Board Wrapping UVA - 10652

算出这些点的凸包后，计算凸多边形的面积

#include <cstdio>
#include <cmath>
#include <vector>
#include <algorithm>
#include <cstring>
#include <iostream>
using namespace std;

const double PI = acos(-1.0);
const double eps = 1e-10;
//    定义点
struct Point
{
    double x, y;
    Point(double x = 0, double y = 0) : x(x), y(y) {}    //构造函数，方便代码编写
};
//
typedef Point Vector;       //向量是点的一个别名
//重载 +, -, *, /, <, == 运算符
Vector operator + (Vector A, Vector B)    //“+”运算符，向量+向量=向量
{
    return Vector(A.x + B.x, A.y + B.y);
}
Vector operator - (Point A, Point B)        //“-”运算符，点-点=向量
{
    return Vector(A.x - B.x, A.y - B.y);
}
Vector operator * (Vector A, double p)      //“*”运算符，向量*数=向量
{
    return Vector(A.x * p, A.y * p);
}
Vector operator / (Vector A, double p)     //“/”运算符，向量/数=向量
{
    return Vector(A.x / p, A.y / p);
}
bool operator < (const Point& a, const Point& b)    //“<”运算符
{
    return a.x < b.x || (a.x == b.x && a.y > b.y);
}
//叉积，两向量组成的三角形的有向面积的两倍
double Cross(Vector A, Vector B)
{
    return A.x * B.y - A.y * B.x;
}
//向量旋转
Vector Rotate(Vector A, double rad)
{
    return Vector(A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad));
}
//多边形有向面积
double PolygonArea(Point* p, int n)
{
    double area = 0;
    for (int i = 1; i < n - 1; i++)
        area += Cross(p[i] - p[0], p[i + 1] - p[0]);
    return area / 2;
}
//角度转换成弧度
double torad(double deg)
{
    return deg / 180 * PI;
}
//计算凸包，输入点数组p，个数为n，输出点数组ch，函数返回凸包顶点数。
//输入不能有重复点，函数执行完后输入的点的顺序被破坏
//如果不希望在凸包的边上有输入点，把两个<=改成<
//在精度要求高时建议用dcmp比较
int ConvexHull(Point* p , int n, Point* ch)
{
    sort(p, p + n);        //先比较x坐标，再比较y坐标
    int m = 0;
    for (int i = 0; i < n; i++) {
        while (m > 1 && Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2]) <= 0) m--;
        ch[m++] = p[i];
    }
    int k = m;
    for (int i = n - 2; i >= 0; i--) {
        while (m > k && Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 1]) <= 0) m--;
        ch[m++] = p[i];
    }
    if (n > 1) m--;
    return m;
}

int main()
{
    int T;
    Point P[2500], ch[2500];
    scanf("%d", &T);
    while (T--)
    {
        int n, pc = 0;
        double area1 = 0;
        scanf("%d", &n);
        for (int i = 0; i < n; i++)
        {
            double x, y, w, h, j, ang;
            scanf("%lf%lf%lf%lf%lf", &x, &y, &w, &h, &j);
            Point o(x, y);
            ang = -torad(j);            //顺时针旋转
            P[pc++] = o + Rotate(Vector(-w/2, -h/2), ang);//先旋转从中心出发的向量
            P[pc++] = o + Rotate(Vector(w/2, -h/2), ang);
            P[pc++] = o + Rotate(Vector(-w/2, h/2), ang);
            P[pc++] = o + Rotate(Vector(w/2, h/2), ang);
            area1 += w * h;                        //累加木板总面积
            
        }
        int m = ConvexHull(P, pc, ch);
        double area2 = PolygonArea(ch, m);
        printf("%.1lf %%\n", area1 * 100 / area2);
    }
    return 0;
}