UVA 10652 Board Wrapping 凸包

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#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;
}