UVA 11437 Triangle Fun 三角形趣题 （二维几何）

题意不说了 ，看图就看懂了= =！

思路：

本来还想是一个纯数学计算题目，算了许久没算出来，经队友指点  恍然大悟！= =！

根据输入的A，B，C三个点坐标算出 AB  BC  CA  三个向量来！

再算出  AD  BE  CF   三个向量，  再算出 三个向量的交点来 就是  R P  E

在构造一遍向量  用叉积算出面积即可！

既然输出整数， 注意四舍五入！

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<cstdlib>
using namespace std;
const double eps = 1e-10;
const int inf = 0x3f3f3f3f;
const double pi = acos(-1.0);
struct Point{
double x,y;
Point(double x = 0,double y = 0):x(x),y(y){}
bool operator < (const Point& rhs) const {
return x < rhs.x || (fabs(x- rhs.x) < eps && y < rhs.y);
}
bool operator == (const Point & rhs) const {
return fabs(x - rhs.x) < eps && fabs(y - rhs.y) < eps;
}
};
typedef Point Vector;
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); }
double Cross(Vector A,Vector B) { return A.x*B.y - B.x*A.y; }
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;
}
int main(){
int n;
scanf("%d",&n);
for (int i = 0; i < n; ++i){
double ax,ay,bx,by,cx,cy;
scanf("%lf %lf %lf %lf %lf %lf",&ax,&ay,&bx,&by,&cx,&cy);
Point A(ax,ay);
Point B(bx,by);
Point C(cx,cy);
Vector AB = B-A;
Vector BC = C-B;
Vector CA = A-C;
Vector AD = AB + BC/3.0;
Vector BE = BC + CA/3.0;
Vector CF = CA + AB/3.0;
Point P = GetLineIntersection(A,AD,B,BE);
Point Q = GetLineIntersection(B,BE,C,CF);
Point R = GetLineIntersection(A,AD,C,CF);
Vector PQ = Q-P;
Vector PR = R-P;
double s = Cross(PQ,PR)/2.0;
printf("%d\n",(int)(s+0.5 + eps));
}
return 0;
}