UVa 11178 (简单练习) Morley's Theorem

题意：

Morley定理：任意三角形中，每个角的三等分线，相交出来的三个点构成一个正三角形。

不过这和题目关系不大，题目所求是正三角形的三个点的坐标，保留6位小数。

分析：

由于对称性，求出D点，EF也是同样的。

用点和向量的形式表示一条直线，向量BA、BC的夹角为a1，则将BC逆时针旋转a1/3可求得 直线BD，同理也可求得直线CD，最后再求交点即可。

 //#define LOCAL
 #include <cstdio>
 #include <cstring>
 #include <algorithm>
 #include <cmath>
 using namespace std;

 struct Point
 {
     double x, y;
     Point(double x=, double y=) :x(x),y(y) {}
 };
 typedef Point Vector;
 const double EPS = 1e-;

 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); }

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

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

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

 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 read_point(void)
 {
     double x, y;
     scanf("%lf%lf", &x, &y);
     return Point(x, y);
 }

 Point GetD(Point A, Point B, Point C)
 {
     Vector v1 = C - B;
     double a1 = Angle(A-B, v1);
     v1 = VRotate(v1, a1/);

     Vector v2 = B - C;
     double a2 = Angle(A-C, v2);
     v2 = VRotate(v2, -a2/);

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

 int main(void)
 {
     #ifdef    LOCAL
         freopen("11178in.txt", "r", stdin);
     #endif

     int T;
     scanf("%d", &T);
     while(T--)
     {
         Point A, B, C, D, E, F;
         A = read_point();
         B = read_point();
         C = read_point();
         D = GetD(A, B, C);
         E = GetD(B, C, A);
         F = GetD(C, A, B);
         printf("%.6lf %.6lf %.6lf %.6lf %.6lf %.6lf\n", D.x, D.y, E.x, E.y, F.x, F.y);
     }

     return ;
 }

代码君