Uva - 10652 - Board Wrapping

题意：给出n个矩形的中心坐标以及长宽和相对于y轴的旋转角度，问矩形总面积与最小外围总面积的百分比（N组测试数据 <= 50，1< n <= 600，0 <= x, y, w, h <=10000， –90° < j <=90°）。

题目链接：http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=1593

——>>先求出矩形的顶点，然后求凸包求面积，求百分比。

#include <cstdio>
#include <cmath>
#include <algorithm>

using namespace std;

const int maxn = 2400 + 10;
const double eps = 1e-10;

int cnt;
double totArea, recArea;

int dcmp(double x){
    if(fabs(x) < eps) return 0;
    else return x < 0 ? -1 : 1;
}

struct Point{
    double x;
    double y;
    Point(double x = 0, double y = 0):x(x), y(y){}
    bool operator < (const Point& e) const{
        return x < e.x || (dcmp(x - e.x) == 0 && y < e.y);
    }
}p[maxn], q[maxn];

typedef Point Vector;

Vector operator + (Point A, Point B){
    return Vector(A.x + B.x, A.y + B.y);
}

Vector operator - (Point A, Point B){
    return Vector(A.x - B.x, A.y - B.y);
}

Vector operator * (Point A, double p){
    return Vector(A.x * p, A.y * p);
}

Vector operator / (Point 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;
}

double Area2(Point A, Point B, Point C){
    return fabs(Cross(B-A, C-A));
}

Vector Rotate(Vector A, double rad){
    return Vector(A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad));
}

int ConvexHull(Point *p, int n, Point* ch){        //Çó͹°ü
    sort(p, p + n);
    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-2]) < 0) m--;
        ch[m++] = p[i];
    }
    if(n > 1) m--;
    return m;
}

double ConvexPolygonArea(Point *p, int n){
    double area = 0;
    for(int i = 1; i < n-1; i++) area += Area2(p[0], p[i], p[i+1]);
    return area / 2;
}

void init(){
    totArea = recArea = cnt = 0;
}

int main()
{
    int N, n;
    scanf("%d", &N);
    while(N--){
        init();
        double x, y, w, h, rad;
        scanf("%d", &n);
        for(int i = 0; i < n; i++){
            scanf("%lf%lf%lf%lf%lf", &x, &y, &w, &h, &rad);
            rad *= acos(-1)/180;
            recArea += w * h;
            p[cnt++] = Rotate(Vector(-w/2, h/2), -rad) + Vector(x, y);
            p[cnt++] = Rotate(Vector(w/2, h/2), -rad) + Vector(x, y);
            p[cnt++] = Rotate(Vector(-w/2, -h/2), -rad) + Vector(x, y);
            p[cnt++] = Rotate(Vector(w/2, -h/2), -rad) + Vector(x, y);
        }
        int m = ConvexHull(p, cnt, q);
        totArea = ConvexPolygonArea(q, m);
        double ret = recArea / totArea * 100;
        printf("%.1f ", ret);
        puts("%");
    }
    return 0;
}