UVA 11178

问题描述：

给定三角形的三个点，求三角形角三平分线连成的内部小三角形的三个点的坐标

这里主要还是几何问题上的大量函数求解问题，

这题的关键是经过两点的确定直线的交点求解问题，我们总是可以利用叉积解决大量问题

通过叉积的比来得到那个方向的向量比例，最后得到点

  1 #include <iostream>
  2 #include <cstdio>
  3 #include <cstring>
  4 #include <cmath>
  5 using namespace std;
  6 //用来保证double的精度问题
  7 #define eps 1e-10
  8 const double PI = acos(-1);
  9 struct Point {
 10     double x, y;
 11     Point(double x=0,double y=0):x(x),y(y){}//构造函数，方便代码编写
 12 };
 13 typedef Point Vector;
 14 
 15 bool operator==(const Point &a,const Point &b)
 16 {
 17     return abs(a.x-b.x)<eps && abs(a.y-b.y)<eps;
 18 }
 19 
 20 Vector operator-(Point a,Point b)
 21 {
 22     return Vector(a.x-b.x,a.y-b.y);
 23 }
 24 
 25 Vector operator+(Vector a,Vector b)
 26 {
 27     return Vector(b.x+a.x,b.y+a.y);
 28 }
 29 
 30 Vector operator*(Vector a,double b)
 31 {
 32     return Vector(a.x*b,a.y*b);
 33 }
 34 
 35 Vector operator/(Vector a,double b)
 36 {
 37     return Vector(a.x/b,a.y/b);
 38 }
 39 
 40 
 41 //两向量的内积
 42 double Dot(Vector a,Vector b)
 43 {
 44     return a.x*b.x + a.y*b.y;
 45 }
 46 
 47 //两向量的叉积
 48 double Cross(Vector a,Vector b)
 49 {
 50     return a.x*b.y - a.y*b.x;
 51 }
 52 
 53 //向量的长度
 54 double length(Vector a)
 55 {
 56     return sqrt(Dot(a,a));
 57 }
 58 
 59 //两向量的夹角弧度
 60 double get_rad(Vector a,Vector b)
 61 {
 62     return acos((Dot(a,b))/length(a)/length(b));
 63 }
 64 
 65 //求一个向量逆时针偏转一定弧度后得到的向量，若是顺时针，我们在弧度上加一个负号就行了
 66 Vector get_revovle(Vector a,double rad)
 67 {
 68     double x = a.x*cos(rad) - a.y*sin(rad);
 69     double y = a.x*sin(rad) + a.y*cos(rad);
 70     return Vector(x,y);
 71 }
 72 
 73 //得到经过两个点的确定直线的交点
 74 Point getLineIntersection(Point p,Vector vp,Point q,Vector vq)
 75 {
 76     Vector u = p-q;
 77     double t = Cross(vq,u) / Cross(vp,vq);
 78     return p+vp*t;
 79 }
 80 
 81 //这个函数求以a为顶点，b，c延伸出1/3弧度处的直线的交点
 82 Point getIntersection(Point a,Point b,Point c)
 83 {
 84     Vector v1 = a-b;
 85     Vector v2 = a-c;
 86     Vector v3 = c-b;
 87     Vector v4 = b-c;
 88     double rad1 = get_rad(v1,v3);
 89     double rad2 = get_rad(v2,v4);
 90     rad1/=3;
 91     rad2/=3;
 92     Vector rev1 = get_revovle(v3,rad1);
 93     Vector rev2 = get_revovle(v4,-rad2);//负数表示顺时针旋转
 94 
 95     return getLineIntersection(b,rev1,c,rev2);
 96 }
 97 
 98 int main()
 99 {
100     int T;
101     double x1,y1,x2,y2,x3,y3;
102     scanf("%d",&T);
103     while(T--){
104         scanf("%lf%lf%lf%lf%lf%lf",&x1,&y1,&x2,&y2,&x3,&y3);
105 
106         Point A(x1,y1);
107         Point B(x2,y2);
108         Point C(x3,y3);
109 
110         Point ans1 = getIntersection(A,B,C);
111         Point ans2 = getIntersection(B,C,A);
112         Point ans3 = getIntersection(C,A,B);
113 
114         printf("%.6f %.6f %.6f %.6f %.6f %.6f
",ans1.x,ans1.y,ans2.x,ans2.y,ans3.x,ans3.y);
115     }
116     return 0;
117 }