计算几何--二维几何基础练习

  1 #include <bits/stdc++.h>
  2 using namespace std;
  3 struct Point
  4 {
  5     double x,y;
  6     Point(double x=0, double y=0):x(x),y(y) {}//构造函数，方便编写代码
  7 };
  8 typedef Point Vector;//别名
  9 //向量+向量=向量，点+向量=点
 10 Vector operator + (Vector A, Vector B){return Vector(A.x+B.x,A.y+B.y);}
 11 //点-点=向量
 12 Vector operator - (Vector A, Vector B){return Vector(A.x-B.x,A.y-B.y);}
 13 //向量*数=向量
 14 Vector operator * (Vector A, double p){return Vector(A.x*p,A.y*p);}
 15 //向量/数=向量
 16 Vector operator / (Vector A, double p){return Vector(A.x/p,A.y/p);}
 17 
 18 bool operator < (const Point& a, const Point& b){return a.x<b.x||(a.x==b.x&&a.y<b.y);}
 19 
 20 const double eps = 1e-10;
 21 int dcmp(double x)
 22 {
 23     if (fabs(x) < eps) return 0;
 24     else return x < 0 ? -1 : 1;
 25 }
 26 
 27 bool operator == (const Point& a, const Point &b){return dcmp(a.x-b.x) == 0 && dcmp(a.y-b.y) == 0;}
 28 
 29 //计算点积、向量长度、夹角函数
 30 double Dot(Vector A, Vector B){return A.x*B.x+A.y*B.y;}
 31 double Length(Vector A){return sqrt(Dot(A,A));}
 32 double Angle(Vector A, Vector B){return acos(Dot(A,B)/Length(A)/Length(B));}
 33 
 34 //计算叉积
 35 double Cross(Vector A,Vector B){return A.x*B.y-A.y*B.x;}
 36 double Area2(Point A, Point B, Point C){return Cross(B-A,C-A);}
 37 
 38 //计算旋转和单位法向量
 39 //rad为弧度
 40 Vector Rotate(Vector A, double rad){return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));}
 41 Vector Normal(Vector A)
 42 {
 43     double L =Length(A);
 44     return Vector(-A.y/L,A.x/L);
 45 }
 46 
 47 //交点，注意精度问题
 48 //调用该函数前请确保两条直线P+tv和Q+tw有唯一交点。当且仅当Cross(v,w)非0
 49 Point GetLineIntersection(Point P, Vector v, Point Q, Vector w)
 50 {
 51     Vector u = P-Q;
 52     double t = Cross(w,u) / Cross(v,w);
 53     return P+v*t;
 54 }
 55 //点到直线的距离。用叉积计算。平行四边形的面积除以底
 56 double DistanceToLine(Point P, Point A, Point B)
 57 {
 58     Vector v1 = B-A,v2= P-A;
 59     return fabs(Cross(v1,v2)) / Length(v1);
 60 }
 61 //点到线段的距离
 62 double DistanceToSegment(Point P, Point A, Point B)
 63 {
 64     if (A==B) return Length(P-A);
 65     Vector v1 = B-A,v2 = P-A,v3=P-B;
 66     if (dcmp(Dot(v1,v2))<0) return Length(v2);
 67     else if (dcmp(Dot(v1,v3))>0) return Length(v3);
 68     else return fabs(Cross(v1,v2)) / Length(v1);
 69 }
 70 //计算投影点
 71 Point GetLineProjection(Point P, Point A, Point B)
 72 {
 73     Vector v = B-A;
 74     return A+v*(Dot(v,P-A) / Dot(v,v));
 75 }
 76 //按“相交规范”判断相交
 77 bool SegmentProperIntersection(Point a1, Point a2, Point b1, Point b2)
 78 {
 79     double c1 = Cross(a2-a1,b1-a1),c2 = Cross(a2-a1,b2-a1),
 80     c3 = Cross(b2-b1,a1-b1),c4 = Cross(b2-b1,a2-b1);
 81     return dcmp(c1)*dcmp(c2)<0 && dcmp(c3)*dcmp(c4)<0;
 82 }
 83 //允许在端点处相交，判断是否发生加入下面一段判断一个点是否在一条线段上的代码
 84 bool OnSegment(Point P,Point a1, Point a2)
 85 {
 86     return dcmp(Cross(a1-P,a2-P)) == 0 && dcmp(Dot(a1-P,a2-P))<0; 
 87 }
 88 //多边形的有向面积
 89 double PolygonArea(Point* p, int n)
 90 {
 91     double area = 0;
 92     for (int i = 1; i < n-1; ++i)
 93     {
 94         area +=Cross(p[i]-p[0],p[i+1]-p[0]);
 95     }
 96     return area/2;
 97 }
 98 Point GetDaan(Point A,Point B,Point C)
 99 {
100     //bc逆时针转
101     Vector v1 = C-B;//直线方向向量
102     double a1=Angle(A-B,v1);
103     v1 = Rotate(v1,a1/3);
104     //bc顺时针转
105     Vector v2 = B-C;
106     double a2=Angle(A-C,v2);
107     v2 = Rotate(v2,-a2/3);//负数表示顺时针旋转
108 
109     return GetLineIntersection(B,v1,C,v2);
110 }
111 int main(int argc, char const *argv[])
112 {
113     int t;
114     cin>>t;
115     while(t--)
116     {
117         Vector a,b,c;
118         Vector d,e,f;//答案
119         cin>>a.x>>a.y>>b.x>>b.y>>c.x>>c.y;
120         d=GetDaan(a,b,c);
121         e=GetDaan(b,c,a);
122         f=GetDaan(c,a,b);
123         printf("%.6f %.6f %.6f %.6f %.6f %.6f\n",d.x,d.y,e.x,e.y,f.x,f.y);
124     }
125     return 0;
126 }