计算几何——多边形 计算几何点类

任务：设计一个二维点类，可以进行一些向量运算
接口：

结构体：point成员变量：    double x,y     点的坐标重载运算符：+，-，*，/，==成员函数：    input()      输入一个点    norm()      计算向量模长相关函数：    double  sqr(double x)          计算一个数的平方    double  det(const point &a, const point &b)          计算两个向量的叉积    double  dot(const point &a, const point &b)          计算两个向量的点积    double  dist(const point &a, const point &b)          计算两个点的距离    point rotate_point(const point &p, double A)         向量op绕原点逆时针旋转A(弧度)

代码

const double pi=acos(-1,0);inline double sqr(double x){    return x*x;}struct point {    double x,y;    point () {}    point (double a, double b) : x(a), y(b) {}    void input() {        scanf("%lf%lf", &x, &y);    }    friend point operator + (const point &a, const point &b){        return point (a.x + b.x, a.y + b.y);    }    friend point operator - (const point &a, const point &b){        return point (a.x - b.x, a.y - b.y);    }    friend point operator == (const point &a, const point &b){        return cmp (a.x - b.x) == 0 && cmp (a.y - b.y) == 0;    }    friend point operator * (const point &a, const double &b){        return point (a.x * b, a.y * b);    }    friend point operator * (const double &a, const point &b){        return point (a * b.x, a * b.y);    }    friend point operator / (const point &a, const double &b){        return point (a.x / b, a.y / b);    }    double norm() {        return sqrt(sqr(x) + sqr(y));    };    double det(const point &a, const point &b){        return a.x * b.y - a.y * b.x;    }    double dot(const point &a, const point &b){        return a.x * b.x + a.y * b.y;    }    double dist(const point &a, const point &b){        return (a-b).norm();    }    point rotate_point(const point &p, double A){        double t.x = p.x, t.y = p.y;        return point(tx * cos(A) - ty * sin(A), tx * sin(A) + ty * cos(A));    }

例题 poj 2653