UVA 11437 Triangle Fun

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转载请注明出处：忆梦http://blog.csdn.net/yimeng2013/article/details/17329917

题目链接：http://uva.onlinejudge.org/external/114/11437.html

计算几何入门题,熟悉使用模板。

题意：求出三角形PQR的面积。

方法一：几何证明面积关系求解：http://blog.csdn.net/freezhanacmore/article/details/8171942

方法二：利用叉积直接求面积：

#include<cstdio>#include<cmath>//定义点struct Point{double x, y;Point(double x = 0, double y = 0) : x(x), y(y) {}};typedef Point Vector; //Vector 为 Point的别名//向量+向量=向量    点+向量=点Vector operator + (Vector A, Vector B) {return Vector(A.x+B.x, A.y+B.y);}//点-点=向量Vector operator - (Point A, Point B) {return Vector(A.x-B.x, A.y-B.y);}//向量*数=向量Vector operator * (Vector A, double p) {return Vector(A.x*p, A.y*p);}//向量/数=向量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);}//点积：两者长度乘积在乘上夹角余弦 XaXb + YaYbdouble 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));}//叉积：两向量v和w的叉积等于v和w组成的三角形的有向面积的两倍 XaYb - XbYadouble 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);}//直线一般用参数表示 P = P0 + tv//如何已知直线上两点A，B ；则方向向量为B-A，所以参数方程为A+（B-A）t//两直线交点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(){Point temp;scanf("%lf %lf", &temp.x, &temp.y);return temp;}Point GetD(Point A, Point B){return (B-A)/3.0 + A;}int main (){int T;scanf("%d", &T);while(T--){Point A, B, C, D, E, F, P, Q, R;A = read_point();B = read_point();C = read_point();D = GetD(B, C);E = GetD(C, A);F = GetD(A, B);P = GetLineIntersection(A, D-A, B, E-B);R = GetLineIntersection(A, D-A, C, F-C);Q = GetLineIntersection(B, E-B, C, F-C);double ans = Area2(P, R, Q) / 2.0;printf("%.0lf\n", fabs(ans));}return 0;}

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