UVA - 11178 Morley's Theorem

按照刘汝佳老师说的，这道题本身没有什么算法可言，

主要是考察选手对于几何算法的应用，

我们已经知道了点A,B,C

如果要求点D的话

我们可以先求出向量C-B的坐标，然后求出向量C-B与A-B的夹角。

再把夹角/3，这样我们就找到了∠CBD的度数。

再把向量C-B逆时针旋转∠CBD度

就求出了点D的坐标，

E，F同理

#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
#define Vector Point
using namespace std;
inline void read(int &n)
{
char c='+';bool flag=0;n=0;
while(c<'0'||c>'9'){c=getchar();if(c=='-')flag=1;}
while(c>='0'&&c<='9')    n=n*10+(c-48),c=getchar();
if(flag==1)n=-n;
}
const double PI=acos(-1);
const double eps=1e-10;
int dcmp(double x)    {return (fabs(x)<eps)?0:(x<0?-1:1);}
struct Point
{
double x,y;
Point(double x=0,double y=0):x(x),y(y){};
};
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;}//点积 ********************
double Length(Vector A){return sqrt(Dot(A,A));}// 求向量的长度
double Angle(Vector A,Vector B){return acos(Dot(A,B) / (Length(A)) / Length(B));} //求两个向量的夹角

double Cross(Vector A,Vector B){return A.x * B.y-A.y * B.x;}// 两个向量的叉积
double 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));}// 向量旋转*********

Point GetLineIntersection(Point P,Point v,Point Q,Point w)// 两直线的交点 ****************
{
Vector u=P-Q;
double t=Cross(w,u)/Cross(v,w);
return P+v*t;
}

double DistanceToLine(Point P,Point A,Point B)// 点P到直线AB的距离
{
Vector v1=B - A;Vector v2= P-A;
return fabs(Cross(v1,v2)) / Length(v1);
}

double DistanceToSegment(Point P,Point A,Point B)// 点P到线段AB的距离
{
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);// 怎么会是大于。。。。。。
else return fabs(Cross(v1,v2)) / Length(v1);
}

Point GetLineProjection(Point P, Point A, Point B)// 求点P在直线AB上的正投影
{
Vector v=B-A;
return A+v*(Dot(v, P-A) / Dot(v,v));
}

bool SegmentProperIntersection(Point a1, Point a2, Point b1,Point b2)//判断两直线是否相交
{
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;
}

double PolygonArae(Point *p,int n)// 求多边形的有向面积
{
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;
}
Point read_point()
{
double x,y;
scanf("%lf%lf",&x,&y);
return Point(x,y);
}
Point getans(Point A,Point B,Point C)
{
Vector v1= C-B;
double ang1=Angle(A-B,v1);
v1=Rotate(v1,ang1/3);

Vector v2= B-C;
double ang2=Angle(A-C,v2);
v2=Rotate(v2,-ang2/3);

return GetLineIntersection(B,v1,C,v2);
}
int main()
{
int T;read(T);
while(T--)
{
Point A,B,C,D,E,F;
A=read_point();
B=read_point();
C=read_point();
D=getans(A,B,C);
E=getans(B,C,A);
F=getans(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;
}