtor operator * (Vtor A,double p) { return Vtor(A.x*p,A.y*p); }

Vtor operator / (Vtor A,double p) { return Vtor(A.x/p,A.y/p); }

bool operator < (Point A,Point B) { return A.x < B.x || (A.x == B.x && A.y < B.y);}

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

bool operator == (Point A,Point B) {return dcmp(A.x - B.x) == 0 && dcmp(A.y - B.y) == 0; }

//向量的点积，长度，夹角

double Dot(Vtor A,Vtor B) { return A.x*B.x + A.y*B.y; }

double Length(Vtor A) { return sqrt(Dot(A,A)); }

double Angle(Vtor A,Vtor B) { return acos(Dot(A,B)/Length(A)/Length(B)); }

//叉积，三角形面积

double Cross(Vtor A,Vtor B) { return A.x*B.y - A.y*B.x; }

double Area2(Point A,Point B,Point C) { return Cross(A - B,C - B); }

//向量的旋转,求向量的单位法线（即左转90度，然后长度归一）

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

Vtor Normal(Vtor A)

{

    double L = Length(A);

    return Vtor(-A.y/L, A.x/L);

}

//直线的交点

Point GetLineIntersection(Point P,Vtor v,Point Q,Vtor w)

{

    Vtor u = P - Q;

    double t = Cross(w,u)/Cross(v,w);

    return P + v*t;

}

//点到直线的距离

double DistanceToLine(Point P,Point A,Point B)

{

    Vtor v1 = B - A;

    return Cross(P,v1)/Length(v1);

}

//点到线段的距离

double DistanceToSegment(Point P,Point A,Point B)

{

    if (A == B) return Length(P - A);

    Vtor v1 =  B - A , v2 = P - A, v3 = P - B;

    if (dcmp(Dot(v1,v2)) < 0) return Length(P - A);

    else if (dcmp(Dot(v1,v3)) > 0) return Length(P - B);

    else return Cross(v1,v2)/Length(v1);

}

//点到直线的映射

Point GetLineProjection(Point P,Point A,Point B)

{

    Vtor v = B - A;

    return A + v*Dot(v,P - A)/Dot(v,v);

}



//判断线段是否规范相交

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(a1 - a2,b1 - a1), c4 = Cross(a1 - a2,b2 - a2);

    return dcmp(c1)*dcmp(c2) < 0 && dcmp(c3)*dcmp(c4) < 0;

}

//判断点是否在一条线段上

bool OnSegment(Point P,Point a1,Point a2)

{

    return dcmp(Cross(a1 - P,a2 - P)) == 0 && dcmp(Dot(a1 - P,a2 - P)) < 0;

}

//多边形面积

double PolgonArea(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;

}



Point solve(Point A,Point B,Point C)

{

    double rad1 = Angle(A - B, C - B)/3.0;

    Vtor v1 = C - B;

    v1 = Rotate(v1,rad1);



    double rad2 = Angle(A - C,B - C)/3.0;

    Vtor v2 = B - C;

    v2 = Rotate(v2,-rad2);



    return GetLineIntersection(B,v1,C,v2);

}

int main()

{



//    Read();

    int T;

    Point A,B,C;

    scanf("%d",&T);

    while (T--)

    {

        scanf("%lf%lf%lf%lf%lf%lf",&A.x,&A.y,&B.x,&B.y,&C.x,&C.y);

        Point D = solve(A,B,C);

        Point E = solve(B,C,A);

        Point F = solve(C,A,B);



        printf("%.6lf %.6lf %.6lf %.6lf %.6lf %.6lf\n",D.x,D.y,E.x,E.y,F.x,F.y);

    }

    return 0;

}

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