Polygons HDU

Polygons

HDU - 1632

 题意：求两个多边形的＂异或＂面积.

半平面交~

#include <bits/stdc++.h>
using namespace std;
const int maxn = 50010;
const int inf = 0x3f3f3f3f;
const double eps = 1e-8;
struct Point {
    double x,y;
    Point (double x = 0, double y = 0) : x(x), y(y) {}
};
typedef Point Vector;
Vector operator + (Vector a, Vector b) {
    return Vector (a.x + b.x, a.y + b.y);
}
Vector operator * (Vector a, double s) {
    return Vector (a.x * s, a.y * s);
}
Vector operator / (Vector a, double p) {
    return Vector (a.x / p, a.y / p);
}
Vector operator - (Point a, Point b) {
    return Vector (a.x - b.x, a.y - b.y);
}
bool operator < (Point a, Point b) {
    return a.x < b.x || (a.x == b.x && a.y < b.y);
}
int dcmp (double x) {
    if(fabs(x) < eps) return 0;
    return x < 0 ? -1 : 1;
}
bool operator == (const Point &a, const Point &b) {
    return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0;
}
double Dot(Vector a, Vector b) {
    return a.x * b.x + a.y * b.y;
}
double Cross (Vector a, Vector b) {
    return a.x * b.y - a.y * b.x;
}
//半平面交
struct Line{
    Point p;
    Vector v;
    double rad;
    Line () {}
    Line (Point p, Vector v) : p(p), v(v) {
        rad = atan2(v.y,v.x);
    }
    bool operator < (const Line &L) const {
        return rad < L.rad;
    }
};
bool OnLeft(Line L, Point p) {
    return Cross(L.v, p - L.p) > 0;
}
Point GetLineIntersection (Line a, Line b) {
    Vector u = a.p - b.p;
    double t = Cross(b.v, u) / Cross(a.v, b.v);
    return a.p + a.v*t;
}

int HalfplaneIntersection(Line *L, int n,Point *poly) {
    sort(L, L+n);
    int first,last;
    Point *p = new Point[n];
    Line *q = new Line[n];  //双端队列
    q[first = last = 0] = L[0];
    for(int i = 1; i < n; i++) {
        while(first < last && !OnLeft(L[i], p[last-1])) last--;   //去尾
        while(first < last && !OnLeft(L[i], p[first])) first++; 
        q[++last] = L[i];
        if(dcmp(Cross(q[last].v, q[last-1].v)) == 0) {
            last--;
            if(OnLeft(q[last], L[i].p)) q[last] = L[i];
        }
        if(first < last) p[last-1] = GetLineIntersection (q[last-1],q[last]);
    }
    while(first < last && !OnLeft(q[first], p[last-1])) last--;  //删除无用平面
    if(last - first <= 1) {
        delete []p;
        delete []q;
       return 0;  //空集    
    }
    p[last] = GetLineIntersection (q[last], q[first]);
    int m = 0;
    for(int i = first; i <= last; i++) poly[m++] = p[i];
    delete []p;
    delete []q;
    return m;
}
Point p1[maxn], p2[maxn], poly[maxn];
Line line[maxn];

double ConvexPolygonArea(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;
}

int main(){
    int n, m;
//    freopen("in.txt", "r", stdin);
    while(scanf("%d", &n) && n){
        for(int i = 0; i < n; i++){
            scanf("%lf %lf", &p1[i].x, &p1[i].y);
        }
        p1[n] = p1[0];
        for(int i = 0; i < n; i++){
           line[i] = Line(p1[i], p1[i] - p1[i+1]);
        }
        scanf("%d", &m);
        for(int i = 0; i < m; i++){
            scanf("%lf %lf", &p2[i].x, &p2[i].y);
        }
        p2[m] = p2[0];
        for(int i = 0; i < m; i++){
            line[i+n] = Line(p2[i], p2[i] - p2[i+1]);
        }
        int sz = HalfplaneIntersection(line, n+m, poly);
        double ans = - ConvexPolygonArea(p1, n) - ConvexPolygonArea(p2, m) - 2*ConvexPolygonArea(poly, sz);
        printf("%8.2lf", ans);
    }
    puts("");
    return 0;
}